Fall Final Review Physics Midterm

A person exerts a force Fp on a rope to pull a block of mass m up a ramp. The rope makes an angle θ2 to the ramp and the ramp makes an angle θ1 to the horizontal, as shown. The force of kinetic friction between the block and the ramp has magnitude Ff. Which of the following expressions is equal to the magnitude of the acceleration a of the block?

(Fpcosθ2-Ff)/m - gsinθ1

Block Y with mass mY falls onto and sticks to block X, which is attached to a vertical spring, as shown in Figure 1. A short time later, as shown in Figure 2, the blocks are momentarily at rest. At that moment, block Y exerts a force of magnitude Fdown on block X, and block X exerts a force of magnitude Fup on block Y. Which of the following correctly relates Fup, Fdown, and mYg at the instant shown in Figure 2 ?

(Fup=Fdown) > myg

In each of the figures shown, a motor pulls identical blocks up a ramp at the same constant speed. Friction between the blocks and the ramp is negligible. Which of the following correctly compares the instantaneous power P delivered by the motor at the instants shown in the figures?

(P1=P2) > P3

A block on a horizontal surface is attached to two horizontal springs, as shown. Both springs are compressed a distance Δx from their unstretched length and the block remains at rest due to static friction between the block and the surface. Which of the following is a correct expression for the magnitude of the force of static friction?

(k1+k2)Δx

A car on a straight track is at position xi and has initial speed vi when it begins to slow down with constant acceleration of magnitude a. When the car reaches position xf it has speed vf. Which of the following is a correct expression for xf?

(v²i-v²f)/2a + xi

Two spheres, with masses indicated in the figure, are connected by a rod with negligible mass. The rod is initially vertical, as shown on the left. The system is then rotated about its center until the rod is horizontal, as shown on the right. What is the total work done by the gravitational force on the system as it rotates from vertical to horizontal?

+60 J

An object on a straight, horizontal track with an initial positive velocity undergoes a constant acceleration of -5m/s² for 4 seconds. Which of the following is the change in velocity of the object during this interval?

-20 m/s

A box of mass 0.5 kg with a fan attached to its top is moving to the right when it reaches a ramp, as shown. As the box slides up the ramp a distance of 4.0 m, the fan exerts a 0.5 N force opposite the direction of the box's motion. The box momentarily comes to rest at the top of the ramp, at a height of 1.0 m above its starting point. There is negligible friction between the box and the ramp. What is the total work done on the box as it slides up the ramp?

-7.0 J

An object of mass m is initially at rest and free to move without friction in any direction in the xy-plane. A constant net force of magnitude F directed in the +x direction acts on the object for 1 s. Immediately thereafter a constant net force of the same magnitude F directed in the +y direction acts on the object for 1 s. After this, no forces act on the object. Which of the following graphs best represents the kinetic energy K of the object as a function of time?

0-1, 1-2 exponential and 2-3 straight horizontal (visual graph)

At time t=0, a car is moving in the positive direction along a straight road. The graph represents the car's velocity v as a function of time t. The car's position at t=0 is x=0. Which of the following graphs could represent the acceleration a of the car as a function of time t?

0-1.5 horizontal at 0, 1.5-4 linear graph from -1 to 0, 4-5 horizontal at 0 (visual graph)

A student of mass 45kg slides down a ramp that is inclined at an angle of 30∘ above the horizontal. The magnitude of the student's acceleration is 2m/s². The coefficient of kinetic friction between the student and the ramp is most nearly

0.35

The cart of mass 10 kg shown above moves without frictional loss on a level table. A 10 N force pulls on the cart horizontally to the right. At the same time, a 30 N force at an angle of 60° above the horizontal pulls on the cart to the left. What is the magnitude of the horizontal acceleration of the cart?

0.5 m/s²

A 10 kg box is at rest on a rough, horizontal surface. The box is pushed to the right by a force of 20N, pushed to the left by a force of 80N, and remains at rest. What is the minimum value of the coefficient of static friction between the box and the surface?

0.6

The figures above show a small block of mass 0.20kg on a track in the shape of a circular arc. The block is released from rest at a height H above the floor, as shown in Figure 1. The block slides along the track with negligible friction and leaves it at a height of 0.40m above the floor and a speed of 3.0m/s at a 30° angle, as shown in Figure 2. The height H is most nearly

0.86 m

An object is initially at the origin. The object changes its position to the right by 4 units. The object then changes its position to the left by 3 units. Which of the following correctly indicates the magnitude of the object's change in position and provides a valid justification?

1 unit, because in one dimension vectors with opposite directions have opposite signs.

A ball is thrown with an initial speed of 20 m/s at an angle of 60° to the ground. If air resistance is negligible, what is the ball's speed at the instant it reaches its maximum height from the ground?

10 m/2

A train is moving to the east at 25m/s relative to the ground. A passenger at the back of the train throws a ball to the west with an initial speed of 15m/s relative to the train. What is the initial velocity of the ball relative to the ground?

10 m/s to the east

A 2 kg block, starting from rest, slides 20 m down a frictionless inclined plane from X to Y, dropping a vertical distance of 10 m as shown above. The magnitude of the net force on the block while it is sliding is most nearly

10.0 N

A block of mass 2.0kg is initially at rest on a horizontal surface. The block is pulled a distance of 10m in 3.0s by an applied force. The coefficients of static and kinetic friction between the surface and the object are μs=0.45 and μk=0.30, respectively. The magnitude of the applied force is most nearly

10.4 N

A force is exerted on a block as the block slides across a horizontal surface. The graph shows the magnitude of the force as a function of the block's position. The total amount of work done on the block by the force during the interval shown in the graph is most nearly

11 J

A 2 kg block, starting from rest, slides 20 m down a frictionless inclined plane from X to Y, dropping a vertical distance of 10 m as shown above. The speed of the block at point Y is most nearly

14 m/s

Two asteroids of mass M are in deep space far away from any other objects. The centers of the asteroids are a distance d apart where d is much larger than the size of the asteroids, and each asteroid exerts a force of magnitude F on the other. At a later time, the mass of each asteroid has increased to 2M and they are a distance d2 apart. What is the magnitude of the force that each asteroid exerts on the other at this later time?

16 F

Planets A and B move in circular orbits at different distances from a star of mass M. Planet A has mass m0 and orbital radius r0. The gravitational potential energy of the Planet A-star system is UA. Planet B has mass 4m0 and orbital radius 2r0. The gravitational potential energy of the Planet B-star system is UB. What is the ratio UA:UB?

1:2

Boxes X and Y are pushed horizontally the same distance by forces with varying magnitudes. The magnitudes of the forces exerted on each box as a function of their positions are shown in the graph. What is the ratio WX:WY of the work done on each box by the forces?

1:3

At time t1, the center of a moon of mass m is a distance d from the center of a planet of mass M. Later, at time t2, the center of the moon is a distance 2d from the center of the planet. The gravitational potential energy of the moon-planet system at time t1 is Ut1, and the gravitational potential of the system at time t2 is Ut2. Which of the following indicates the ratio of the gravitational potential energy of the moon-planet system Ut1/Ut2 ?

2

A 60kg person is riding in an elevator. At time t1, the elevator is accelerating downward with a magnitude of 2m/s². A short time later, at time t2, the elevator is accelerating upward with a magnitude of 2m/s². The ratio of the normal force exerted by the elevator on the person at time t1 to that at time t2 is most nearly

2 : 3

The figure above shows the forces exerted on a block that is sliding on a horizontal surface: the gravitational force of 40 N, the 40 N normal force exerted by the surface, and a frictional force exerted to the left. The coefficient of friction between the block and the surface is 0.20. The acceleration of the block is most nearly

2.0 m/s² to the left

The graph shows speed v as a function of time t for a 0.20kg object traveling along a straight, horizontal track. The change in the kinetic energy of the object over the time interval shown in the graph is most nearly

2.5 J

The figures above show a small block of mass 0.20kg on a track in the shape of a circular arc. The block is released from rest at a height H above the floor, as shown in Figure 1. The block slides along the track with negligible friction and leaves it at a height of 0.40m above the floor and a speed of 3.0m/s at a 30° angle, as shown in Figure 2. After the block leaves the track, what is the block's speed when it reaches the highest point of its motion?

2.6 m/s

A 1.5kg cart starts from rest and then accelerates at a constant rate of 2m/s² to the right for 5s. The displacement of the cart over this time interval is most nearly

25 m

A new planet is discovered that has twice the Earth's mass and twice the Earth's radius. On the surface of this new planet, a person who weighs 500 N on Earth would experience a gravitational force of

250 N

A student pushes a wall with a force of magnitude Fs-w. The wall exerts a force of magnitude Fw-s on the student. The student then pushes harder on the wall, exerting a force of magnitude 2Fs-w on the wall. The magnitude of the force that the wall then exerts on the student is Responses

2Fw-s

The free-body diagram shows the three forces exerted on an object. Each square in the grid is 1N by 1N. What is the magnitude of the vector sum of the forces exerted on the object?

2N

A hypothetical spherical planet of mass M and radius R is made of a uniform substance and has a gravitational field g at its surface. Suppose eight of these identical planets collide and combine into a new uniform, spherical planet. What will the gravitational field on the surface of this new planet be in terms of g?

2g

A box of mass m is initially at rest on a horizontal surface. The box is then pulled to the right and travels a distance d in time t with a constant acceleration. Which of the following is a correct expression for the average power delivered to the box during time t?

2md²/t³

A satellite of mass ms is in a circular orbit at a height h above the surface of Earth, which has a mass ME and a radius RE. What is the period of the satellite's orbit?

2pisqrt((RE+h)²/GME)

Car A is traveling to the right at a constant velocity vA. At time t=0, it passes Car B, which is at rest. At the same time (t=0), Car B begins to accelerate with a constant acceleration of magnitude aB, as shown in Figure 1. Car B has a velocity of vB when it reaches the same position as Car A at time t=tf, as shown in Figure 2. Which of the following, if any, is an expression for the time it takes for Car B to catch up to Car A?

2vA/aB

The system shown above is released from rest. If friction is negligible, the acceleration of the 4.0 kg block sliding on the table shown above is most nearly

3.3 m/s²

A constant force of 900 N pushes a 100 kg mass up the inclined plane shown above at a uniform speed of 4 m/s. The power developed by the 900 N force is most nearly

3600 W

A horizontal, uniform board of weight 125 N and length 4 m is supported by vertical chains at each end. A person weighing 500 N is sitting on the board. The tension in the right chain is 250 N. What is the tension in the left chain?

375 N

In Figure 1, a satellite of mass m is a distance D from the center of an asteroid of mass M. The satellite then fires its thrusters to move away from the asteroid and when it reaches a distance 2D from the center of the asteroid, its mass is m2, as shown in Figure 2. What is the change in the gravitational potential energy of the asteroid-satellite system between Figure 1 and Figure 2?

3GmM /4D

The left figure shows a block at rest on a rough inclined surface. The block is attached to a wall by a string of negligible mass. The vector sum of the forces is zero. The right figure shows the free-body diagram for the block. The string is cut and the vector sum of the forces on the block remains zero. Which of the following free-body diagrams could show the forces exerted on the block after the string is cut?

4 down, 2 left 2 up, 2 right 2 up (visual)

A car is driving east on a straight, level road with a speed of 20m/s when it begins to accelerate eastward at a constant rate. After 5s the car has a speed of 40m/s to the east. The acceleration of the car during the 5s time interval is

4 m/s²

In a lab, a block weighing 80 N is attached to a spring scale, and both are pulled to the right on a horizontal surface, as shown above. Friction between the block and the surface is negligible. What is the acceleration of the block when the scale reads 32 N?

4.0 m/s²

A child has a toy tied to the end of a string and whirls the toy at constant speed in a horizontal circular path of radius R. The toy completes each revolution of its motion in a time period T. What is the magnitude of the acceleration of the toy?

4pi²R/T²

An object of mass m travels in a horizontal circular path of radius r at constant speed. The object's period of revolution is T. What is the centripetal acceleration of the object?

4pi²r/T²

The diagram shows the directions and magnitudes of the forces exerted on a puck on a horizontal surface. What is the magnitude of the vector sum of the forces exerted on the puck?

5 N

An object is thrown with a horizontal velocity of 20 m/s from a cliff that is 125 m above level ground. If air resistance is negligible, the time that it takes the object to fall to the ground from the cliff is most nearly

5 s

The graph above represents position x versus time t for an object being acted on by a constant force. The average speed during the interval between 1 s and 2 s is most nearly

6 m/s

A car of mass 1300kg is traveling on a highway at a speed of 25m/s. The car passes a truck that is moving in the same direction at a speed of 15m/s. From the perspective of an observer in the truck, what is the kinetic energy of the car?

6.5 x 10⁴J

A rope of negligible mass supports a block that weighs 30 N, as shown above. The breaking strength of the rope is 50 N. The largest acceleration that can be given to the block by pulling up on it with the rope without breaking the rope is most nearly

6.7 m/s²

While traveling in its elliptical orbit around the Sun, Mars gains speed during the part of the orbit where it is getting closer to the Sun. Which of the following can be used to explain this gain in speed?

As Mars gets closer to the Sun, the Mars-Sun system loses potential energy and Mars gains kinetic energy.

A motor swings a ball on a string in a vertical circle such that the tension in the string is constant throughout the ball's motion. Which of the following correctly indicates at which point the ball has the greatest speed and provides a valid justification?

At the topmost point, because the tension force and gravitational force are both directed toward the center of the ball's motion.

A block is at rest in equilibrium on a vertical spring, as shown. Which of the following could correctly indicate the types of energy present in the block-spring-Earth system and in the block-spring system?

B

A satellite is in a circular orbit around Earth. In Scenario 1, the radius of the satellite's orbit is changed slightly such that the gravitational potential energy of the satellite-Earth system increases. In Scenario 2, the radius of the satellite's orbit is changed slightly such that the gravitational potential energy of the satellite-Earth system decreases. Which of the following correctly indicates how the radius of the satellite's orbit changes in each scenario?

B

Three vehicles pass each other traveling on a three-lane roadway. Vehicle A is moving west with speed vA relative to the road; Vehicle B is moving east with speed vB relative to the road; and Vehicle C is moving east with speed vC relative to the road. Assume east is the positive direction. What is the velocity of Vehicle B relative to observers in Vehicle A and in Vehicle C?

B

A block released from rest at position A slides with negligible friction down an inclined track, around a vertical loop, and then along a horizontal portion of the track, as shown above. The block never leaves the track. After the block is released, in which of the following sequences of positions is the speed of the block ordered from fastest to slowest?

B E C D

Why can the gravitational field strength g near Earth's surface be approximated as constant?

Because distance scales near Earth's surface are very small compared to Earth's radius.

A block is pushed up a ramp at a constant speed v. A second block of equal mass is pushed up a second, steeper ramp at the same constant speed v. Frictional forces between the blocks and the ramps are negligible. Why is the instantaneous power delivered to the block on the steeper ramp greater than the instantaneous power delivered to the block on the less steep ramp?

Because the component of gravity parallel to the ramp is greater on the steeper ramp

A rower performs four rowing trials on a lake. In each trial, the average force Favg that the rower exerts on the boat, the distance d the boat travels, and the elapsed time Δt are recorded. The data for each trial are in the table. During which trial is the greatest average power delivered to the boat?

C

A student slides a box across a level floor in a straight, horizontal path as shown in the picture. At time t1, the box is moving to the right at 1m/s. At time t2, the box is moving to the left at 1m/s. Which of the following correctly describes the speed and velocity at the times t1 and t2?

C

A vertical spring is at its unstretched length L0 when an egg is gently placed on the spring, as shown in Figure 1. The egg is then slowly lowered until it reaches equilibrium and remains at rest, as shown in Figure 2. Which of the following correctly describes the change in the gravitational potential energy ΔUg of the Earth-egg system and the change in the potential energy of the spring, ΔUs?

C

The motion of a particle along a straight line is represented by the position versus time graph above. At which of the labeled points on the graph is the magnitude of the acceleration of the particle greatest?

C

Because distance scales near Earth's surface are very small compared to Earth's radius.

C > B > A

A spring-loaded toy is launched straight upward from the surface of a table. In Case 1, the toy is caught at the instant that it reaches its highest point and held at rest. In Case 2, the toy is allowed to rise, then fall back to the table. In which case is the magnitude of the average velocity of the toy's free-fall motion the greatest?

Case 1, because the toy has a greater displacement

At the instant shown, a paper airplane is moving horizontally to the right. The air exerts two independent forces on the plane: an upward lift force with magnitude less than the plane's weight and a resistive drag force. Which of the following correctly describes the change in velocity, if any, of the plane in the horizontal and vertical directions at this instant?

D

During time interval Δt1, a car starts from rest and speeds up at a constant rate to the right until reaching a final velocity vf. Then, during time interval Δt2 the car slows down at a constant rate until it comes to rest. Which of the following correctly indicates whether the signs and directions of the car's acceleration during the two time intervals are the same or different?

D

A car is moving with constant speed v0 when a tree falls into the roadway at t=0. It takes the driver a time T to react and apply the brakes. The car then slows with a constant acceleration of magnitude a. Which of the following equations correctly expresses the distance D traveled by the car from time t=0 to the instant the car comes to rest?

D = v0T + v²0/2a

Students A and B are standing inside a train that is accelerating to the right with a magnitude of 2m/s². Student A throws a ball to the left toward Student B with a horizontal velocity of magnitude 4m/s relative to the train. At the instant the ball leaves Student A's hand, the speed of the train relative to the ground is 10m/s to the right. The ball takes 0.5 second to reach Student B. Immediately before the ball reaches Student B, the horizontal speed of the ball relative to the ground is

6m/s

A block of mass 2 kg slides along a horizontal tabletop. A horizontal applied force of 12 N and a vertical applied force of 15 N act on the block, as shown above. If the coefficient of kinetic friction between the block and the table is 0.2, the frictional force exerted on the block is most nearly

7 N

A block of mass m is hanging in equilibrium from a spring. The block stretches the spring to length L, as shown in Figure 1. The block is removed, and the spring returns to its unstretched length of 3L/4. If a larger block with mass 4m is hung from the spring and slowly lowered until it is in equilibrium, what will the new length of the spring be?

7L/4

A duck flies past a truck that is at rest. The duck takes 2.1 seconds to fly at constant speed vd from the back of the truck to the front. Later, the truck travels along a flat, straight roadway with a constant speed 3/4vd. The duck again flies past the truck with constant speed vd, flying in the same direction that the truck is moving. How long does it take the duck to fly from the back of the truck to the front in this case?

8.4 seconds

Two solid spheres of radius R made of the same type of steel are placed in contact, as shown in the figures above. The magnitude of the gravitational force that they exert on each other is F1. When two other solid spheres of radius 3R made of this steel are placed in contact, what is the magnitude of the gravitational force that they exert on each other?

81F1

An object of mass m=3.0kg is attached to one end of a string with negligible mass and length L=0.80m. The object is released from rest at time t=0, when the string is horizontal. At time t=t1 the object is at the location shown in the figure, where the string is vertical. Which of the following is most nearly the magnitude of the tension in the string at time t=t1?

90 N

A person is standing on a skateboard that is initially at rest, as shown. The person and the skateboard have a combined mass m. The person then exerts an average horizontal force of magnitude F on the skateboard over a distance Δx. The person and skateboard then travel up a ramp until they reach a flat section at height h with speed v. Frictional forces are negligible. Which of the following comparisons must be true?

FΔx> mgh

A satellite of mass m and speed v moves in a stable, circular orbit around a planet of mass M. What is the radius of the satellite's orbit?

GM/v²

Three objects can only move along a straight, level path. The graphs below show the position d of each of the objects plotted as a function of time t. (graphs) The sum of the forces on the object is zero in which of the cases?

I and II only

Three forces act on an object. If the object is in translational equilibrium, which of the following must be true? I. The vector sum of the three forces must equal zero II. The magnitudes of the three forces must be equal III. All three forces must be parallel.

I only

A planet of mass m orbits a star of mass M, where m<<M. The orbit is circular, its radius is r, and its period is T. True statements about the planet's orbit include which of the following? I. The orbital speed equals 2πr / T II. The gravitational force equals GMm / r² III. If the orbital radius r were greater, T would also be greater.

I, II and III

A bucket rests on top of a crate, which rests on a floor, as shown in the diagram. The bucket is lifted off the crate. How does the force due to microscopic interactions between the crate and the floor change, if at all, as the bucket is lifted off the crate?

It decreases.

A block released from rest at position A slides with negligible friction down an inclined track, around a vertical loop, and then along a horizontal portion of the track, as shown above. The block never leaves the track. Which of the following is true of the net force on the block when it is at position C ?

It has components both to the left and vertically downward.

A block of mass m hangs in equilibrium from an ideal spring inside an elevator, as shown. The elevator moves downward at a constant speed and the length of the spring is x1. The elevator then gradually slows to a stop with constant acceleration. Which of the following statements correctly describes the length of the spring while the elevator is decelerating?

It is constant and greater than x1.

Boxes A and B are made of the same material and are both at rest on the same rough incline. Box A has mass m and Box B has mass 2m. Which of the following claims about the magnitude of the force of static friction exerted on the boxes by the surface is correct?

It is greater for box B.

A puck is sliding with constant speed across a smooth, horizontal surface with negligible friction. The puck then reaches a rough, horizontal section with non-negligible friction. A student claims that the translational kinetic energy of the object will be increasing when it is sliding on the rough section. Which of the following correctly indicates whether the claim is correct and provides a valid justification?

It is not correct, because the frictional force accelerates the puck, causing its speed to decrease.

A skydiver with an open parachute falls toward the ground at a constant speed. Is the mechanical energy of the skydiver-Earth system constant as the skydiver descends? Why or why not?

No, because the potential energy of the system decreases, and the kinetic energy of the skydiver remains constant.

Two crates are at rest on a flat surface. A student exerts a continuous force of magnitude F on the first crate that causes the crate to accelerate over a distance d in time t. The second crate is accelerated by the same continuous force of magnitude F over the same distance d, but in half the time. The student claims that the same average power is delivered to both crates by the force. Is the claim correct? Why or why not?

No, because the time the force was applied to each crate is different.

Figure A and Figure B both show two velocity vectors. Let A→ and B→ be the vector sums of the velocity vectors in Figure A and Figure B, respectively. Are the speed and the velocity of A→ the same as the speed and velocity of B→?

No, because the vectors are in opposite directions, which means the velocities are different.

The forces exerted on an object at a particular instant are represented in the free-body diagram. The magnitude of each force is drawn to scale. A student claims that the vector sum of the forces on the object is equal to zero. Is the student's claim valid? Why or why not?

No, because the vertical components of the forces do not completely add to zero.

An astronaut jumps from the surface of the Moon and follows the path shown by the dashed line. At Point P, the astronaut is at the highest point in the path. Air resistance is negligible. Is the astronaut in equilibrium? Why or why not?

No, because there is a downward net force on the astronaut.

A block accelerates from rest until it reaches a maximum speed, and then stops accelerating. Which of the following statements about the net work done on the block are correct? Assume frictional forces are negligible.

Non-zero net work is being done on the block only when it is accelerating.

A ball is thrown straight up in the air. When the ball reaches its highest point, which of the following is true?

None of the above

A box is pulled to the right with constant speed across a rough horizontal surface. The box is subject to the four forces shown in the diagram: a tension force FT, a friction force Ff, a normal force FN, and a gravitational force Fg. Which of the following pair of these forces, if any, represents an interacting force pair described by Newton's third law?

None of the four forces are an interacting force pair because all four forces are exerted on the same object.

For which of the following motions of an object must the acceleration always be zero? I. Any motion in a straight line II. Simple harmonic motion III. Any motion in a circle

None of these motions guarantees zero acceleration.

Two objects, X and Y, accelerate from rest with the same constant acceleration. Object X accelerates for twice the time as object Y. Which of the following is true of these objects at the end of their respective periods of acceleration?

Object X has traveled four times as far as object Y.

Block A hangs from a light string that passes over a light pulley and is attached to block B, which is on a level horizontal frictionless table, as shown above. Students are to determine the mass of block B from the motion of the two-block system after it is released from rest. They plan to measure the time block A takes to reach the floor. The students must also take which of the following measurements to determine the mass of block B?

Only the mass of block A and the distance block A falls to reach the floor

At time t1, a train on a horizontal track has speed v and acceleration a. A short time later, time t2, the train has speed 2v and acceleration a. How does the instantaneous power P1 delivered to the train at time t1 compare to the instantaneous power P2 delivered to the train at time t2?

P1 < P2

Projectiles 1 and 2 are launched from level ground at the same time and follow the trajectories shown in the figure. Which one of the projectiles, if either, returns to the ground first, and why?

Projectile 2, because it will have a smaller initial vertical velocity.

The graphs above represent the position x, velocity v, and acceleration a as a function of time t for a marble moving in one dimension. Which of the following could describe the motion of the marble?

Rolling up a ramp and then rolling back down

Three wheels are arranged as shown in the diagram. Wheel B has radius R and period TB. Wheel A has radius 2R3, and Wheel C has a radius R4. The wheels turn each other without slipping. Which of the following correctly relates the period TA of Wheel A to the period TC of Wheel C?

TA= 8/3 TC

Two blocks, of mass m and 2m, are initially at rest on a horizontal frictionless surface. A force F is exerted individually on each block, as shown above. The graph shows how F varies with time t. Which block has the greatest average power provided to it between t = 0 s and t = 3 s?

The block of mass m

A car starts from position x=0 at time t=0 and drives along a straight track. The graph shows the position of the car as a function of t2. Which of the following statements correctly describes the motion of the car?

The car is speeding up at a constant rate, then continues to speed up but at a slower constant rate

A cart moves along a horizontal, one-dimensional track according to the position-time graph shown, where positive position values represent locations to the right of the origin. Which of the following statements correctly describe the cart's instantaneous velocity at time 5s?

The cart is moving left with speed 0.5cm/s.

Two stars in deep space are very far from any other objects. The two stars orbit the center of mass of the two-star system in circular orbits at constant speed. Which of the following claims is correct about the motion of the center of mass of the two-star system?

The center of mass does not accelerate.

Vectors M→ and N→ are parallel to the y-axis. Let a=|M→+N→| and b=|M→|+|N→|. A student claims that is possible that a<b. Which of the following indicates whether the claim is correct and provides a valid justification?

The claim is correct, because the vectors M→ and N→ could be in opposite directions.

A block is attached to a compressed, horizontal spring. A person is initially holding the block in place at position x=−A as shown in the figure. The person then slowly moves the block at a constant speed through position x=0, at which point the spring is at its relaxed length, and then to position x=+A. Which of the following correctly describes how the potential energy in the spring-block system changes as the block is moved from x=−A to x=+A?

The potential energy decreases and then increases

A puck slides freely across the horizontal surface of a frozen pond with negligible friction. Which of the following is true of the motion of the puck?

The puck will slide with a constant velocity.

The diagram shows the forces exerted on an object. Which of the following correctly indicates the direction of the change in the object's velocity, and provides a valid justification?

To the left only, because the vertical components of the forces are balanced, but the horizontal components are not balanced.

A hollow plastic ball hangs at rest from a string at an angle, as shown. There is a force on the ball from the string directed up and to the left, and a downward gravitational force. There is also a constant flow of air around the ball, and the vector sum of all the forces exerted on the ball is equal to zero. Which of the following statements correctly indicates a possible direction of the force exerted on the ball by the air, and provides a valid justification?

To the right, because it will balance the leftward component of the force from the string

A block is held at rest against a compressed spring at point A at the top of a frictionless track of height h, as shown above. The block is released, loses contact with the spring at point B, and slides along the track until it passes point C, also at height h. How do the potential energy U of the block-Earth system and the kinetic energy K of the block at point C compare with those at point A ?

Uc=Ua and Kc>Ka

One end of a rod of negligible mass is attached to a block and the other end is attached to a pivot. Initially, the block is held in place with the rod horizontal. The block is then released and swings down through its lowest point, as shown, before swinging back up again. Frictional forces are negligible. Which of the following statements correctly indicate the work done on the block while it is swinging down?

Work is done only by the gravitational force.

A student is riding on a bus that is traveling east at a constant speed. The student walks toward the front of the bus. A stationary observer outside the bus standing on the road claims that the student is moving faster than the bus. Is the claim correct? Why or why not?

Yes, because according to the stationary observer, the student's velocity is the velocity of the bus plus the velocity of the student relative to the bus.

A rowboat moving in a lake is accelerating at a constant rate towards the shore. An observer in another boat moving at a constant velocity measures the row boat's acceleration. A second observer, standing still on the shore, also measures the acceleration of the rowboat. Are the two accelerations measured by the two observers the same? Why or why not?

Yes, because both observers are in inertial reference frames.

One end of a string is held in place and the other end of the string is attached to a disk. The disk can be set in motion and travel in a circular path with constant speed along a horizontal surface. A force sensor with negligible mass is attached to the string, as shown in the figure. There is negligible friction between both the disk and force sensor and the surface. A student sketches the graph shown of the force measured by the force sensor for several values of the speed. Is the student's sketch accurate? Why or why not?

Yes, because centripetal force increases proportional to the square of the speed.

A cart is moving along a straight track and has velocity +0.5m/s and positive acceleration at time 1s. At time 3s, the cart reaches a maximum speed. At time 4s, the cart again has velocity +0.5m/s, but with negative acceleration. A student claims that the average acceleration of the cart between time 1s and 4s time is zero. Is the student's claim correct? Why or why not?

Yes, because the final velocity of the cart is equal to the initial velocity.

A student launches a marble of mass mA with initial speed vA at an angle θA above the horizontal, as shown in the diagram. The marble reaches a maximum height of hA above the tabletop. The student launches another marble with a mass 12mA at the same speed and angle as the first marble. Will the maximum height of the second marble be equal to hA? Why or why not?

Yes, because the initial vertical components of the velocity are the same for both marbles.

A person standing on an escalator is not moving relative to the escalator steps. The escalator steps are moving up and to the right at constant velocity. Let the force that the escalator step exerts on the person's feet be Ffeet and let the force that the person's feet exert on the escalator step be Fstep. Do these two forces have equal magnitude?

Yes, because the person and the step create an interacting force pair.

A person driving a car suddenly applies the brakes. The car takes 4 s to come to rest while traveling 20 m at constant acceleration. Can the speed of the car immediately before the brakes were applied be determined without first determining the car's acceleration?

Yes, by determining the average speed while braking and doubling it.

A steel ball supported by a stick rotates in a circle of radius r, as shown above. The direction of the net force acting on the ball when it is in the position shown is indicated by which of the following?

arrow towards the center of the circle (visual)

A student uses a force probe to exert varying forces on the ends of vertical springs A, B, and C. The student then sketches the magnitude of the applied force as a function of the length of the spring for each spring, as shown. Which of the following correctly compares the spring constants k of each spring?

kA > kB > kC

A compressed spring mounted on a disk can project a small ball. When the disk is not rotating, as shown in the top view above, the ball moves radially outward. The disk then rotates in a counterclockwise direction as seen from above, and the ball is projected outward at the instant the disk is in the position shown above. Which of the following best shows the subsequent path of the ball relative to the ground?

line towards 2oclock (visual)

A person of mass m is standing on a scale in an elevator that is accelerating downward with an acceleration of magnitude a. Which of the following is a correct expression for the normal force exerted on the person by the scale?

m(g-a)

A rock of mass m slides toward a ramp and has speed v0 when it reaches the bottom of the ramp, which is at an angle θ to the horizontal, as shown. The coefficient of kinetic friction between the rock and the ramp is μk. The rock slides a distance d up the hill before stopping at a vertical distance h above the bottom of the ramp. Which of the following expressions is equal to the force of friction exerted on the rock?

m(v²0-2gh) / 2d

Blocks A and B, of masses mA and mB, respectively, are at rest on a horizontal surface with negligible friction. Block A is attached to the table. Block C of mass mC is suspended by a string that is tied to Block B and passes over a pulley as shown. The blocks all remain at rest. Which of the following gives the magnitude of the force exerted by Block A on Block B?

mcg

A horizontal force is exerted on a block of mass m, initially at rest, causing the block to accelerate at a constant rate across a rough horizontal surface. Friction forces are negligible. After time t, the block has speed v and has traveled a distance x. Which of the following is a correct expression for the average power delivered to the block during the time t?

mv²/2t

A solid metal ball and a hollow plastic ball of the same external radius are released from rest in a large vacuum chamber. When each has fallen 1 m, they both have the same

speed

A skydiver is falling through the air attached to a parachute. The mass of the skydiver-parachute system is m. The upward force of air resistance exerted on the system is given by the equation Fair=Av2, where A is a constant that depends on the shape of the parachute and v is the speed of the system. After falling a short time, the system reaches a constant speed vT. Which of the following is a correct expression for vT?

sqrt(mg/A)

A projectile is launched horizontally off a cliff of known height h with speed v0 and reaches the ground a time t after being launched. Another identical projectile is launched horizontally off the same cliff with speed 2v0. How long does it take the second projectile to reach the ground?

t

A vertical spring is attached to the floor, as shown in Figure 1. An object of mass m1 is placed on top of the spring and slowly lowered, compressing the spring a distance x1 from its unstretched length, until it reaches equilibrium, as shown in Figure 2. Next, an object of mass m2 is placed on top of the first object and slowly lowered, compressing the spring an additional distance x2. The system is again in equilibrium in Figure 3. Which of the following correctly relates x2 to x1?

x2= m2/m1 x1

At time t=0, a car is moving in the positive direction along a straight road. The graph represents the car's velocity v as a function of time t. The car's position at t=0 is x=0. The position of the car at times 1s, 2s, is 3s are x1, x2, and x3, respectively. Which of the following correctly ranks x1, x2, and x3 from greatest to least?

x3 > x2 > x1

Planet 1 of mass M1 is located at position x=0. Planet 2 of mass M2 is located at position x=L. Which of the following equations correctly indicates the position xeq along the x-axis where an object could be placed and experience no acceleration?

xeq=(√m1/√m1 + √m2) L

A rope pulls a block of mass 2m to the right along a horizontal surface, as shown in the left figure. The block of mass 2m exerts a force on a block of mass m with magnitude F2m,m that varies with time, as shown in the graph on the right. The blocks remain in contact during the time interval shown in the graph. Which of the following correctly shows the magnitude Fm,2m of the force that the block of mass m exerts on the block of mass 2m during the same interval?

y goes from 1-3 (visual)

Sphere 1 and Sphere 2 are both initially touching the ceiling and are then lowered until they are resting on the floor, as shown. Both spheres have mass M, but Sphere 2 has a larger radius than Sphere 1. Which of the following correctly compares the magnitudes of the changes in the gravitational potential energies, |ΔU1| and |ΔU2|, of the sphere-Earth systems for each sphere when they are lowered from the ceiling to the floor?

|ΔU1|>|ΔU2|

Figure 1 shows the power P1 delivered to an object over the time interval indicated which results in change in energy ΔE1. Figure 2 shows the power P2 delivered to an identical object over the same time interval which results in change in energy ΔE2. Which of the following correctly compares ΔE1 to ΔE2, and provides a valid justification?

ΔE1=ΔE2, because the area bounded by the function and the horizontal axis is the same in both graphs

An asteroid is moving directly toward a planet, as shown in Figure 1. At a later time, as shown in Figure 2, the asteroid is closer to the planet and still moving directly toward it. The change to the planet's velocity is negligible. Which of the following correctly describe the change in the total mechanical energy of the asteroid-planet system, ΔEtot, and the change in the kinetic energy of the asteroid, ΔK, between Figure 1 and Figure 2?

ΔEtot=0; ΔK >0

A constant force F0 is exerted continuously on a block that is initially at rest on a horizontal surface. The change in kinetic energy of the block while the block is moved from position x=0 to x=50cm is ΔK1, and the change in kinetic energy of the block as the block is moved from x=50cm to x=100cm is ΔK2. How does ΔK1 compare to ΔK2, and why?

ΔK2=ΔK1 because the applied force does the same work on the block between 0cm to 50cm and between 50cm to 100cm.

At time t1, a car is traveling to the west with speed v. At time t2, the car is traveling to the east with speed v. Which of the following correctly indicates the change in the kinetic energy ΔK of the car between times t1 and t2, and provides a valid justification?

ΔK=0, because the mass and the speed of the car are the same at t1 and t2.

A block is pressed against a horizontal spring, compressing the spring, as shown at the top of the figure. The block is then moved, compressing the spring a distance d, which changes the potential energy in the spring by an amount ΔU1. The spring is then compressed an additional distance d, which then changes the potential energy in the spring by an amount ΔU2. Which of the following, if any, correctly compares ΔU2 to ΔU1?

ΔU2> ΔU1

An object is dropped from a tall building at time t=0s and reaches the ground at t=10s. Which of the following correctly compares the distance Δx0−2 traveled by the object between t=0s and t=2s, the distance Δx4−6 traveled between t=4s and t=6s, and the distance Δx8-10 traveled between t=8s and t=10s?

Δx8-10 > Δx 4-6 > Δx0-2

In scenarios A, B, and C, shown in the figure, blocks with the masses indicated are attached to identical vertical springs. The block in each scenario is slowly lowered until it reaches equilibrium. Which of the following correctly ranks the distances ΔxA,ΔxB, and ΔxC that each block is lowered?

Δxc > (ΔxA=ΔxB)

The water in a river moves uniformly to the east with speed vr, as shown. A boat on the river starts from the south edge of the river and the boat's motor gives the boat a constant speed of vb to the north relative to the water. The width of the river is w. When the boat reaches the north edge of the river, it has an eastward displacement of Δx relative to its starting position. Which of the following expressions is equal to vr?

Δxvb/w

A cart rolls along a track that is inclined at an angle of 37° to the horizontal, as shown. At the moment shown, there are three forces exerted on the cart: a downward force of magnitude 50N, a drag force of magnitude 20N, and a normal force from the track of magnitude 40N, as shown in the free-body diagram. The magnitude of the vector sum of the forces on the cart is most nearly

10 N

An object has a weight W when it is on the surface of a planet of radius R. What will be the gravitational force on the object after it has been moved to a distance of 4R from the center of the planet?

1/16 W

A block of mass m is attached to a horizontal spring, as shown, and is free to move on a horizontal surface at a height h above the ground. Friction between the block and the surface is negligible. The block is initially held at rest at position x=−A with the spring compressed. The block is released, and it moves to the right, passing position x=0, at which point the spring is at its unstretched length, with speed v0. The block then momentarily comes to rest at position x=+A. Which of the following is a correct expression for the total mechanical energy of the system consisting of only the spring and the block after the block is released?

1/2 kA²

A rock of mass m is thrown horizontally off a building from a height h, as shown above. The speed of the rock as it leaves the thrower's hand at the edge of the building is vo What is the kinetic energy of the rock just before it hits the ground?

1/2 mv²0 + mgh

The graph shows the position as a function of time for an object of mass 5kg moving in one dimension. The kinetic energy of the object at 5 s is most nearly

10 J

Block A is initially held at rest on a horizontal table and is connected to a horizontal ideal spring that is fixed to a wall. The spring is initially at its relaxed length. Block A is connected to Block B by a string passing over a pulley, as shown. There is friction between Block A and the table. When Block A is released, Block B moves downward, and Block A moves to the right along the surface of the table until the system returns to rest. How do the mechanical energies of the two-block - spring system and the two-block -spring - Earth system change from when Block A is held at rest to when the blocks return to rest?

A

Vectors A and B are parallel to x-axis. Vector C is defined to be the vector sum of A and B, or C = A + B. Vector C has the same direction as vector B and the magnitudes of B and C are related by B > C. Which of the following claims is correct about the relative directions and magnitudes of vectors A and B?

A < B and the vectors have opposite directions.

A cart is constrained to move along a straight line. A varying net force along the direction of motion is exerted on the cart. The cart's velocity v as a function of time t is shown in the graph above. The five labeled points divide the graph into four sections. For which segment does the cart move the greatest distance?

AB

An object of mass m is initially at rest and free to move without friction in any direction in the xy-plane. A constant net force of magnitude F directed in the +x direction acts on the object for 1 s. Immediately thereafter a constant net force of the same magnitude F directed in the +y direction acts on the object for 1 s. After this, no forces act on the object. Which of the following vectors could represent the velocity of the object at the end of 3 s, assuming the scales on the x and y axes are equal?

C, tip is at est. (1.3, 1.3)

Cars A, B, C, and D are moving along a straight track. The table indicates their velocities and accelerations at the same instant. Which car has the acceleration with the greatest magnitude?

Car C

Three carts are free to move left or right on a horizontal track. Each cart experiences a constant acceleration. The initial and final velocities of each cart are indicted in the table. Which cart, if any, has a leftward acceleration?

Cart 1

A cart equipped with a launcher launches a dart horizontally, as shown. The dart is always given the same horizontal velocity vdart relative to the cart. In Trial 1, the cart is at rest at Point P a distance D from a target and launches the dart toward the target. The dart takes a time t1 to reach the target. In Trial 2, the cart is moving toward the target with constant speed vcart and launches the dart at the instant the cart is at Point P. The dart takes a time t2 to reach the target. The cart has a negligible change in speed during the launch. Which of the following is a correct expression for the cart's speed vcart?

D/t2 - D/t1

A block is released from rest at the top of a rough ramp. There is significant friction between the block and the ramp, but the block's speed increases as the block slides down the ramp. Which of the following correctly indicates whether the total mechanical energy of the block-Earth system decreases or remains the same, and provides a valid justification?

Decreases, because a force external to the system is dissipating energy

A cart starts from rest and moves to the right along a flat surface. The velocity of the cart as a function of time is represented in the graph. Which of the following quantities are the same for both segment A and segment B of the graph?

Displacement

A person exerts an upward force on a box, as shown above. The box may be moving upward, downward, or not at all while the person exerts the upward force. For which of the following motions of the box is the work done by the person on the box correctly indicated?

Downward with increasing speed and Negative

At time t0, a block is held at rest against a compressed horizontal spring, as shown. The total mechanical energy of the block-spring-Earth system is E0. The block is then released, slides down the track, and is traveling on a flat section of the track at time t1. The total mechanical energy of the block-spring-Earth system at time t1 is E1. Friction between the block and the track is negligible. Which of the following is true of E1 and E0?

E1=E0

A block is attached to one end of a horizontal ideal spring whose other end is attached to a wall. The spring is initially unstretched and its right end is at position x=0. The block is then pulled until it is at a position x=+A, as shown in Figure 1, where the spring exerts a force of magnitude F on the block. The spring is then moved to a position x=-A, as shown in Figure 2. Which of the following correctly indicates the magnitude and direction of the force the spring exerts on the block in Figure 2?

F to the right

A small car with mass m and speed 2v and a large car with mass 2m and speed v both travel the same circular section of an unbanked road. If the frictional force required to keep the small car on the road without skidding is F, then the frictional force required to keep the large car on the road without skidding is

F/2

An object is moving in the positive x-direction while a net force directed along the x-axis is exerted on the object. The figure above shows the force as a function of position. What is the net work done on the object over the distance shown?

F0d

A box moves with constant speed to the right along a horizontal surface with negligible friction. Two forces, with magnitudes F1 and F2, are exerted on the box at angles θ1 and θ2, respectively, as shown. Which of the following is a correct expression for F1 in terms of F2?

F1=F2(sinθ2/cosθ1)

A block of mass m slides between two rough plates as it moves downward without stopping. The sides of the block stay in contact with the plates throughout its motion and the plates exert constant normal forces on the block. In Figure 1, the block has half its length between the plates, and the left plate exerts a force F1 on it. In Figure 2, the block is entirely between the plates, and the left plate exerts a force F2 on it. In Figure 3, half of the block's length has exited the plates, and the left plate exerts a force F3 on it. Which of the following correctly compares the forces F1, F2, and F3?

F1=F2=F3

Two satellites are in circular orbits around Earth. Satellite 1 has mass m0 and an orbital radius of 2RE, where RE is the radius of Earth. Satellite 2 has mass 2m0 and an orbital radius of 3RE. Which of the following correctly compares the magnitude F of the force exerted by Earth on each satellite and the speed v of each satellite? Responses

F1>F2 and v1>v2

Elevator A is moving upward at a constant speed of 4m/s and Elevator B is moving downward at a constant speed of 2m/s. In each elevator, a 10kg object is on a scale. The scale in Elevator A reads FA and the scale in Elevator B reads FB. Which of the following correctly compares FA and FB, and provides a valid justification?

FA=FB because both elevators are traveling with a constant speed.

An object is subject to multiple forces that result in the object having horizontal and vertical velocity components vx and vy, respectively as a function of time, as shown. Which of the following diagrams could represent the forces exerted on the object?

FBD 3 +y ,2 +x ,4-y2-x

A delivery drone of mass Md carries a physics textbook of mass Mtb. At the instant shown, the drone has an upward acceleration. The normal force exerted on the textbook is FN. Which of the following is a correct expression for the magnitude of the acceleration of the drone?

FN/Mtb -g

A box of mass M slides along a horizontal surface. The forces exerted on the box are indicated in the figure. There is negligible friction between the box and the horizontal surface. Which of the following expressions is equal to the magnitude of the acceleration of the box?

FT(1-cosθ) / M

A string of negligible mass is attached to a box of mass m. With the string taut, the box sits at rest on top of a scale, as shown. The scale has a force reading of FN. Which of the following must be a correct equation for the magnitude FT of the tension in the string?

FT= mg- FN

A rope is attached to two heavy chain links that are connected to each other, as shown. The rope is pulling the chain links up at a constant speed. The top chain link exerts a force of magnitude FTB on the bottom link, and the bottom link exerts a force of magnitude FBT on the top link. Which of the following correctly compares FTB and FBT and provides a valid justification?

FTB=FBT, because the chain links are an interacting Newton's third law pair.

A motor-powered conveyor belt exerts a horizontal force F on a box of mass m, as shown. The conveyor belt moves the box a distance d in a time t. Which expression is equal to the power delivered to the box?

Fd/t

A heavy, uniform rope hangs from a ceiling and is not long enough to touch the floor. Which of the following best compares the magnitude of the tension force in the middle of the rope, Fmid, to the magnitude of the tension at the top of the rope near the ceiling, Ftop?

Fmid= Ftop/2

The figures above show a small block of mass 0.20kg on a track in the shape of a circular arc. The block is released from rest at a height H above the floor, as shown in Figure 1. The block slides along the track with negligible friction and leaves it at a height of 0.40m above the floor and a speed of 3.0m/s at a 30° angle, as shown in Figure 2. The magnitude of the gravitational force exerted on the block is Fg, and the magnitude of the normal force exerted by the track on the block is Fn. Which of the following correctly compares the magnitudes of these two forces when the block is at the lowest point on the track?

Fn > Fg

A box is given a sudden push up a ramp. Friction between the box and the ramp is not negligible. Which of the following diagrams best represents the directions of the actual forces acting on the box as it moves upward after the push?

Fn, mg , Fk (up down left visual)

At the instant shown in the figure, Cart A is moving to the right with speed v, Cart B is at rest, and Cart C is moving to the left with speed v. The kinetic energy of Cart A relative to Cart B is KAB and the kinetic energy of Cart A relative to Cart C is KAC. All three carts have the same mass. Which of the following correctly compares KAB and KAC, and provides a valid justification?

KAB<KAC, because the speed of Cart A relative to Cart B is less than the speed of Cart A relative to Cart C.

A cart begins to move from rest on a horizontal track. The acceleration of the cart as a function of time is shown in the graph. Which of the following correctly indicates the magnitude of the average velocity of the cart during the interval shown, and provides a valid explanation?

Less than 2m/s because the cart is traveling at a speed of 2m/s or less during the time interval.

At time t=0, a car is traveling on a straight, level road and the driver begins to apply the brakes. The car slows down and eventually stops at time ts. The magnitude of the acceleration of the car as a function of time is equal to Ct, where C is a positive constant. Which of the following graphs could represent the magnitude Fnet of the net force on the car as a function of time?

Linear graph starts from 0 (visual)

On the surface of Earth, a spacecraft has weight Fg,E. The mass and radius of Earth are ME and RE, respectively. The spacecraft lands on a distant planet, and its weight on the surface of the planet is Fg,E/4. Which of the following are possible combinations of mass and radius of the distant planet?

ME and 2RE

A cart is moving along a horizontal circular track. At the instant shown, the cart is moving to the right and its speed is increasing. A student claims that the net force on the cart is directed toward the center of the track. Is the claim correct? Why or why not?

No, because the cart has both a tangential acceleration parallel to the track and a centripetal acceleration perpendicular to the track.

A force of static friction is exerted on an object and is directed to the right. Which of the following statements about the direction of the object's acceleration is true?

There is not enough information to make a claim about the direction of the object's acceleration.

A person of mass 90kg stands on a scale in an elevator. The scale reads 1100N. Which of the following is a correct claim about the direction of the elevator's motion?

The elevator could possibly be moving downward and slowing down

In Figure 1, a force of magnitude F is exerted horizontally on a box resting on a rough, horizontal surface. A force exerted horizontally with a magnitude greater than F will cause the box to slide. In Figure 2, the force F is removed and a force of magnitude F/2 is then exerted on the same box. Which of the following statements about the box in Figure 2 must be true?

The force of static friction on the box will be equal to F/2.

An object is released from rest near the surface of Earth. Initially, the object accelerates as it begins to fall towards the Earth's surface. Earth's atmosphere exerts a resistive force on the object, and it reaches a terminal velocity before landing. Which of the following claims about the gravitational potential energy of the object-Earth system is true?

The gravitational potential energy decreases both during the initial acceleration period and as the object falls at terminal velocity.

A projectile is moving vertically in the +y-direction, with acceleration in the -y-direction. Which of the following correctly describes the kinetic energy of the projectile?

The kinetic energy is decreasing.

Two people are throwing a ball back and forth. At the instant shown in the figure, Person A is not moving relative to the ground, the ball is moving horizontally to the right, and Person B is running to the left. Which of the following claims about the kinetic energy of the ball is correct?

The kinetic energy of the ball relative to Person A is less than the kinetic energy of the ball relative to Person B.

A hammer drives a nail into a piece of wood that is at rest. At the instant shown, the hammer is in contact with the nail and the nail is accelerating downward. Which of the following claims correctly compares the magnitudes of the forces between the hammer, nail, and wood at this instant?

The magnitude of the force that the hammer exerts on the nail is equal to the magnitude of the force that the nail exerts on the hammer.

A block slides to the right across a rough horizontal surface. Which of the following correctly indicates whether the mechanical energy of the block-Earth system decreases or stays the same as the block slides, and provides a valid justification?

The mechanical energy decreases because energy is dissipated by the external force of friction.

An object attached to one end of a string moves in a circle at constant speed. Which of the following is correct?

The object is accelerating as it moves.

At time t=0, an object moving along the x-axis is initially moving in the +x-direction with a speed of 1.0m/s. The object's velocity is measured in one-second intervals and recorded in the table. Which of the following claims best describes the kinetic energy of the object?

The object's kinetic energy decreases, then increases.

Water in a river flows uniformly to the east with a speed of 5m/s relative to the shore. A boat is traveling to the west at 10m/s relative to the water. A passenger on the boat is walking at 5m/s to the east, toward the back of the boat. Which of the following statements about the passenger's velocity is correct and gives the correct reason?

The passenger is stationary relative to the shore because the boat is moving at 5m/s relative to the shore and the passenger is moving at 5m/s relative to the boat in the opposite direction.

A student has a calibrated spring scale that measures force with a precision of ±0.05N. At sea level, the student holds the scale vertically with a 100g object attached to it, and the scale reads 1.00N. The student then brings the scale and the object to the top of a 1000m high mountain and again holds the scale vertically with the 100g object attached. Which of the following correctly describes the scale's reading, and provides valid justification for the claim?

The scale reading is between 0.95N and 1.05N, because the height of the mountain is negligible compared to the radius of the earth.

A cart is constrained to move along a straight line. A varying net force along the direction of motion is exerted on the cart. The cart's velocity v as a function of time t is shown in the graph above. The five labeled points divide the graph into four sections. During some part of the motion, the work done on the cart is negative. What feature of the motion indicates this?

The speed is decreasing.

A block is released from rest and slides down a ramp. The surface of the ramp has three rough sections where the friction between the surface and the block is not negligible, as shown by the shaded regions above. Measuring which of the following will allow for the best estimate of the block's instantaneous acceleration when the block is at the midpoint of the ramp?

The speed of the block at points just before and just after the midpoint and the time it takes the block to travel between them

Two identical crates are connected by heavy strings with non-negligible mass, as shown in the diagram. An upward force is applied to String 1 which causes the blocks-strings system to accelerate upward at a constant acceleration. Which claim is true concerning the tension in String 2?

The tension in String 2 is greatest where it connects to the upper block because it has to support the weight of the string and Block 2.

A person holds a string that is attached to a box. The person allows the box to move straight downward at a constant speed v, as shown. The weight of the box is 5N. Which of the following claims about the tension in the string is correct?

The tension must be equal to 5 N.

Two boxes of unequal mass are pulled upward at a constant speed by String 1, as shown. Box 1 and Box 2 are connected by String 2. Both String 1 and String 2 are ideal strings. Which of the following correctly describes the tension in String 2 at Point A and Point B ?

The tensions at Point A and Point B are equal.

An athlete sprints back and forth along a straight track. The athlete starts at a position of 0m, and the athlete's average speed and final position are shown in the table for five successive time intervals. Assume the athlete has a constant speed during each interval and quickly changes direction during the transitions between intervals. During which transition does the athlete's change in velocity have the greatest magnitude?

The transition between intervals B and C.

The graph shows the position x of an object as a function of time t as it moves along the x-axis. Which of the following claims about the motion of the object during the time interval shown is correct?

The velocity and acceleration are both in the -x-direction

Two applied forces are exerted on a box that slides along a flat surface with negligible friction. The force on the right is at an angle θ to the horizontal, as shown. The box is initially moving to the right at a constant velocity. The angle θ is then slowly decreased, but the magnitudes of the applied forces remain constant. Which of the following correctly describes the motion of the box as the angle is decreased?

The velocity of the box changes because the sum of the horizontal components of the forces no longer equals zero.

A platform of mass m is held at rest by two ropes connected to its ends, as shown in the diagram on the left. A block, also of mass m, is placed on the center of the platform. A student draws a free-body diagram representing the forces exerted on the platform while it is at rest, as shown in the diagram on the right. Which of the following claims best explains why the diagram is incorrect?

The vertical forces are unbalanced.

A weight is attached to a vertical spring that is fixed to a ceiling. The weight is held at rest at Point A and then released. The weight falls downward, reaches its lowest position at Point C, and then begins to move upward. The weight then bounces up and down several times and then eventually comes to rest at Point B. Which of the following statements about the motion of the weight must be true whenever the weight is between points B and C?

The weight's acceleration is upward.

A system consists of two identical blocks connected by a rod of negligible mass. At the instant shown, the velocity of the center of mass is zero and the system has a nonzero acceleration to the right. Which of the following statements must be true?

There is a net force exerted on the system directed to the right.

A block hangs at rest from a spring, stretching the spring to length L, as shown in the left figure. The block is then completely submerged in a tank of water and comes to rest, as shown in the right figure. It is observed that, with the block in the water, the spring's length is less than L. Which of the following correctly indicates why the spring's length decreases when the block is submerged?

There is an additional force exerted on the block.

The graphs represent the speed of a ball thrown downward as a function of time near the surface of two planets. Which of the following correctly relates the acceleration a1 of the ball near the surface of Planet 1 and the acceleration a2 of the ball near the surface of Planet 2?

a1 > a2 > 0

Crate 1 of mass m1 is connected to Crate 2 of mass m2 by a string with negligible mass. The crates are on a rough, horizontal surface. Crate 2 is pulled to the right with constant acceleration by a force of constant magnitude F. Crate 1 experiences a friction force f1 and Crate 2 experiences a friction force f2, both of which are less than F. After a short period of time, the string breaks. The force F continues to be exerted on Crate 2. Which of the following are correct expressions for the magnitude a1 of the acceleration of Crate 1 and the magnitude acm of the acceleration of the two-crate system's center of mass after the string breaks?

a1=f1/m1 and acm= (F-f1-f2)/ m1+m2

A cart is constrained to move along a straight line. A varying net force along the direction of motion is exerted on the cart. The cart's velocity v as a function of time t is shown in the graph above. The five labeled points divide the graph into four sections. Which of the following correctly ranks the magnitude of the average acceleration of the cart during the four sections of the graph?

aCD > aAB > aDE > aBC

In which of the following free-body diagrams is the magnitude of the vector sum of the forces the greatest?

all arrows point right (visual)

A person throws a marble straight up into the air, releasing it a short height above the ground and catching it at that same height. If air resistance is negligible, which of the following graphs of position y versus time t is correct for the motion of the marble as it goes up and then comes down?

bell shaped graph (visual)

Balls 1 and 2 are each thrown horizontally from the same height above level ground, but ball 2 has a greater initial velocity after leaving the thrower's hand. If air resistance is negligible, how do the accelerations of the balls and the times it takes them to hit the ground compare?

both equal

In Scenario 1, a block of mass m slides across a rough floor with initial speed v. The block slides a distance d1 before coming to rest. In Scenario 2, a block of mass 2m, made of the same material as the block in Scenario 1, slides across the same rough floor with the same initial speed v. The block slides a distance d2 before coming to rest. How do d1 and d2 compare?

d1=d2

An object if thrown with an initial speed v near the surface of Earth. Assume that air resistance is negligible and the gravitational field is constant. If the object is thrown vertically upward, the direction and magnitude of its acceleration while it is in the air is

downward and constant

An object is thrown with an initial speed v near the surface of Earth. Assume that air resistance is negligible and the gravitational field is constant. If the object is thrown horizontally, the direction and magnitude of its acceleration while it is in the air is

downward and constant

In an experiment, a horizontal force is exerted on a cart as it moves along a straight, horizontal track with negligible friction. Several trials are performed, and in each trial the total work done on the cart is the same, but the magnitude F of the applied force and the distance d that the cart is pushed are varied. Which of the following graphs best represents how F depends on d?

exponential decay graph (visual)

A sled slides along a vertical circular track of radius r, as shown. There is negligible friction between the sled and the track. At the bottommost point of the track, the sled has speed vb. Which of the following graphs best show the normal force exerted by the track on the sled at the bottommost point of the track as a function of vb?

exponential graph that starts above 0 (visual)

In Trial 1, a sphere is projected horizontally from an initial height L and travels horizontally a distance L before reaching the floor. The sphere's initial velocity for this trial is v1 and the time required for the sphere to reach the floor is t1. In Trial 2, the sphere is projected horizontally from an initial height 2L and travels horizontally a distance 2L before reaching the floor. The sphere's initial velocity for this trial is v2 and the time required for the sphere to reach the floor is t2. Which of the following pairs of equations correctly relates t2 and v2 to t1 and v1?

t2=√2t1 and v2=√2v1

A projectile is launched from level ground with initial velocity v0, at an angle θ above horizontal. Which of the following is an expression for the total time the projectile is in the air?

t= (2v0sinθ)/g

A spacecraft in deep space fires its thruster, which ejects fuel from the spacecraft. The ejected fuel exerts a constant force on the spacecraft and the total mass of the spacecraft decreases at a constant rate. Which of the following graphs best represents the acceleration of the spacecraft as a function of time while the thruster is firing?

the only positive graph (visual)

A satellite orbits Earth in a circle of radius R with speed v. The satellite is then moved into a new circular orbit with radius 3R. What tangential speed must the satellite have in order to maintain the new orbit?

v/√3

A cart moves along a straight, level track. At time t=0s, the cart has a speed of v0 to the right. At time t=1s, the cart has a speed of v1 to the left. Which of the following correctly describes the magnitude and direction of the change Δv→ in the cart's velocity between t=0s and t=1s?

v1 + v0 to the left

Two cars pass by each other on a straight road. Car 1 has a speed v0 to the right and Car 2 has the same speed to the left. Immediately after passing each other, both cars experience a constant acceleration a0 directed to the left. At the instant Car 1 comes to rest, what is the speed v2 of Car 2?

v2 = 2v0

A ball is projected horizontally with initial speed v0 from a platform of height h on Earth. The ball's speed immediately before touching the ground is ve. The experiment is repeated on the Moon so that the ball is projected horizontally with the same speed from the same height. The acceleration due to gravity is less on the Moon than on the Earth. The ball's speed just before touching the ground is vm. Which speed is greater, and why?

ve, because the ball on the Moon achieves a smaller vertical component of velocity before reaching the ground

The graph shows the vertical position as a function of time for an object launched from the ground. Which of the following graphs correctly shows the vertical position of the object as a function of time if the object was launched at the same angle but with twice the initial speed?

vertex y value is approx 120 (visual)

A plane flies horizontally with constant speed vp−g relative to the ground. While in flight, the plane ejects exhaust in the opposite direction at a speed ve−p relative to the plane. Which expression correctly represents the velocity of the exhaust relative to the ground?

vp-g - ve-p

A penny of mass m is revolving at the edge of a spinning turntable of radius r, as shown. The penny has a constant tangential speed v, which is the maximum speed the penny can have without slipping. Which of the following is a correct expression for the coefficient of static friction, μs, between the penny and the turntable?

v²/rg

A nail is placed upside-down on a board, as shown. The coefficients of static and kinetic friction between the nail and the board are μs and μk, respectively. The left end of the board is slowly raised so that the board's angle θ with the horizontal increases. As soon as the nail begins to slide down the board without tipping over, the board is held in place at that angle. The nail continues to slide down the board with constant velocity. Which of the following can be concluded about μs and μk based on these observations?

μk is nearly equal to μs

A ball is projected horizontally from a table with height H above the ground. The ball lands after a time t1, hitting the ground a horizontal distance D away from the edge of the table, as shown. Which of the following is a correct expression for the instantaneous speed of the ball immediately before it reaches the ground?

√(D/t1)²+(gt1)²

A rocket lifts a payload upward from the surface of Earth. The radius of Earth is R, and the weight of the payload on the surface of Earth is W. The force of Earth's gravity on the payload is W/2 when the rocket's distance from the center of Earth is

√2R

A rock of mass m is thrown horizontally off a building from a height h, as shown above. The speed of the rock as it leaves the thrower's hand at the edge of the building is vo How much time does it take the rock to travel from the edge of the building to the ground?

√2h/g

A force of magnitude F is exerted on a block along a horizontal surface over a distance d, doing work W1. The force is exerted at an angle of 30° above horizontal and there is negligible friction between the block and the surface. Another force of magnitude F pushes an identical block along the same surface over a distance d, but the force is exerted at an angle of 60° above the horizontal. This second force does work W2. What is the ratio W1:W2?

√3 : 1

A sled is traveling with speed vi along flat ground when it reaches a hill. The sled moves up the hill to a flat section of height h where it has speed vf, as shown. Friction between the sled and the ground is negligible. What is the sled's final speed vf?

√v²-2gh