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Class 9 Science Case Study Questions Chapter 9 Force and Laws of Motion

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Case study Questions in Class 9 Science Chapter 9 are very important to solve for your exam. Class 9 Science Chapter 9 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving  Class 9 Science Case Study Questions  Chapter 9 Force and Laws of Motion

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In CBSE Class 9 Science Paper, Students will have to answer some questions based on Assertion and Reason. There will be a few questions based on case studies and passage-based as well. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

Force and Laws of Motion Case Study Questions With Answers

Here, we have provided case-based/passage-based questions for Class 9 Science  Chapter 9 Force and Laws of Motion

Case Study/Passage-Based Questions

Case Study 1: The sum of the momentum of the two objects before the collision is equal to the sum of momentum after the collision provided there is no external unbalanced force acting on them. This is known as the law of conservation of momentum. This statement can alternatively be given as the total momentum of the two objects is unchanged or conserved by the collision. The Law of conservation of momentum is applicable to the system of particles. Answer the following questions.

(i)Law of conservation of momentum is applicable to

(a) A system of particles

(b) Only for 2 particles

(c) Only for 1 particle

(d) None of the above

Answer: (a) A system of particles

(ii) Law of conservation of momentum holds good provided that

(a) There should be external unbalanced force acting on particles

(b) There should not be any external unbalanced force acting on particles

(c) No internal forces acting on particles

Answer: (b) There should not be any external unbalanced force acting on particles

(iii)The total momentum of the two objects when collision occurs is

(a) Changed

(b) Remains conserved

(c) Become zero

Answer: (b) Remains conserved

(iv) State law of conservation of momentum.

Answer: The sum of momentum of the two objects before collision is equal to the sum of momentum after the collision provided there is no external unbalanced force acting on them. This is known as the law of conservation of momentum. This statement can alternatively be given as the total momentum of the two objects is unchanged or conserved by the collision.

(v) If action and Reaction are equal in magnitude and opposite in direction then why they do not cancel each other?

Answer: Action and Reaction are equal in magnitude and opposite in direction but they do not cancel each other because they are not action on sane object. As these forces are acting on different object hence produces different acceleration and does not cancel each other.

Case Study 2: The third law of motion states that when one object exerts a force on another object, the second object instantaneously exerts a force back on the first. These two forces are always equal in magnitude but opposite in direction. These forces act on different objects and never on the same object. It is important to note that even though the action and reaction forces are always equal in magnitude; these forces may not produce accelerations of equal magnitudes, this is because each force acts on a different object that may have a different mass. The two opposing forces are also known as action and reaction forces. Answer the following questions.

(i) Action reaction forces are always

(a) Equal and in the same direction

(b) Equal and in the opposite direction

(c) Unequal and in the same direction

Answer: (b) Equal and in the opposite direction

(ii) Which of the following is correct about action reaction forces?

(a) They act on different objects

(b) They are equal in magnitude and opposite in direction

(c) Both forces acted on different object simultaneously

(d) All the above

Answer: (d) All the above

(iii) State third law of motion

Answer: The third law of motion states that when one object exerts a force on another object, the second object instantaneously exerts a force back on the first. These two forces are always equal in magnitude but opposite in direction. These forces act on different objects and neveron the same object.

(iv) Give 5 examples of third law of motion

Answer: Examples of third law of motion are Swimming or rowing a boat. •Static friction while pushing an object. •Walking. •Standing on the ground or sitting on a chair. •The upward thrust of a rocket. •Resting against a wall or tree.

Case Study 3:

Force is a push or pull that can change the state of motion of an object. According to Newton’s first law of motion, an object at rest will remain at rest, and an object in motion will continue moving with a constant velocity in a straight line unless acted upon by an external force. This is known as the law of inertia. Newton’s second law of motion states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Mathematically, this can be expressed as F = ma, where F is the force, m is the mass of the object, and a is the acceleration produced. Newton’s third law of motion states that for every action, there is an equal and opposite reaction. This means that whenever an object exerts a force on another object, the second object exerts an equal and opposite force on the first object. Understanding the concepts of force and the laws of motion helps us explain the behavior of objects and the factors that influence their motion.

What is force? a) A change in the state of motion of an object b) A push or pull that can change the state of motion of an object c) The mass of an object d) The velocity of an object Answer: b) A push or pull that can change the state of motion of an object

What does Newton’s first law of motion state? a) An object at rest will remain at rest, and an object in motion will continue moving with a constant velocity in a straight line unless acted upon by an external force. b) The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. c) For every action, there is an equal and opposite reaction. d) The force exerted by an object is equal to its mass multiplied by its acceleration. Answer: a) An object at rest will remain at rest, and an object in motion will continue moving with a constant velocity in a straight line unless acted upon by an external force.

What is Newton’s second law of motion? a) An object at rest will remain at rest, and an object in motion will continue moving with a constant velocity in a straight line unless acted upon by an external force. b) The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. c) For every action, there is an equal and opposite reaction. d) The force exerted by an object is equal to its mass multiplied by its acceleration. Answer: b) The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

What is Newton’s third law of motion? a) An object at rest will remain at rest, and an object in motion will continue moving with a constant velocity in a straight line unless acted upon by an external force. b) The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. c) For every action, there is an equal and opposite reaction. d) The force exerted by an object is equal to its mass multiplied by its acceleration. Answer: c) For every action, there is an equal and opposite reaction.

How do the concepts of force and the laws of motion help us? a) Explain the behavior of objects and the factors that influence their motion. b) Calculate the speed of objects. c) Classify objects into different categories. d) Determine the position of objects. Answer: a) Explain the behavior of objects and the factors that influence their motion.

Hope the information shed above regarding Case Study and Passage Based Questions for Class 9 Science Chapter 9 Force and Laws of Motion with Answers Pdf free download has been useful to an extent. If you have any other queries about CBSE Class 9 Science Force and Laws of Motion Case Study and passage-based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible By Team Study Rate

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Class 11 Physics Case Study Questions Chapter 4 Motion In A Plane

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In Class 11 Final Exams there will be Case studies and Passage Based Questions will be asked, So practice these types of questions. Study Rate is always there to help you. Free PDF Downloads of CBSE Class 11 Physics Chapter 4 Case Study and Passage-Based Questions with Answers were Prepared Based on the Latest Exam Pattern. Students can solve Class 11 Physics Case Study Questions Motion In A Plane  to know their preparation level.

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In CBSE Class 11 Physics Paper, There will be a few questions based on case studies and passage-based as well. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

Motion In A Plane Case Study Questions With Answers

Here, we have provided case-based/passage-based questions for Class 11 Physics  Chapter 4 Motion In A Plane

Case Study/Passage-Based Questions

Case Study 1: When an object follows a circular path at a constant speed, the motion of the object is called uniform circular motion. The word “uniform” refers to the speed, which is uniform (constant) throughout the motion. Suppose an object is moving with uniform speed v in a circle of radius R Since the velocity of the object is changing continuously in direction, the object undergoes acceleration. Let us find the magnitude and the direction of this acceleration. Thus, the acceleration of an object moving with speed v in a circle of radius R has a magnitude V2/R and is always directed towards the center. This is why this acceleration is called centripetal acceleration (a term proposed by Newton). A thorough analysis of centripetal acceleration was first published in 1673 by the Dutch scientist Christiaan Huygens (1629-1695) but it was probably known to Newton also some years earlier. “Centripetal” comes from a Greek term that means ‘center-seeking’. Since v and R are constant, the magnitude of the centripetal acceleration is also constant. However, the direction changes pointing always toward the center. Therefore, centripetal acceleration is not a constant vector. We can express centripetal acceleration ac in terms of angular speed as

a c  = ω 2 R

The time taken by an object to make one revolution is known as its time period T and the number of revolutions made in one second is called its frequency v (=1/ T ). However, during this time the distance moved by the object is  s  = 2π R . Therefore,  v  = 2π R / T  =2π Rv  In terms of frequency n, we have

v  = 2π Rv

ac  = 4π 2 v 2 R

1) SI unit of angular velocity is

d) None of these

Answer: a) Rev/sec

2) A centripetal acceleration is not a constant vector. True or false?

Answer: a) True

3) What does the term “uniform” refer to in uniform circular motion? a) Constant acceleration b) Constant radius c) Constant velocity d) Constant speed

Answer: d) Constant speed

4) How is the direction of centripetal acceleration characterized? a) Always pointing outward b) Always pointing toward the center c) Constant in one direction d) Changing randomly

Answer: b) Always pointing toward the center

5) Who first published a thorough analysis of centripetal acceleration? a) Isaac Newton b) Albert Einstein c) Christiaan Huygens d) Galileo Galilei

Answer: c) Christiaan Huygens

Case Study 2: We consider the motion of a projectile. An object that is in flight after being thrown or projected is called a projectile. Such a projectile might be a football, a cricket ball, a baseball or any other object. The motion of a projectile may be thought of as the result of two separate, simultaneously occurring components of motion. One component is along a horizontal direction without any acceleration and the other is along the vertical direction with constant acceleration due to the force of gravity. It was Galileo who first stated this independency of the horizontal and the vertical components of projectile motion in his Dialogue on the great world systems.

Horizontal range of a projectile:  The horizontal distance traveled by a projectile from its initial position (x = y = 0) to the position where it passes y = 0 during its fall is called the horizontal range, R. It is the distance traveled during the time of flight T f . Therefore, the range

R is R = ( v 0  cos θ 0 ) ( T f )

R = (v 0  cos θ 0 ) (2 v 0  sin θ 0 )/g

R = (v 0 2  sin 2 θ 0 )/g

This shows that for a given projection velocity, R is maximum when sin 2θ 0  is maximum, i.e., when  θ 0  = 45 0 . The maximum horizontal range is, therefore

R= v 0 2 /g

Maximum height of a projectile:  Maximum height that can be achieved during projectile and it is given by

H m  = (v 0  sin θ 0 ) 2 /2g

Who first stated the independency of horizontal and vertical components of projectile motion? a) Isaac Newton b) Albert Einstein c) Galileo Galilei d) Johannes Kepler

Answer: c) Galileo Galilei

The horizontal range is directly dependent on: a) The initial velocity and angle of projection b) The maximum height and time of flight c) Gravity and maximum height d) Only the initial velocity

Answer: a) The initial velocity and angle of projection

At what angle θ is the horizontal range of the projectile maximum? a) 30° b) 45° c) 60° d) 90°

Answer: b) 45°

Hope the information shed above regarding Case Study and Passage Based Questions for Class 11 Physics Chapter 4 Motion In A Plane with Answers Pdf free download has been useful to an extent. If you have any other queries about CBSE Class 11 Physics Motion In A Plane Case Study and Passage Based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible. By Team Study Rate

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Case Study Questions of Chapter 9 Force and Laws of Motion PDF Download

Case study Questions on Class 9 Science Chapter 9 are very important to solve for your exam. Class 9 Science Chapter 9 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving case study-based questions for Class 9 Science Chapter 9 Force and Laws of Motion

In CBSE Class 9 Science Paper, Students will have to answer some questions based on Assertion and Reason. There will be a few questions based on case studies and passage-based as well. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

Force and Laws of Motion Case Study Questions With answers

Here, we have provided case-based/passage-based questions for Class 9 Science  Chapter 9 Force and Laws of Motion

Case Study/Passage-Based Questions

Question 1:

The sum of the momentum of the two objects before the collision is equal to the sum of momentum after the collision provided there is no external unbalanced force acting on them. This is known as the law of conservation of momentum. This statement can alternatively be given as the total momentum of the two objects is unchanged or conserved by the collision. The Law of conservation of momentum is applicable to the system of particles. Answer the following questions.

(i)Law of conservation of momentum is applicable to

(a) A system of particles

(b) Only for 2 particles

(c) Only for 1 particle

(d) None of the above

Answer: (a) A system of particles

(ii) Law of conservation of momentum holds good provided that

(a) There should be external unbalanced force acting on particles

(b) There should not be any external unbalanced force acting on particles

(c) No internal forces acting on particles

Answer: (b) There should not be any external unbalanced force acting on particles

(iii)The total momentum of the two objects when collision occurs is

(a) Changed

(b) Remains conserved

(c) Become zero

Answer: (b) Remains conserved

(iv) State law of conservation of momentum.

Answer: The sum of momentum of the two objects before collision is equal to the sum of momentum after the collision provided there is no external unbalanced force acting on them. This is known as the law of conservation of momentum. This statement can alternatively be given as the total momentum of the two objects is unchanged or conserved by the collision.

(v) If action and Reaction are equal in magnitude and opposite in direction then why they do not cancel each other?

Answer: Action and Reaction are equal in magnitude and opposite in direction but they do not cancel each other because they are not action on sane object. As these forces are acting on different object hence produces different acceleration and does not cancel each other.

Question 2:

The third law of motion states that when one object exerts a force on another object, the second object instantaneously exerts a force back on the first. These two forces are always equal in magnitude but opposite in direction. These forces act on different objects and never on the same object. It is important to note that even though the action and reaction forces are always equal in magnitude; these forces may not produce accelerations of equal magnitudes, this is because each force acts on a different object that may have a different mass. The two opposing forces are also known as action and reaction forces. Answer the following questions.

(i) Action reaction forces are always

(a) Equal and in the same direction

(b) Equal and in the opposite direction

(c) Unequal and in the same direction

Answer: (b) Equal and in the opposite direction

(ii) Which of the following is correct about action reaction forces?

(a) They act on different objects

(b) They are equal in magnitude and opposite in direction

(c) Both forces acted on different object simultaneously

(d) All the above

Answer: (d) All the above

(iii) State third law of motion

Answer: The third law of motion states that when one object exerts a force on another object, the second object instantaneously exerts a force back on the first. These two forces are always equal in magnitude but opposite in direction. These forces act on different objects and neveron the same object.

(iv) Give 5 examples of third law of motion

Answer: Examples of third law of motion are Swimming or rowing a boat. •Static friction while pushing an object. •Walking. •Standing on the ground or sitting on a chair. •The upward thrust of a rocket. •Resting against a wall or tree.

Hope the information shed above regarding Case Study and Passage Based Questions for Class 9 Science Chapter 9 Force and Laws of Motion with Answers Pdf free download has been useful to an extent. If you have any other queries about CBSE Class 9 Science Force and Laws of Motion Case Study and passage-based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible

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Fundamentals

Velocity is a vector that is fully described by a numerical value (such as 20 m/s) and a direction. Objects that move along a circular path have a velocity vector that is directed tangent to the pat h.  Such objects are also experiencing an acceleration and a net force. Acceleration and net force are both vector quantities that have a direction that is  towards the center of the circle .  

About This Question

There are three similar versions of this question. Here is one of those versions:  

The speed in Case A is twice that of Case B. The circle’s radius in Case A is twice that of Case B. The object mass is the same in each case. How does the net force in Case A compare to the net force in Case B?

How to Think About This Situation

What this question isn't about.

Physics is a course that can be filled with formulas. And one way that students often use those formulas is as a recipe to solve problems. They are given numerical values for some of the variables in the equation. They plug those values into the equation. Maybe they do some algebraic manipulation of the equation. And finally they solve for the unknown value. That's not what's going on in this question. Put your calculator and your plug-and-chug mentality away because they won't do you much good on this question.  

What This Question Is About

In this question, you will need to use the  F = m•v 2 /R  equation. But  you need to use it as a guide to thinking about how differing m ,  v and R values would affect the net force experienced by an object. In this question, you will have to think proportionally. That's quite different than plug-and-chug thinking.   

Here's How to Think About It:

So thinking about the  F = m•v 2 /R  equation involves proportional reasoning. The net force is directly proportional to the square of speed AND inversely proportional to the radius.  If one case has two times the speed then it would have four times the net force. And if one case had one-half the speed, then it would have one-fourth the net force. You will need to find the multiplying factor that results from any difference in speed value between the two cases.  But that's not all. You also have to consider the radius. And the thinking works differently for radius since the net force is inversely proportional to the radius. If Case A has one-half the radius, then that would result in two times the net force. And if Case A has two times the radius, then that would result in one-half the net force. You will need to find the multiplying factor that results from any difference in radius value between the two cases.  Now once you have determined the multiplying factor for speed and the multiplying factor for the radius, you can put the two multiplying factors together to determine the answer. You will have to multiply the multipying factors. Take your time ... maybe jot down a note on some scratch paper ... and work out the answer thoughtfully using the proportional reasoning described in the previous two paragraphs.  

Learn More at The Physics Classroom Tutorial

Try these links to The Physics Classroom Tutorial for more help with the mathematics of force for objects moving in a circle. Mathematics of Circular Motion

Justices Appear to Side With City Trying to Regulate Homeless Encampments

The Supreme Court appeared split along ideological lines in the case, which has sweeping implications for how the cities nationwide deal with a growing issue.

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Abbie VanSickle

Reporting from Washington

Supreme Court Seems Poised to Uphold Local Bans on Homeless Encampments

A majority of the Supreme Court appeared inclined on Monday to uphold a series of local ordinances that allowed a small Oregon city to ban homeless people from sleeping or camping in public spaces.

The justices seemed split along ideological lines in the case, which has sweeping implications for how the country deals with a growing homelessness crisis.

In a lengthy and, at times, fiery argument that lasted almost two and a half hours, questioning from the justices reflected the complexity of the homelessness debate. They weighed the status of poverty and the civil rights of homeless people against the ability of cities to clear public spaces like parks and sidewalks to address concerns about health and safety. They wrestled with what lines could be drawn to regulate homelessness — and, crucially, who should make those rules.

The conservative majority appeared sympathetic to arguments by the city of Grants Pass, Ore., that homelessness is a complicated issue best handled by local lawmakers and communities, not judges. The liberal justices strongly resisted that notion.

Chief Justice John G. Roberts Jr. calmly cut to the central point that seemed to resonate with the conservative wing: “Why would you think that these nine people are the best people to judge and weigh those policy judgments?”

In impassioned questioning, the liberal justices pushed back sharply on the city’s argument that homelessness was not a status protected under the Eighth Amendment’s prohibition on cruel and unusual punishment.

“Could you criminalize the status of homelessness?” Justice Elena Kagan asked the city’s lawyer, Theane D. Evangelis.

“Well, I don’t think that homelessness is a status like drug addiction,” Ms. Evangelis responded.

“Homelessness is a status,” Justice Kagan replied. “It’s the status of not having a home.”

The issue of how far local governments can go to regulate homelessness has given rise to unusual alliances across the political spectrum, with some leaders of left-leaning cities and states joining with conservative groups to urge the justices to clarify the extent of their legal authority in clearing encampments that have proliferated across the West in recent years.

Many leaders of Western states and cities have contended that decisions by the U.S. Court of Appeals for the Ninth Circuit, which oversees nine Western states, have been interpreted in ways that have limited the flexibility of governments to tackle the problem.

The case stems from a series of local ordinances in Grants Pass, a town of about 40,000 in southern Oregon. City officials stepped up enforcement of local laws in 2013 after residents began to complain about people sleeping, urinating and defecating outside.

Three homeless residents of Grants Pass challenged those ordinances in 2018, arguing that the city had violated the Eighth Amendment.

Grants Pass contended that the Eighth Amendment was the wrong framework because it is typically aimed at punishments, not at laws. It added that a Supreme Court ruling striking down its ordinances would set a troubling precedent that would tie the hands of local governments around the country and fuel sprawling encampments.

The case is among the last to be argued this term, which means that it is unlikely to be decided before late June or perhaps in early July, since the Supreme Court now has a backlog of pending decisions in major cases.

As arguments were underway, about 100 demonstrators protested outside the court, chanting, “SCOTUS, now’s the time, homelessness is not a crime!” and holding signs that read “Housing Justice” and “Housing is a human right.”

Kelsi B. Corkran, the lawyer representing the homeless plaintiffs, asserted that the use of the Eighth Amendment in the case was appropriate and therefore an issue the court was suited to address. “I don’t think there’s any question that being poor is a status,” she said. “It’s a status that can change over time and at that point you wouldn’t be part of the class, but I don’t think it changes the fact that it is a status.”

In heated questioning with the lawyer for the city, Justice Kagan pointed to the city’s ordinances that allow the authorities to ticket people for sleeping with bedding in public, asking whether cities could outlaw other basic human needs like breathing.

“Sleeping is a biological necessity,” Justice Kagan said. “It’s sort of like breathing. I mean, you could say breathing is conduct, too. But, presumably, you would not think that it’s OK to criminalize breathing in public, and for a homeless person who has no place to go, sleeping in public is kind of like breathing in public.”

Justice Ketanji Brown Jackson made a similar analogy, asking whether a city could prohibit eating in public because of concerns about sanitation, trash and rodents. Most people would be fine, she said, because they could just eat at restaurants or somewhere indoors, but not everyone.

“Some people don’t have that option,” Justice Jackson said. “They have to eat in public, because they’re unhoused and they can’t afford to go to a restaurant.”

Ms. Evangelis said she did not think that such laws would violate the Eighth Amendment and, bringing the discussion back to Grants Pass and its ordinances, added that the city was arguing that states and local governments should drive policymaking.

“We think that it is harmful for people to be living in public spaces, on streets and in parks,” Ms. Evangelis said. “Whatever bedding materials, when humans are living in those conditions, we think that that’s not compassionate and that there’s no dignity in that.”

That elicited sharp commentary from Justice Sonia Sotomayor, who said: “Where do we put them if every city, every village, every town lacks compassion and passes a law identical to this? Where are they supposed to sleep? Are they supposed to kill themselves not sleeping?”

Several conservative justices seemed skeptical of the practicalities of following the rule laid out by the lower appeals court. The appeals court had determined that a city could not penalize people for being involuntarily homeless if the city did not have enough shelter beds for its homeless population. The justices seemed particularly concerned with how to decide whether a city had enough shelter beds and who would be responsible for sorting out such complex issues day to day.

“I think one of the questions is, who takes care of it on the ground?” Justice Brett M. Kavanaugh asked a lawyer for the federal government, Edwin S. Kneedler. “Is it going to be federal judges? Or is it the local jurisdictions with — working with the nonprofits and religious organizations?”

The Biden administration had joined the case, siding with neither party, arguing that Grants Pass’s laws probably violated the Eighth Amendment but that the lower court erred by not requiring an examination into each homeless person’s circumstances.

Several justices wrestled with how to think of someone’s state of being versus their conduct.

The plaintiffs’ argument rests in part on a 1962 case, Robinson v. California , in which the Supreme Court held that laws imposing penalties on people for narcotics addiction violated the Eighth Amendment because they punished a state of being, not a specific action, like drug possession or sale. In a similar fashion, the plaintiffs contend, Grants Pass is punishing people for being involuntarily homeless, not for specific actions.

That argument held sway in a separate case, Martin v. Boise, in 2018. In that case, a panel of judges from the U.S. Court of Appeals for the Ninth Circuit ruled that Boise, Idaho, had violated the constitutional rights of homeless people by imposing criminal penalties for sleeping and camping outdoors, even though the city did not have enough shelter beds.

Ms. Evangelis argued that the appeals court’s approach had “proven unworkable.”

“Cities are struggling to apply arbitrary, shifting standards in the field,” she said, adding that the Supreme Court should “end the Ninth Circuit’s failed experiment, which has fueled the spread of encampments while harming those it purports to protect.”

Chief Justice Roberts grappled with what was the best tack, asking whether homelessness was truly a state of being in the same way that being addicted to drugs is.

“What is the analytic approach to deciding whether something’s a status or a situation of conduct?” he asked. “You can remove the homeless status in an instant if you move to a shelter or situations otherwise change. And, of course, it can be moved the other way as well if you’re kicked out of the shelter, whatever.”

Adam Liptak and Aishvarya Kavi contributed reporting. Kitty Bennett contributed research.

Adam Liptak

What’s next: A decision will most likely land in late June.

Now that the arguments are complete, the justices will cast tentative votes at a private conference in the coming days. The senior justice in the majority will then assign the majority opinion to a colleague, or perhaps keep it.

Draft opinions, almost certainly including concurrences and dissents, will then be prepared and exchanged.

The case was among the last to be argued this term, meaning that it would almost certainly not be decided until late June, when the term typically ends.

But there is even more reason to think that the decision will come then, or perhaps in early July, as the Supreme Court is facing a formidable backlog of pending decisions in major cases. Among them are ones on the fate and scope of the prosecution of former President Donald J. Trump for plotting to subvert the 2020 election, access to abortion, the First Amendment rights of social media companies and the power of administrative agencies.

In an ordinary term, the case on homelessness would be one of a small handful of blockbusters. This year, it will be one of many that are set to land, one after another, in a few hectic weeks in early summer.

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Shawn Hubler

“The Supreme Court has an opportunity to strike a balance that allows officials to enforce reasonable limits on public camping while treating folks with compassion,” Gov. Gavin Newsom of California said on social media earlier this morning. But as today’s arguments demonstrated, even if the court makes it easier to police tent camps, it is unclear whether there is much middle ground.

Aishvarya Kavi

The rally outside the court has ended and the majority of protesters have gone. Some have left their signs, reading “Housing not handcuffs,” taped to the fences blocking off the court steps.

Jesse Rabinowitz, the communications director for the National Homelessness Law Center, which helped bring the case against Grants Pass, worked to organize the rally and said hundreds of people had joined throughout the morning. “We can’t predict what the court’s going to do," he said. "But we know that every time a court has heard this case, they have agreed with us that punishing people for sleeping outside when there’s nowhere else to go is cruel and unusual.”

After an argument that lasted almost two and a half hours, it seemed reasonably clear that a majority of the justices were inclined to favor Grants Pass and its ability to decide how to regulate homeless encampments.

Their general rationale appeared to be these were policy questions best left to local officials, not constitutional questions for the courts.

As cities await the court’s ruling, they are continuing to explore ways to take a tougher stance on homeless encampments. Later this week, officials in Portland, Ore., will discuss strategies for cracking down on these sites. Last year, the city’s mayor had moved to ban camping during daytime hours, but that effort was halted by a court ruling.

Theane D. Evangelis, the city’s lawyer, returns to the lectern for a brief rebuttal.

Conor Dougherty

Several justices have asked how the status of homelessness is defined. This is a tricky question. The annual Point-in-Time count , the nation’s annual tally of the homeless population, logs people who sleep outside as well as in shelters.

Justice Alito is exploring what it means to be homeless. Corkran says it’s the status of not having a fixed, regular nighttime address.

Chief Justice Roberts is back to asking if being a bank robber is a status. By the logic of the 1962 Robinson ruling , you can in theory be a bank robber ... so long as you don’t rob banks.

Kelsi B. Corkran, a lawyer for the homeless people challenging the city ordinance, will argue for 25 minutes before a round of one-by-one questions.

Pamela Baker, Noemi Serrano and Heather Simms, who work with the unhoused population across New Jersey, drove to Washington on Monday morning to take part in the protests outside the Supreme Court. After having worked to combat homelessness for 16 years, Baker said seeing this case “seems like we’re kind of taking some steps backwards, to be honest.”

Serrano, who said she has been homeless herself, said, “That is why it’s important that we are here, because there are so many families just like mine, that don’t have the access to housing — despite the fact that they work many hours, despite the fact that they’re doing everything they can.”

Justice Kavanaugh proposes an escape hatch: a “necessity defense” to criminal charges against people with nowhere else to sleep.

Justice Kavanaugh has done volunteer work serving food to homeless people.

Justice Gorsuch asks hypothetically whether it is cruel and unusual to cite or arrest mentally ill or addicted people who refuse offers of shelter. But in most cities, the demand among homeless people for shelter beds and long-term housing far outstrips the supply.

Kneedler, the government lawyer, says there are questions about whether the lead plaintiffs are actually covered by the law. He urges the justices to send the case back to the lower courts to explore whether this is the right case in which to rule on its constitutionality.

Laura Grace, 36, a case manager with Valley Youth House, a Pennsylvania nonprofit, works with young adults who are homeless, including those who have aged out of foster care. She said she sees the case before the court as a result of society’s inability to see homelessness as a problem that can be solved.“Nobody wants to acknowledge this,” she said, “because if we’re seeing this as a problem, then we have to come up with a solution to make it go away.”

This 2018 Idaho case set the stage for the one before the Supreme Court today.

To understand how the case being argued before the Supreme Court on Monday became such a political flashpoint, look to Boise, Idaho.

There, in 2009, a group of homeless residents — and their subsequent victory in the courts — set the stage for the case in Grants Pass, Ore., and has become a focus of broader political frustration over a sharp rise in homelessness.

That March, the police in Boise cited Robert Martin, who was homeless, for sleeping outside. Mr. Martin, along with five other homeless plaintiffs, sued the city. Their legal strategy, inspired by a case in Los Angeles that successfully challenged the city’s sweeps of Skid Row, home to one of the country’s largest homeless populations, centered on the Eighth Amendment.

Lawyers said Boise had violated the amendment’s prohibition against cruel and unusual punishment by clearing people from the streets with no place to go.

An appeals court, the U.S. Court of Appeals for the Ninth Circuit, which covers nine Western states, agreed, blocking law enforcement from citing people for sleeping outside if they had no access to alternative shelter. If no such option exists, the court held, the government cannot criminalize homeless people for sleeping on public property outdoors. The court found that these people were involuntarily homeless, meaning they had no other choice.

Mr. Martin, who now lives in a recreational vehicle in northern Idaho where he grew up, said the ruling by the court was empowering.

“Before, when we did get the tickets and everything, we didn’t feel as if we were fully part of society, in a sense,” he said in a recent interview. “We were constantly — not just with the tickets but with other things as well, we felt like we were something to be swept under the rug.”

But the case also roused fears among cities, particularly those in the Western states, that the ruling would lead to a surge in homelessness and, by extension, encampments in public spaces.

In asking the Supreme Court to take up the case, the city of Boise contended that the decision by the appeals court had created a new right that was not grounded in the Constitution and would paralyze the ability of cities and states to address homelessness.

“The consequences of the Ninth Circuit’s erroneous decision have already been — and will continue to be — far-reaching and catastrophic,” it said, adding, “Public encampments, now protected by the Constitution under the Ninth Circuit’s decision, have spawned crime and violence, incubated disease, and created environmental hazards that threaten the lives and well-being both of those living on the streets and the public at large.”

The court ultimately declined to take up the Boise case, citing no reasons, as is typical in petitions for review. By then, the Grants Pass case was working its way through the court system.

The justices are batting around a question that many cities find vexing, which is whether an individual can be cited or compelled to shelter when that specific person is offered a bed, or whether the Ninth Circuit’s ruling in Martin V. Boise means a city needs shelter for its entire homeless population before it can enforce anti-camping rules.

Roughly a hundred protesters are gathered at the steps of the Supreme Court rallying for the rights of those who are homeless. Many are carrying signs that read “Housing Justice” and “Housing is a human right.”

Justice Sotomayor discusses the history of Grants Pass trying to deter homelessness, including public officials openly talking about pushing homeless people to go elsewhere. As some cities take a harsh posture to oust homeless residents, other communities fear that they will be left to take on the burden. It is a complexity that has left some city leaders calling for more federal action.

Chief Justice Roberts asks a central question about the role of the Supreme Court: “Why do you think these nine people are the best people to judge and weigh those policy judgments?”

Justice Roberts asks whether the analysis changes if beds become available at a nearby homeless shelter. Advocates for homeless people say cities have plenty of tools to police encampments and are just avoiding the obvious but expensive solution: housing their occupants.

Justice Sotomayor says the real goal of the law is to make homeless people leave town.

The Biden administration has sought a middle path.

The Biden administration has taken a middle position in the case, filing a brief “in support of neither party.” It has entrusted the delicate task of navigating the charged issues to Edwin S. Kneedler, a deputy solicitor general who has argued more than 150 cases before the Supreme Court.

The administration agrees with the basic point pressed by the lawyers for the plaintiffs: Making homelessness a crime violates the Eighth Amendment’s prohibition of cruel and unusual punishment.

At the same time, the administration says the appeals court went astray by “failing to require a more particularized inquiry into the circumstances of the individuals subject to the city’s ordinances.” In other words, the administration seems unconvinced that the plaintiffs have proven, at least so far, that their own rights were violated.

The tension between the constitutional question in the case and the messy realities on the ground may help explain the administration’s mixed message. In its brief, for instance, the administration acknowledged that the federal government recently helped clear a homeless encampment in downtown Washington.

“In February 2023, the United States Park Police, in conjunction with the District of Columbia Department of Health and Human Services, closed a 70-person encampment at McPherson Square,” the brief said. “The decision to close the encampment was made after it was determined that illegal drug activity and a volatile atmosphere at the encampment impeded social services outreach and endangered social services providers, mental health clinicians, homeless individuals and the public.”

The federal government participates in most Supreme Court arguments, whether as a party or, as here, a friend of the court. And it often urges the justices to take cautious and incremental steps, particularly when its own interests may be affected.

The administration’s arguments appeared to leave both parties frustrated. Lawyers for the homeless plaintiffs, on the one hand, said the issue of the administration’s reservations about whether the ordinances applied to particular individuals was not before the justices.

On the other, the city accused the administration of a kind of verbal sleight of hand by saying that the challenged ordinances “effectively criminalize the status of homelessness.” That, the city said, is a willful misunderstanding of what it called “commonplace public-camping ordinances.”

“The repeated ‘effectively’ qualifier,” the city’s lawyers wrote, “gives the game away.”

Is homelessness an involuntary state of being?

The plaintiffs challenging ordinances in Grants Pass, Ore., that make it illegal to sleep outside are relying on a Supreme Court decision from 1962 to make a novel analogy: Homelessness, like drug addiction, is a state of being that cannot be punished.

In that decision, Robinson v. California , the court ruled that laws criminalizing a person for being addicted to narcotics violated the Eighth Amendment’s prohibition on cruel and unusual punishment.

The dispute arose after Lawrence Robinson was stopped in Los Angeles by a police officer. The officer questioned him and found physical markings that pointed to injection drug use. But the officer found no evidence that Mr. Robinson was under the influence of drugs at the time or that he had any drugs on him, either for personal use or sale.

The officer arrested Mr. Robinson, who was then convicted under a California law that made it a crime to be addicted to narcotics and sentenced to 90 days in the county jail.

Mr. Robinson sued, challenging his conviction under the argument that being addicted to narcotics was not in and of itself a crime, but rather that it was a state of being because it required no specific action.

In a 6-to-2 decision , the justices sided with Mr. Robinson, overturning his conviction.

Justice Potter Stewart, writing for the majority, wrote that such laws were analogous to making it “a criminal offense for a person to be mentally ill, or a leper, or to be afflicted with a venereal disease.” Although a government might find that people with such issues must undergo some type of treatment to protect the safety or health of others, the majority held that a law that made it a criminal offense to have a such a disease would “doubtless be universally thought to be an infliction of cruel and unusual punishment.”

The plaintiffs in Grants Pass are pointing to this precedent to argue that cities cannot ban sleeping with bedding in all public spaces without offering adequate shelter beds. The Robinson decision, they said in a brief , “certainly prohibits jurisdictions from punishing people for universal biological necessities like sleeping and using a blanket to survive cold temperatures when they have no choice but to be outside.”

The city of Grants Pass contends that the case and others that rely on it do not apply to its attempts to enforce its ordinances, arguing that its laws do not punish people for being homeless but instead are aimed at regulating conduct.

Lawyers for the city argued in a brief that “the court need not overrule Robinson here because this case does not involve a status crime, but there is no basis to extend its outlier reasoning any further.”

The court revisited the question of whether someone could be charged for a state of being, rather than an action, in 1968 in Powell v. Texas. In that case, police officers in Texas arrested Leroy Powell for public intoxication, and Mr. Powell made a similar argument: that public drunkenness was a compulsive symptom of chronic alcoholism, not something he could choose to stop.

But a four-justice plurality found that Mr. Powell’s conviction did not violate the Eighth Amendment. Justice Thurgood Marshall, writing for the plurality, found that the record before the court showed that Mr. Powell was not punished for his alcoholism but rather for being drunk in public.

The outcome of the case could have reverberations not just in the West, but also across the country.

Tent encampments lining public parks and city sidewalks. Piles of garbage, human waste and used needles. According to leaders across the political spectrum who have asked the Supreme Court to address homelessness, those are the consequences of a sharp increase in homelessness that have forced many cities to “a breaking point.”

Although the case before the court on Monday centers on the narrow issue of whether the Eighth Amendment’s prohibition on cruel and unusual punishment shields homeless people with no options for shelter from fines, fees and jail time, officials and advocates across the country are watching the case closely for its potential to reshape homelessness policy.

The case underscores deep divisions over how best to address homelessness and how much leeway to give to local and state officials to help solve the problem.

Theane Evangelis, a lawyer for the city of Grants Pass, Ore., who also represented the city of Boise, Idaho, in a similar case in 2018, warned that “the stakes could not be higher for every city in the country.”

If the Supreme Court upheld an appeals court ruling on behalf of the homeless plaintiffs, she added, cities everywhere “would find their hands tied just like Grants Pass, and the problem of growing encampments will spread throughout the country.”

Those who side with the homeless plaintiffs counter that the issue before the court is a focused one, on how to interpret the Constitution. The cities’ willingness to embrace solutions like more affordable housing will determine whether the homelessness crisis will begin to abate, they say.

“The first thing for folks who aren’t in this field — or understanding the nuances of this case — to understand is that nobody wants a country where people are forced to sleep outside,” said Ann Oliva, chief executive of the National Alliance to End Homelessness, an advocacy group founded in the 1980s with bipartisan roots.

In briefs, supporters of Grants Pass have contended that local and state policymakers, not judges, are best placed to devise homelessness policies.

The cases from Grants Pass and Boise had allowed “federal judges to serve as the nation’s ‘homelessness policy czars,’” wrote the Cicero Institute , a Texas policy group critical of longstanding federal policy that channels funds to programs to provide the homeless with permanent housing without requiring people to undergo mental health or drug treatment.

Lawyers for the National Alliance to End Homelessness say that imposing penalties, rather than providing housing and services, ignores the roots of the issue.

In its brief to the court, the group said that the city of Grants Pass and its defenders, “rather than working to end it,” sought “to banish homeless people out of sight and out of mind.”

“The threat of criminal penalties does not reduce homelessness,” the brief argued. “At most, it drives unsheltered homeless people into hiding, leading to greater health and safety concerns for localities. Criminal punishment for peaceably sleeping outside as an unsheltered homeless person is not only cruel and unusual in violation of the Eighth Amendment, but unnecessary, expensive and counterproductive.”

Reporting from Sacramento

In a rare alliance, California Democrats side with conservatives on encampments.

The Goldwater Institute and Gov. Gavin Newsom of California ordinarily have little in common. One is a conservative think tank in Arizona, the other a Democrat leading one of the nation’s most liberal states.

But for the past six years, they have been aligned on one highly charged issue : the need for some legal way to clear homeless encampments that have proliferated in cities throughout the West.

On Monday, the Supreme Court will consider an Oregon case that could reshape homelessness policy nationally. On its face, The City of Grants Pass v. Johnson asks how far cities can constitutionally go to restrict sleeping and camping in parks and on sidewalks.

More broadly, however, the case deals with one of the thorniest aspects of the homelessness crisis — the balance between the government’s responsibility to protect public health and the human right to exist without housing.

The conflict has been particularly acute in the West, where the U.S. Court of Appeals for the Ninth Circuit, in San Francisco, has issued opinions over the past six years that officials blame for the sprawling tent encampments in public spaces that have spread since the pandemic. As voters’ frustration has grown, Democratic and Republican leaders alike have called for greater authority to ban such camping, only to have the courts reject them.

Advocates for homeless people, the American Psychiatric Association and several left-leaning states, including New York, Illinois and Minnesota, argue that criminalizing homelessness only worsens the problem. More effective, they say, is focusing on housing, treatment, education and jobs for people who are homeless.

In the nine Western states in the Ninth Circuit’s jurisdiction, however, officials have increasingly begged the court to explicitly define the point at which a community can reclaim its shared spaces without triggering lawsuits. Some echo conservative appointees on the Ninth Circuit like Judge Daniel Bress, who issued a scathing response last year after the liberal majority voted not to give the Grants Pass case a rehearing before the full appeals court. (The three-judge had panel found that penalties for bunking outdoors violated the Constitution if the local population of homeless people exceeded the city’s shelter capacity.)

The Ninth Circuit, he wrote, need only look to its doorstep to see the fruit of its decision — a dystopia of “homelessness, drug addiction, barely concealed narcotics dealing, severe mental health impairment” and post-Covid “hollowing out.”

In Phoenix, where a massive encampment near the Arizona State Capitol consumed millions of state dollars and years of litigation, Timothy Sandefur, vice president for legal affairs of the Goldwater Institute, noted that both sides had asked the court for clarification.

“It just shows,” he said, “that across the board, the Ninth Circuit ruling that you have a constitutional right to sleep in a public park is unworkable and has got to be reversed.”

In California, where more than 180,000 people are homeless, Mr. Newsom wrote in his brief to the court that he opposes criminalizing homelessness, but that decisions like the one in Grants Pass “have impeded not only the ability to enforce basic health and safety measures, but also the ability to move people into available shelter beds and temporary housing.” Since his election in 2018, California has pumped more than $20 billion into programs to address homelessness, including specialized housing , a new court-based approach for dealing with addiction and mental illness and a $6.38 billion bond .

At a news conference last week, he recalled pitching in to dismantle one tent camp in Oakland that “felt like a scene out of a ‘Raiders of the Lost Ark’ where, you know, thousands and thousands of rats appeared running all around us.”

“This is to me just about common sense, not about ideology,” the governor said.

How one town’s fight over homelessness could shape a national crisis.

Inside a warming shelter, Laura Gutowski detailed how her life had changed since she became homeless two and a half years ago in Grants Pass, a former timber hub in the foothills of southern Oregon.

Her husband’s death left her without steady income. She lived in a sedan, and then in a tent, in sight of the elementary school where her son was once a student. She constantly scrambled to move her belongings to avoid racking up more fines from the police.

“I never expected it to come to this,” said Ms. Gutowski, 55. She is one of several hundred homeless people in this city of about 40,000 that is at the center of a major case before the Supreme Court on Monday with broad ramifications for the nationwide struggle with homelessness.

After Grants Pass stepped up enforcement of local ordinances that banned sleeping and camping in public spaces by ticketing, fining and jailing homeless people, lower courts ruled that it amounted to “cruel and unusual punishment” by penalizing people who had nowhere else to go.

Many states and cities that are increasingly overwhelmed by homelessness are hoping the Supreme Court overturns that decision — or severely limits it. They argue that it has crippled their efforts to address sprawling encampments, rampant public drug use and fearful constituents who say they cannot safely use public spaces.

That prospect has alarmed homeless people and their advocates, who contend that a ruling against them would lead cities to fall back on jails, instead of solutions like affordable housing and social services.

The case highlights the fierce divide over the thorny issue of how to regulate homelessness.

Theane Evangelis, a lawyer representing Grants Pass, said the Supreme Court’s decision would reverberate widely. If it does not overturn the lower-court decision, she said, cities around the United States “would find their hands tied just like Grants Pass, and the problem of growing encampments will spread throughout the country.”

Ed Johnson, a lawyer for the Oregon Law Center, a nonprofit legal aid group, who represents the homeless residents, said a ruling against them would strip them of their few protections. “Can a city make it illegal on every inch of city land, every minute of the day, for people to live outside when they have nowhere else to go?” he said.

Homelessness across the country climbed to the highest total on record last year, increasing by 12 percent to more than 650,000 people, according to a count by the federal government.

The case centers on an unusual use of the Eighth Amendment.

At the core of the Supreme Court battle over a small Oregon town’s treatment of its homeless people is a narrow question: Does the Eighth Amendment’s prohibition on cruel and unusual treatment apply to a city’s efforts to crack down on public sleeping and camping?

The Eighth Amendment is most commonly applied to punishments, not to laws themselves, and it is often the focus of litigation around the death penalty , solitary confinement and life without the possibility of parole .

But in the case on Monday, lawyers for a group of homeless residents argue that the Eighth Amendment bars the city from enforcing a series of local ordinances that, taken together, ban sleeping outside with bedding or camping in any public space in the city. Because the town, Grants Pass, has no homeless shelter, unaffiliated with any religious group, that is open to everyone, they argue, all homeless people there are involuntarily homeless and cannot be punished for having nowhere to go.

To make that argument, the homeless plaintiffs have looked to rulings that apply the amendment beyond punishments themselves and to the concept that a person cannot be penalized for their state of being.

In one landmark 1962 decision, Robinson v. California , the court found that a person could not be punished for being addicted to drugs, paving the way for subsequent applications. Because those rulings found that the Eighth Amendment prohibits punishing people for having “an involuntary status,” the homeless plaintiffs say that it would also be relevant to their situation. They add that they are being disciplined for circumstances outside their control, in this instance “universal biological necessities like sleeping and using a blanket to survive cold temperatures when they have no choice but to be outside.”

The city argues that this is an inappropriate use of the Eighth Amendment and a fundamental misunderstanding of its purpose.

Two legal experts, in filing a friend-of-the-court brief siding with Grants Pass, argued that the Constitution did bar criminalizing someone’s state of being, rather than their specific conduct. But that prohibition, the law professors — Peter W. Low of the University of Virginia and Joel S. Johnson of Pepperdine — added, had a “shaky Eighth Amendment footing.”

NY court will publish transcripts from Trump's hush money trial. Here's how you can access them.

New York courts will publish daily transcripts of former President Donald Trump's hush money trial , officials have announced.

New York typically does not allow audio or visual coverage in court rooms, meaning the public is unable to watch the first criminal trial of a former president in U.S. history live.

But certified transcripts of each day's proceedings will be posted to the New York State Unified Court System's media website by the end of the following business day, according to a news release Monday . Transcripts can be expensive and sometimes unavailable, depending on the location or particular court system.

“This historic case, which has generated unparalleled public interest, calls for this historic step by the court system," First Deputy Chief Administrative Judge Norman St. George said in the news release. "This will serve to enhance public understanding of the trial with minimum disruption to the courtroom proceedings.”

Donald Trump trial live updates: Donald Trump trial live updates: Latest from gag order arguments, David Pecker testimony

Prep for the polls: See who is running for president and compare where they stand on key issues in our Voter Guide

What is Donald Trump on trial for in New York?

Trump has pleaded not guilty to charges that he falsified business records to cover up a hush money payment to porn star Stormy Daniels that was designed to unlawfully interfere in the 2016 presidential election.

Trump's former lawyer Michael Cohen  issued the payment and violated federal campaign finance laws, according to prosecutors. But they also argue Trump authorized the payment to help his presidential campaign and falsified records to cover up the checks he sent to reimburse Cohen for the hush money.

The trial kicked off April 15 with jury selection , which concluded Friday. Both legal teams gave their opening arguments Monday, and the prosecution called its first witness: David Pecker , former head of the tabloid the National Enquirer's parent company.

Pro-Palestinian campus protests and Baltimore fights Dali ship owners: Morning Rundown

A judge considers whether Donald Trump violated a gag order by calling key figures in his hush money trial ‘’sleaze bags.’’ Arrests escalate tensions at campus Gaza protests. And a study shows how the definition of “old age” is shifting.

  Here’s what to know today.

Judge will weigh if Trump violated gag order before witness testimony continues

Former President Donald Trump’s trial to determine whether he falsified business records is set to pick back up with more testimony from former American Media chief David Pecker. But first, Judge Juan Merchan will consider whether Trump should be held in contempt over a series of posts on Truth Social calling Michael Cohen and Stormy Daniels ‘’sleaze bags’’ that prosecutors argue violated a gag order. 

The hearing to consider whether Trump violated rules follows a day of opening statements from both sides. It marked the first time time New York prosecutors have laid out their case against Trump. They told a story of a “criminal scheme to corrupt the 2016 presidential election.” And that “he covered up that criminal scheme by lying in his New York business records over and over and over again,” said Michael Colangelo, a lawyer with Manhattan District Attorney Alvin Bragg’s office.

Colangelo also quoted from the widely publicized “Access Hollywood” tape, which caught Trump on a hot mic saying he could grope women without their consent because “when you’re a star, they let you do it.”

This is Morning Rundown, a weekday newsletter to start your morning. Sign up here to get it in your inbox.

Trump attorney Todd Blanche went straight to trying to tear apart the prosecution’s story. He said there was “nothing wrong with trying to influence an election.” He added, “It’s called democracy.”

Blanche also alleged adult film star Stormy Daniels was trying to “extort” money from Trump, and that ex-Trump lawyer Michael Cohen was waging a vendetta against him. Here’s what else happened on the fifth day of the trial.

Trump was seen with his eyes closed as Merchan began the day by running through rote procedural matters. He began to focus more intently on key players in the room when opening statements began, and became even more animated when Pecker, the prosecution’s first witness, took the stand.

As senior politics reporter Jonathan Allen wrote in an analysis: Trump’s “entire demeanor changed over the course of a day, hinting that he plans to be an active participant in this trial going forward.” Read the full analysis here.  

Senate holds key test vote on Ukraine aid

The Senate is expected to vote to advance the House-passed package that includes $60 billion in aid to Ukraine and a provision that could lead to a nationwide ban on TikTok. The package also includes $26 billion in aid to Israel and humanitarian relief in Gaza, in addition to $8 billion for security in Taiwan and the Indo-Pacific. 

This afternoon’s vote isn’t on final passage of the bill, but is instead about whether senators can reach a deal to quickly vote to pass the bill the same day, or whether they will have to wait until tomorrow. The outcome of the vote is nonetheless a key indicator of whether the legislation has enough support to head to President Joe Biden’s desk. If it passes, TikTok’s China-based parent company will have nine months — or the president could extend it to a year — to sell the popular social media platform or be banned in the U.S. Here’s what else to know.

Arrests at NYU, Yale as campus protests escalate

New York police said they were “ready” to take Gaza war protesters into custody again at the request of New York University if demonstrators refused to leave. The statement came hours after several arrests were made last night. The number of people arrested, as well as the charges against them, were not available.

The tensions at NYU coincide with escalating campus protests across the U.S. over the war in Gaza. Forty-seven protesters at Yale University were arrested earlier yesterday. Classes at Columbia University will be hybrid for the rest of the spring semester, the school’s provost said, in light of recent protests. Here’s what else happened.

More on the tensions at college campuses:  

• Some faculty members at Morehouse College  have raised concerns  about plans for President Joe Biden to deliver a commencement address there next month.

A study considers the question: When does ‘old age’ begin?

People’s definition of “old age” seems to be skewing later and later, according to a new study, which asked people about their perceptions of age over the course of 25 years. The study found that people in their mid-60s believe old age starts at 75. But the older people got, the later they thought old age began. The generation in which participants were born also influenced their perception.

Experts say there is one important caveat to the research, which was published in the American Psychological Association’s Psychology and Aging journal. The study’s participants lived in Germany, where life expectancy has risen in the past few decades. But U.S. life expectancy declined from 79 in 2019 to 76 in 2021, which could skew the study’s results elsewhere.

Still, experts say the study offers insight into how people’s perspectives on aging change as they get older.

Baltimore battles Dali ship owners in bridge collapse

The City of Baltimore is seeking a jury trial in its effort to hold the owners of the Dali cargo ship liable for the collapse of the Francis Scott Key Bridge. In new court filings, Mayor Brandon Scott and the Baltimore City Council argued that Grace Ocean Private Ltd. and Synergy Marine Pte Ltd. “put a clearly unseaworthy vessel into the water.” The city also said the companies’ effort to limit responsibility for the vessel and the cargo’s value at $43.6 million is “substantially less than the amount that will be claimed for losses and damages” from the March 26 crash that killed six construction workers. The Port of Baltimore generated over $70 billion last year alone, the city said. 

The city alleges that the alarms on the Dali sounded “even before leaving the port,” but the ship left anyway. The court filings also take aim at crew members , accusing the companies of staffing the ship with people who lacked proper skill or training. 

Politics in Brief

Pennsylvania primaries: A key contest in the fight for control of the Senate, a moderate Republican put to the test and a district where the war in Gaza is front and center. Here’s what to watch for in the Pennsylvania primaries. 

EMILY’s List: As Trump moves closer to selecting his running mate, a major Democratic abortion rights advocacy group is focusing its annual “On Notice” list on “extremist” candidates. 

RFK Jr.’s influence: Trump has recently stepped up his efforts to brand third-party presidential candidate Robert F. Kennedy Jr. as left-wing and Biden’s problem. It’s a sign that he and his allies are worried that Trump may have more to lose from Kennedy’s presence on the ballot.

Supreme Court: Conservative justices appeared skeptical about a challenge to an Oregon city’s ordinances that punish homeless people for camping on public property when they have nowhere else to go.

Want more politics news? Sign up for From the Politics Desk to get exclusive reporting and analysis delivered to your inbox every weekday evening.  Subscribe here.

Staff Pick: Pastor vows to fight Satan’s influence in Metropolis

As I drove toward the city of Metropolis, Illinois, earlier this month, a billboard invited me to visit the “Home of Superman.” The small town, which shares a name with the city from DC Comics, is known for welcoming outsiders. But that reputation has been tested in recent months, as a local Christian pastor has rallied his congregation to stand against “evil” forces that he says have been encroaching on their community, via the public library.

The conflict — what some are calling “a battle for the soul” of Metropolis — follows a national pattern of Christian conservatives waging what they view as a spiritual battle inside libraries, as they seek to restrict access to LGBTQ-affirming books. But unlike comic books and the Bible,  the story I found in Metropolis  did not break along obvious ideological lines or black-and-white depictions of good and evil.  —  Mike Hixenbaugh,  senior investigative reporter

In Case You Missed It

• Hospitalized women are less likely to die or be readmitted to the hospital if they are treated by female doctors, a new study found.
• A beloved ostrich at a Kansas zoo named Karen died after swallowing a staff member’s keys .
• Comedian Arj Barker defended his decision to ask a breastfeeding mother and her baby to leave his comedy show.
• Five people, including two children, were found dead inside an Oklahoma City home.
• Mall retailer Express filed for Chapter 11 bankruptcy protection , but a group of investors is looking to acquire and save the company.

Select: Online Shopping, Simplified

Earth Week is here, and with it comes savings on everything you need for spring activities.  Shop the best sales  across categories including garden and outdoor, beauty and wellness, and apparel and accessories.

  Sign up to The Selection  newsletter for exclusive reviews and shopping content from NBC Select.

Thanks for reading today’s Morning Rundown. Today’s newsletter was curated for you by Elizabeth Robinson. If you’re a fan, please send a link to your family and friends. They can sign-up here .

Elizabeth Robinson is a newsletter editor for NBC News, based in Los Angeles.

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Class 11th Physics - System of Particles and Rotational Motion Case Study Questions and Answers 2022 - 2023

By QB365 on 08 Sep, 2022

QB365 provides a detailed and simple solution for every Possible Case Study Questions in Class 11 Physics Subject - System of Particles and Rotational Motion, CBSE. It will help Students to get more practice questions, Students can Practice these question papers in addition to score best marks.

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System of particles and rotational motion case study questions with answer key.

11th Standard CBSE

Final Semester - June 2015

The centre of mass of a body is a point at which the entire mass of the body is supposed to be concentrated. The  \(\vec{r}\)  of c.m of the system of two particles of masses m 1  and m 2 with position vector  \(\vec{r}_{1} \text { and } \vec{r}_{2}\)  i s given by  \(\vec{r}=\frac{m_{1} \vec{r}_{1}+m_{2} \vec{r}_{2}}{m_{1}+m_{2}}\)   for an isolated system, where no external force is acting  \(\overrightarrow{v_{c m}}\)  = constant Under no circumstance, the velocity of centre of mass of an isolated system can undergo a change. (i) What should be the position of the centre of mass of a system of two particles of unequal masses? (ii) An electron and a proton move towards each other with velocities v 1  and v 2 respectively. What is the velocity of their centre of mass? (iii) Two bodies of masses 1kg and 2 kg are located at (1, 2) and (-1, 3) respesctively, determine the coordinates of the centre of mass. (iv) A bomb dropped from an aeroplane in level flight explodes in the middle. How would be the motion of centre of mass of the fragments? (v) Two blocks of masses 5 kg and 2 kg are placed on a frictionless surface and connected by a spring. An external kick gives a velocity of 14 ms -1  to the heavier block in the direction of the lighter one. Determine the velocity gained by the centre of mass. (vi) Can centre of mass of a body lie where there is absolutely no mass? Give example. (vii) Can centre of mass of a body coincide with the geometrical centre of the body?

Moment of inertia of a body about a given axis is the rotational inertia of the body about that axis. It is represented by 1= MK 2 , where M is mass of body and K is radius of gy ration of the body about that axis. it is a scalar quantity, which is measured in kg m 2 . When a body rotates about a given axis and the axis of rotation also moves, then total K.E of body = K.E of translation + kinetic energy of rotation. \(K=\frac{1}{2} m v^{2}+\frac{1}{2} I \omega^{2}\) (i) Is the M.I of a body about a given axis is vector or scalar quantity? (ii) On what factors does M.I of a body depend? (iii) Determine the moment of inertia of circular disc and circular ring of same mass and radius about an axis perpendicular to plane. (iv) A 40 kg flywheel in the form of a uniform circular disc of diameter 1 m is making 120 rpm. What is the M.I about a transverse axis through its centre? (v) Determine kinetic of rotation of the flywheel in the above case. (vi) Calculate radius of gyration of a cylindrical rod of mass m and length L about an axis of rotation perpendicular to its length and passing through its centre, (vii) Determine the ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius about a tangential axis in the plane of the ring.

Angular momentum of a rotating body is measure of quantity of motion in rotational motion about an axis which is measured by product of moment of inertia and angular velocity i.e., L =  \(I \omega\)  . It is moment of linear momentum about axis of rotation. Being a vector quantity its direction is along the axis of rotation. In the absencse of an external torque, angular momentum vector remains constant. (i) If angular momentum is conserved in a system whose moment of inertia is decreased, will its rotational kinetic energy be also conserved? Explain. (ii) Why spin angular velocity of a star is greatly enhanced when it collapses under gravitational pull and becomes a neutron star? (iii) A Person sits near the edge of a circular platform revolving with a uniform angular speed. What will be the change in the motion of the platform? (iv) What would happen if the person starts moving from the edge toward the centre of the platform? (v) Why are there two propellers in a helicopter? (vi) A thin uniform circular disc of mass M and Radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with an angular velocity  \(\omega \text { . }\)  Another disc of same dimensions but of mass  \(\frac{\boldsymbol{M}}{\mathbf{4}}\)   is placed gentally 4 on the first disc coaxially show that angular velocity of the system is  \(\frac{4}{5} \omega.\)  

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System of particles and rotational motion case study questions with answer key answer keys.

(i) The centre of mass of a system of two particles of .. unequal masses is closer to heavier particles. Since m 1 r 1  + m 2 r 2 = 0, when c.m is at origin \(\therefore \quad r_{2}=\frac{-m_{1} r_{1}}{m_{2}} \text { if } m_{2}>m_{1} \text { then } r_{2}<r_{1}\)   (ii) As the force of attraction is mutual, the system is inertial i.e., system without external force, therefore, v cm = 0. (iii) Here m 1  = 1 kg, m 2 = 2kg, x 1  = 1,Y 1  =2, x 2 =-1,Y 2  = 3 coordinates of the centre of mass are \(x=\frac{m_{1} x_{1}+m_{2} x_{2}}{m_{1}+m_{2}}=-\frac{1}{3}\)   \(y=\frac{m_{1} y_{1}+m_{2} y_{2}}{m_{1}+m_{2}}=\frac{8}{3}\)   (iv) As the explosion is due to internal forces only, the centre of mass of fragments continues to follow the same parabolic path which it would have followed if there was not explosion. (v) Here m 1  = 5kg, m 2 = 2 kg v 1  = 14 ms -1 , v2 = 0, v cm = ? \(v_{c m}=\frac{m_{1} v_{1}+m_{2} v_{2}}{m_{1}+m_{2}}\)   =  \(\frac{5 \times 14+2 \times 0}{5+2}=\frac{70}{7}=10 \mathrm{~ms}^{-1}\)   (vi) Yes, for example, the centre of mass of a uniform circular ring lies at the centre of the ring where there IS no mass. (vii) Yes, when a body has uniform mass density, its centre of mass shall coincide with its geometrical centre.

(i) Moment of inertia of a body about a given axis is a scalar quantity. (ii) Moment of inertia of a body depends on (i) Mass of the body (ii) Size and shape of the body (iii) axis of rotation of the body. (iii)  \(I_{d i s c}=\frac{1}{2} M R^{2}, I_{r i n g}=M R^{2}\)   (iv)  \(\mathrm{I}=\frac{1}{2} M R^{2}=\frac{1}{2} \times 40\left(\frac{1}{2}\right)^{2}=5 \mathrm{~kg} \mathrm{~m}^{2}\)   (v) K.E of rotation =  \(\frac{1}{2} I \omega^{2}=\frac{1}{2} I(2 \pi n)^{2}\)   \(\frac{1}{2} \times 5\left(2 \pi \times \frac{120}{60}\right)^{2}=394.8 \mathrm{~J}\)   (vi)  \(I=\frac{M L^{2}}{2}=M K^{2} \text { or } K=\frac{L}{2 \sqrt{3}}\)    (vii)  \(I_{1}=M K_{1}^{2}=\frac{5}{4} M R^{2} \Rightarrow K_{1}=\sqrt{\frac{5}{4}} R\)   M.I of circular ring of same radius about a tangential axis in the plane of the ring. \(I_{1}=M K_{2}^{2}=\frac{3}{2} M R^{2}\)   \(K_{2}=\sqrt{\frac{3}{2} R}\)   \(\therefore \quad \frac{K_{1}}{K_{2}}=\sqrt{\frac{5}{4} \times \frac{2}{3}}=\sqrt{\frac{5}{6}}\)    

(i) Here  \(L=I \omega\)   =   constant, K.E =  \(\frac{1}{2} I \omega^{2}\)   K. E =  \(\frac{L^{2}}{2 I} \Rightarrow \mathrm{K} . \mathrm{E} \alpha \frac{1}{I}\)   therefore when M.l decreases, K.E of rotation (K.E) increases and not remain conserved. (ii) On collapsing under gravitational pull, the size of star decreases. (iii) Therefore, its moment of inertia decreases. As angular momentum  \((L=I \omega)\)  is conserved and 1 decreases, therefore, spin angular velocity co increases. (iii) Since  \(L=I \omega\)  = Constant, since moment of inertia 1 increases, therefore, will decrease. (iv) As the person starts moving from the edge towards the centre of platform, therefore. M.I goes on decreasing. Hence co goes on increasing. (v) If the helicopter had only one propeller, then due to conservation of angular momentum, the helicopter itself would turn in opposite direction. Thus two propellers provide helicopter a steady movement. (vi) Initial angular momentum of one disc L =  \(I \omega=\frac{1}{2} M R^{2} \omega\)  angular momentum remain conserved \(\mathrm{I} \omega=\mathrm{I}^{\prime} \omega^{\prime}\) . Since no external torque act. \(I^{\prime}=\frac{1}{2} M R^{2}+\frac{1}{2}\left(\frac{M}{4}\right) R^{2}=\frac{5}{8} M R^{2}\)   Therefore,  \(\omega^{\prime}=\frac{I \omega}{I^{\prime}}=\frac{\frac{1}{2} M R^{2} \omega}{\frac{5}{8} M R^{2}}=\frac{4}{5} \omega\) .

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Case Study Questions Class 11 Physics Laws Of Motion

Case study questions class 11 physics chapter 5 laws of motion.

CBSE Class 11 Case Study Questions Physics Laws Of Motion. Important Case Study Questions for Class 11 Board Exam Students. Here we have arranged some Important Case Base Questions for students who are searching for Paragraph Based Questions Laws Of Motion.

At Case Study Questions there will given a Paragraph. In where some Important Questions will made on that respective Case Based Study. There will various types of marks will given 1 marks, 2 marks, 3 marks, 4 marks.

CBSE Case Study Questions Class 11 Physics Laws Of Motion

Case study – 1.

Newton’s first law of motion states that If the net external force on a body is zero, its acceleration is zero. Acceleration can be non zero only if there is a net external force on the body. To summaries, if the net external force is zero, a body at rest continues to remain at rest and a body in motion continues to move with a uniform velocity. This property of the body is called inertia. Inertia means ‘resistance to change’. A body does not change its state of rest or uniform motion, unless an external force compels it to change that state.  In other words, all objects resist a change in their state of motion. In a qualitative way, the tendency of undisturbed objects to stay at rest or to keep moving with the same velocity is called inertia. Consider a book at rest on a horizontal surface. It is subject to two external forces: the force due to gravity (i.e. its weight W) acting downward and the upward force on the book by the table, the normal force R. R is a self-adjusting force. This is an example of the kind of situation mentioned above. The forces are not quite known fully but the state of motion is known. We observe the book to be at rest. Therefore, we conclude from the first law that the magnitude of R equals that of W. A statement often encountered is : Since W = R, forces cancel and, therefore, the book is at rest”. This is incorrect reasoning. The correct statement is: “Since the book is observed to be at rest, the net external force on it must be zero, according to the first law. This implies that the normal force R must be equal and opposite to the weight W ” .

1) The book on table is at rest. The force of gravity here is balanced by

a) Force of friction

b) Normal reaction by table on book

c) Weight of table

d) none of these

2) If no external force acts on object which is at rest. it will

a) remain at rest

b) start to move

c) both a and b can possible

3) Define inertia.

4) State Newton’s first law of motion.

5) Explain why book on table remains at rest.

Answer Key –

3) the tendency of undisturbed objects to stay at rest or to keep moving with the same velocity is called inertia.

4) Newton’s first law of motion states that If the net external force on a body is zero, its acceleration is zero. Acceleration can be non zero only if there is a net external force on the body

5) Consider a book at rest on a horizontal surface. It is subject to two external forces: the force due to gravity (i.e. its weight W) acting downward and the upward force on the book by the table, the normal force R. This is an example of the kind of situation mentioned above. Magnitude of R equals that of W. This implies that the normal force R must be equal and opposite to the weight W” .

Case Study – 2

Momentum of a body is defined to be the product of its mass m and velocity v, and is denoted By p:

Momentum is clearly a vector quantity. SI unit is kg m/s. The following common experiences indicate the importance of this quantity for considering the effect of force on motion. Suppose a light-weight vehicle (say a small car) and a heavy weight vehicle (say a loaded truck) is parked on a horizontal road. We all know that a much greater force is needed to push the truck than the car to bring them to the same speed in same time. Similarly, a greater opposing force is needed to stop a heavy body than a light body in the same time, if they are moving with the same speed.

• If two stones, one light and the other heavy, are dropped from the top of a building, a person on the ground will find it easier to catch the light stone than the heavy stone. The mass of a body is thus an important parameter that determines the effect of force on its motion.
• Speed is another important parameter to consider. A bullet fired by a gun can easily pierce human tissue before it stops, resulting in casualty. The same bullet fired with moderate speed will not cause much damage. Thus for a given mass, the greater the speed, the greater is the opposing force needed to stop the body in a certain time. Taken together, the product of mass and velocity, that is momentum, is evidently a relevant variable of motion. The greater the change in the momentum in a given time, the greater is the force that needs to be applied.

1) SI unit of momentum is

b) Kg m/s 2

d) None of these

2) Momentum is

a) Scalar quantity

b) Vector quantity

3) Define momentum. Give its SI unit.

4) Explain with example how mass of body is important for determining effect of force on its motion?

5) Explain with example how speed is important for determining effect of force on its motion?

Answer key-2

3) Momentum of a body is defined to be the product of its mass m and velocity v, and is denoted By p:

Momentum is clearly a vector quantity. SI unit is kg m/s.

4) If two stones, one light and the other heavy, are dropped from the top of a building, a person on the ground will find it easier to catch the light stone than the heavy stone. The mass of a body is thus an important parameter that determines the effect of force on its motion.

5) Speed is important parameter to consider. A bullet fired by a gun can easily pierce human tissue before it stops, resulting in casualty. The same bullet fired with moderate speed will not cause much damage. Thus for a given mass, the greater the speed, the greater is the opposing force needed to stop the body in a certain time.

Case Study – 3

The first law refers to the simple case when the net external force on a body is zero. The second law of motion refers to the general situation when there is net external force acting on the body. It relates the net external force to the acceleration of the body.

These qualitative observations lead to the second law of motion expressed by Newton as follow:

The rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction in which the force acts. Thus, if under the action of a force F for time interval Δt, the velocity of a body of mass m changes from v to v + Δv i.e. its initial momentum

p = m v changes by Δp = mΔv . According to the Second Law

Where k is a constant of proportionality. Mathematically,

F = ma, the unit of force is kg-m/s 2 or Newton, which has the symbol N. Let us note at this stage some important points about the second law:

• In the second law, F = 0 implies a = 0. The second law is obviously consistent with the first law.
• The second law of motion is a vector law.
• The second law of motion given by is applicable to a single point particle as well as to the rigid body but internal forces is not considered in F.
• The second law of motion is a local relation which means that force F at a point in space (location of the particle) at a certain instant of time is related to a at that point at that instant. Answer the following questions.

1) SI unit of force is

d) None of the above

2) According to second law of motion The rate of change of momentum of a body is directly proportional to

a) Velocity of body

b) Applied force

c) Only mass of body

d) None of the above.

3) The second law of motion is

a) Vector law

b) Scalar law

4) State second law of motion.

5) Write a note on 2 nd law of motion. Enlist some deductions from 2 nd law

Answer key -3

4) The second law of motion is quantitative expression of force and it states that the rate of change of momentum of an object is proportional to the applied unbalanced force in the direction of force. Mathematically, F = ma, the unit of force is kg-m/s 2 or Newton.

5) The rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction in which the force acts. Thus, if under the action of a force F for time interval Δt, the velocity of a body of mass m changes from v to v + Δv i.e. its initial momentum

p = m v changes by Δp = mΔv. According to the Second Law

• The second law of motion is a local relation which means that force F at a point in space (location of the particle) at a certain instant of time is related to a at that point at that instant.

Case Study – 4

4.) The product of force and time which is the change in momentum of the body remains a measurable quantity. This product is called impulse

Impulse = Force × time duration

= Change in momentum

Large force acting for a short time to produce a finite change in momentum is called an impulsive force.

The third law of motion states that when one object exerts a force on another object, the second object instantaneously exerts a force back on the first. These two forces are always equal in magnitude but opposite in direction. These forces act on different objects and never on the same object. The two opposing forces are also known as action and reaction forces.

Answer the following questions. The second and third laws of motion lead to an important consequence: the law of conservation of momentum. Take a familiar example. A bullet is fired from a gun. If the force on the bullet by the gun is F, the force on the gun by the bullet is – F, according to the third law. The two forces act for a common interval of time Δt. According to the second law, FΔt is the change in momentum of the bullet and – F Δt is the change in momentum of the gun. Since initially, both are at rest, the change in momentum equals the final momentum for each. Thus if pb is the momentum of the bullet after firing and pg is the recoil momentum of the gun,

pg = – pb i.e. pb + pg = 0  That is, the total momentum of the (bullet + gun) system is conserved. Thus in an isolated system (i.e. a system with no external force), mutual forces between pairs of particles in the system can cause momentum change in individual particles, but since the mutual forces for each pair are equal and opposite, the momentum changes cancel in pairs and the total momentum remains unchanged. This fact is known as the law of conservation of momentum. The total momentum of an isolated system of interacting particles is conserved.

1) Action reaction forces acts on bodies in order that

a) Action acts first then reaction force comes

b) reaction acts first then action force comes

c) both action reaction act at same time

2) Which of the following is correct about action reaction forces?

a) They act on different objects

b) They are equal in magnitude and opposite in direction

c) Both forces acted on different object simultaneously

d) All the above

3) State Newton’s third law of motion

4) Define impulse. Give its formula.

5) State law of conservation of momentum

Answer key – 4

3) The third law of motion states that when one object exerts a force on another object, the second object instantaneously exerts a force back on the first. These two forces are always equal in magnitude but opposite in direction. These forces act on different objects and never on the same object.

4) The product of force and time which is the change in momentum of the body remains a measurable quantity. This product is called impulse

5) The total momentum of isolated system particles is conserved. Isolated system means no external force.

Case Study – 5

Friction: Let us return to the example of a body of mass m at rest on a horizontal table. The force of gravity (mg) is cancelled by the normal reaction force (N) of the table. Now suppose a force F is applied horizontally to the body. We know from experience that a small applied force may not be enough to move the body. But if the applied force F were the only external force on the body, it must move with acceleration F/m, however small. Clearly, the body remains at rest because some other force comes into play in the horizontal direction and opposes the applied force F, resulting in zero net force on the body. This force f s parallel to the surface of the body in contact with the table is known as frictional force, or simply friction. When there is no applied force, there is no static friction. It comes into play the moment there is an applied force. As the applied force F increases, fs also increases, remaining equal and opposite to the applied force (up to a certain limit), keeping the body at rest. Hence, it is called static friction. Static friction opposes impending motion. The term impending motion means motion that would take place (but does not actually take place) under the applied force, if friction were absent. It is found experimentally that the limiting value of static friction (f s )max f is independent of the area of contact and varies with the normal force(N) approximately as :

(f s )max = μ N

where μs is a constant of proportionality depending only on the nature of the surfaces in contact. The constant μs is called the coefficient of static friction. The law of static friction may thus be written as

  f s ≤ μsN

Frictional force that opposes relative motion between surfaces in contact is called kinetic or sliding friction and is denoted by f k . Kinetic friction, like static friction, is found to be independent of the area of contact. Further, it is nearly independent of the velocity. It satisfies a law similar to that for static friction:

f k = μ k N

1) Force of static friction is directly proportional to

a) Normal reaction

b) Force by gravity

c) Velocity of body

2) Coefficient of kinetic friction is independent of area of contact. True or false?

3) Give formula for law of static friction

4) Explain law of static friction

5) Explain kinetic friction.

Answer key-5

3) The law of static friction can be written as

Where μs is coefficient of static friction and N is normal reaction.

4) It is found experimentally that the limiting value of static friction (f s ) max f is independent of the area of contact and varies with the normal force(N) approximately as : (f s )max = μ N . where μs is a constant of proportionality depending only on the nature of the surfaces in contact. The constant μs is called the coefficient of static friction. The law of static friction may thus be written as f s ≤ μsN

5) Frictional force that opposes relative motion between surfaces in contact is called kinetic or sliding friction and is denoted by f k   and given by f k = μ k N

Kinetic friction, like static friction, is found to be independent of the area of contact. Further, it is nearly independent of the velocity.

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