practice ap physics exams
20. A system consists of two objects having masses m₁ and m₂ where m₁ < m₂. The objects are connected by a massless string, hung over a pulley as shown, and then released. When the object of mass m₂ has descended a distance h, the potential energy of the system has decreased by
(m₂ - m₁)gh
25. A 1.0 kg block is attached to an unstretched spring of spring constant 50 N/m and released from rest from the position shown in Figure 1 below. The block oscillates for a while and eventually stops moving 0.20 m above its starting point, as shown in Figure 2. What is the change in potential energy of the block-spring-Earth system between Figure 1 and Figure 2 ?
-1.0 J
29. A man carries a 10 kg crate across a 15 m room at a constant speed. How much total work is done by the man on the box?
0 J
3. Two cars are attached by a chain. Each car pulls with a force of 1000 N. The tension in the chain is: 1/1
1000 N
44. A ball of mass m is initially rolling across a level surface at velocity v when it hits a wall and bounces off, rolling v/2 in the opposite direction. What is the impulse applied to the ball?
3mv/2
A super bouncy ball is dropped from 1 m from the ground, it bounces off the floor and reaches a new height of 0.75 m, at which of the indicated moments will the ball have the greatest speed?
B
35. Two astronauts are connected by a taut cable and are initially at rest with respect to a nearby space station. Astronaut X throws a large container to Astronaut Y. Figure 1 below shows the astronauts immediately after the container is thrown by Astronaut X, and Figure 2 shows the astronauts immediately after the container is caught by Astronaut Y. Which of the following describes the location of the center of mass of the Astronauts-cable-container system in Figure 2 compared to Figure 1?
Does not move
16. An elevator carrying a person of mass m is moving upward and slowing down. How does the magnitude F of the force exerted on the person by the elevator floor compare with the magnitude mg of the gravitational force?
F < mg
A young girl pulls a cart along the ground at a constant speed by applying Fpull. The arrows in the diagram correctly indicate the directions but not necessarily the magnitudes of the various forces on the cart. Which of the following relations among the various force magnitudes, W, f, N, Fpull is correct?
Fpull > f and N < W
39. A student is asked to determine the work done on a block of wood when the block is pulled horizontally using an attached string. The student is supplied with a spring scale, a stopwatch, and a meterstick. Which of the following graphical analysis techniques will allow the student to determine the work done on the block by the string?
Graphing the force as a function of distance and calculating the area under the curve
40. A stationary cart attached to a force gauge is on a straight, horizontal, frictionless track. A student uses the force gauge to move the cart, and the gauge produces the graph of force as a function of time shown. How does the momentum of the cart change during the time interval 0 s to 20 s?
The momentum increases in magnitude at first, then decreases without reversing direction
4. A rubber ball with the mass 0.20 kg is dropped vertically from a height of 1.5m above a floor. The ball bounces off the floor, and during the bounce 0.60 J of energy is dissipated. What is the maximum height of the ball after the bounce.
1.2 m
49. Two automobiles are 150 kilometers apart and traveling toward each other. One automobile is moving at 60 km/h and the other is moving at 40 km/h. In how many hours will they meet?
1.5 hours
A 2‑kg block slides down a 30° incline as shown with an acceleration of 2 m/s/s. Which of the following correctly indicates the magnitudes of the forces acting up and down the incline?
10 N down the plane, 6 N up the plane
10. Block A of mass 2.0 kg is released from rest at the top of a 3.6 m long plane inclined at an angle of 30°, as shown in the figure below. After sliding on the horizontal surface, block A hits and sticks to block B, which is at rest and has mass 3.0 kg. Assume friction is negligible. The speed of the blocks after the collision is most nearly
2.4 m/s
A marble is rolled down a slight incline. Two students record the distance d from the top of the incline to the bottom and the time t it takes for the marble to reach the bottom. Which of the following expressions correctly describes the final velocity of the marble in terms of d and t?
2d/t
Two identical blocks of weight W are placed one on top of the other as shown in the diagram. The upper block is tied to the wall. The lower block is pulled to the right with a force F. The coefficient of static friction between all surfaces in contact is μ. What is the largest force F that can be exerted before the lower block starts to slip?
3μW
30. A point charge of magnitude 2q exerts an electrostatic force of magnitude F on a point charge of magnitude q that is a distance R away. What is the magnitude of the force that the 2q point charge exerts on a point charge of magnitude 3q that is a distance R/5 away?
75F
18. A cart is moving on a level track in the positive x-direction. A force acting parallel to the x-axis is exerted on the cart. The graph below shows the net force exerted on the cart as a function of displacement. As the cart travels from x = 0 m to x = 4 m , what is the net change in the kinetic energy of the cart?
An increase of 10 J
Two astronauts are connected by a taut cable and are initially at rest with respect to a nearby space station. Astronaut X throws a large container to Astronaut Y. Figure 1 shows the astronauts immediately after the container is thrown by Astronaut X, and Figure 2 shows the astronauts immediately after the container is caught by Astronaut Y. Which of the following describes the motion of Astronaut Y in Figure 2 ?
At rest
A student sets up an experiment to measure the force experienced by two vehicles during a collision. Each vehicle has a digital force gauge attached to the bumper that will measure the instantaneous force on each object. The first vehicle is a large truck that weighs four times the smaller vehicle (a Tesla). Which force gauge will measure the largest force?
Both gauges will measure the same force
36. The graph below shows the potential energy U of a system as one object in the system moves along the x-axis and the rest of the system does not move. Six evenly-spaced points along the x-axis are labeled. At point H, the object is moving in the positive x-direction and the mechanical energy of the system is5.0 J. As the object moves, no energy enters or leaves the system. Which of the following describes the magnitude of the momentum of the object in the first two straight-line segments shown in the graph as the object moves from point H to point J ?
During HI, momentum is constant but nonzero. During IJ, momentum is increasing
An elevator carrying a person of mass m is moving upward and slowing down. How does the magnitude F of the force exerted on the person by the elevator floor compare with the magnitude mg of the gravitational force?
F < mg
Spring scales are used to measure the net force applied to an object; a sonic motion detector is used to measure the object's resulting acceleration. A graph is constructed with the net force on the vertical axis and the acceleration on the horizontal axis. Which of the following quantities is directly measured using the slope of this graph?
Inertial mass
An object started at rest at the origin and accelerates according to the graph. Which of the following scenarios could describe the position and velocity of the object at time T?
It has a positive position and a positive velocity
A uniform rope of weight 50 N hangs from a hook as shown. A box of weight 100 N hangs from the rope. What is the tension in the rope? Note that the rope is NOT massless.
It varies from 100 N at the bottom to 150 N at the top
38. A brother and sister are standing next to each other at rest on a surface of frictionless ice. The brother's mass is exactly twice that of his sister's.The sister suddenly pushes her brother. As a result, the sister moves with kinetic energy K. What is the resulting kinetic energy of the brother?
K/2
A spacecraft is in orbit around the earth at a constant speed. Which forces act on a spacecraft in orbit to keep it moving at a constant speed around the earth?
The force of gravity acting towards the earth
In the picture shown, crate is first pushed across a horizontal wooden board (case A). The crate is then pushed across the same wooden board while the board is tilted (case B). How does the force required to overcome friction in the inclined case B compared to the horizontal case A?
The inclined case has less frictional force
A man throws a rock at a coconut hanging high on a tree some distance away. By coincidence the coconut falls just as he releases the rock. To his surprise, his rock hits the coconut on its way towards the ground. If the rock had flown in a straight line, unaffected by gravity along its trajectory, where would the rock have hit the tree? Assume air resistance is not a factor in this problem.
The initial position of the coconut
9. A man steps onto the escalator below that is moving diagonally upwards at a constant velocity. What will be the direction of the net force on the man at the instant shown where he transitions from the bottom part to the angled portion of the escalator?
Upwards and to the left
44. An object hangs in equilibrium from a spring, as shown below. The object is then displaced to one of the labeled points X, Y, or Z . Which of the following correctly ranks the elastic potential energy stored in the spring when the object is at each of the three positions?
Y > X > Z
A boy and his father are ice skating while holding hands. The father is pulling his son to help him go faster. The mass of the father is 4 times the mass of the boy. If the father accelerates forward, the force that the boy applies on the father is:
equal to the force of the father on the boy
This graph represents the relationship between the mass of a number of marbles and their measured weight on an alien world. The slope of the graph is a representation of the:
gravitational field strength
26. Blocks A and B, of masses mA and mB , are at rest on a frictionless surface, as shown below, with block A fixed to the table. Block C of mass mC is suspended by a string that is tied to block B over an ideal pulley. Which of the following gives the magnitude of the force exerted by block A on block B ?
mCg
Which of the following expressions could be used to determine the velocity of the spacecraft given the mass of the spacecraft m, the mass of earth Me, and the radius R if it were placed back next to earth?
square root of G M/r
46. An empty sled of mass M moves without friction across a frozen pond at speed v₀. Two objects are dropped vertically into the sled one at a time: first an object of mass m and then an object of mass 2m. Afterward the sled moves with speed v. What would be the final speed of the sled if the objects were dropped into it in reverse order?
v
23. Three spheres, with masses indicated below, are initially far away from each other, and the gravitational potential energy of the three-sphere system is zero. The spheres are then brought together until each sphere is a distance r from the other two, as shown below. What is the new gravitational potential energy of the three-sphere system?
-5Gm²/r
A box moves from one conveyor belt moving 4 m/s to a second conveyor belt which moves at 10 m/s as shown. What is the acceleration of the box at point P? Assume the box does not slip along the conveyor belt surfaces.
0 m/s/s
27. A meteoroid is in a circular orbit 600 km below the surface of a distant planet. The planet has the same mass as Earth but has a radius that is 90% of Earth's (where Earth's radius is approximately 6370 km). The acceleration of the meteoroid due to the gravitational force exerted by the planet is most nearly
10 m/s² toward the center of the planet
Two people are pulling on the ends of a rope. Each person pulls with a force of 100 N. The tension in the rope is:
100 N
An object is moving to the west at a constant speed. Three forces are exerted on the object. One force is 10 N directed due north, and another is 10 N directed due west. What is the magnitude and direction of the third force if the object is to continue moving to the west at a constant speed?
10√2 N , directed southeast
A motion sensor is used to collect the following data for the velocity of a vehicle during a collision with a wall. What is the total displacement of the vehicle from time t = 0 to time t = 12 s ?
12 m
To analyze the characteristics and performance of the brakes on a 1500 kg car, researchers collected the data shown in the table. It shows the car's speed when the brakes are first applied and the corresponding braking distance required to stop the car. The magnitude of the average braking force on the car is most nearly:
12,000 N
7. A student sets an object attached to a spring into oscillatory motion and uses a position sensor to record the displacement of the object from equilibrium as a function of time. A portion of the recorded data is shown in the figure below. The total distance traveled by the object between 0.35 s and 0.40 s is most nearly
2 cm
49. Object A has mass 2 kg and is traveling to the right at speed 3 m/s. Object B is traveling to the left at 3 m/s . The objects collide head-on, and afterward each has a speed of 3 m/s. Which of the following could be the mass of object B ? Select two answers.
2 kg Negligible compared to 2 kg
17. A spring has a force constant of 100 N/m and an unstretched length of 0.07 m. One end is attached to a post that is free to rotate in the center of a smooth table, as shown in the top view below. The other end is attached to a 1 kg disc moving in uniform circular motion on the table, which stretches the spring by 0.03 m. Friction is negligible. What is the centripetal force on the disc?
3 N
A textbook weighs 30 N at sea level. Earth's radius is 6400 km. Which of the following is the best estimate for the textbook's weight on a mountain peak located 6 km above sea level?
30 N
A horizontal, uniform board of weight 200 N and length 4 m is supported by vertical chains at each end. A person weighing 400 N is hanging from the board. The tension in the right chain is 250 N. What is the tension in the left chain?
350 N
An object is dropped from height he on earth and takes time te to reach the ground. On a different planet the ball is dropped from twice the original height and takes twice as much time. Assuming air resistance is negligible on both planets, what is the free fall acceleration on this other planet?
5 m/s/s
A toy car moves 3.0 m to the North in one second. The car then moves at 9.0 m/s due South for two seconds. What is the average velocity of the car for this three second trip?
5.0 m/s
A rope of negligible mass supports a block that weighs 30 N, as shown. The rope will break if the tension exceeds 50N. 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/s/s
Three identical spherical weights all begin at an identical height above the ground with no initial vertical velocity. Weight A is dropped straight downwards. Weight B slides down a frictionless ramp. Weight C is thrown out horizontally and takes a parabolic path to the ground, striking exactly at the base of the ramp. The initial positions and velocity vectors for each object are given below. Which of the following rankings describes the time taken for each ball to hit the ground?
B > A = C
A ball initially moves horizontally with velocity vi, as shown. Which of the following final velocities would have required the greatest acceleration?
B northeast
A horizontal, uniform board of weight 200 N and length 4 m is supported by vertical chains at each end. A person weighing 400 N is hanging from the board. The tension in the right chain is 250 N. Which of the following describes where the person is hanging?
Between the chains, but closer to the left-hand chain
11. Three blocks of masses 3m, 2m, and m are connected to strings A, B, and C as shown below. The blocks are pulled along a rough surface by a force of magnitude F exerted by string C. The coefficient of friction between each block and the surface is the same. Which string must be the strongest in order not to break?
C
At which of the following locations between the earth and the moon would an object be most likely to experience the least net gravitational force?
C
Blocks A and B, of masses A and B , are at rest on a frictionless surface, as shown, with block A fixed to the table. Block C of mass C is suspended by a string that is tied to block B over an ideal pulley. Which of the following gives the magnitude of the force exerted by block A on block B? (HINT: since A is the mass of A the weight would be Ag)
Cg
A mass is suspended from two wires as shown. Which of the following graphs accurately depict what would happen to the tension T1 as the angle Θ increases.
D starts above 0 on y axis, exponential increasing
19. 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. The magnitude of the velocity of the object is increasing in which cases?
III only, starts at 0 exponential graph increasing
A spacecraft is in orbit around the earth at a constant speed. If the spacecraft was transported to orbit a planet with twice the mass, but the spacecraft was placed into the orbit at the same distance R, how would the velocity have to be adjusted to keep it in orbit?
It would increase, but not quite double
27. An object is launched vertically upward from ground level. It rises to a maximum height H. If air resistance is negligible, which of the following must be true for the object when it is at a height H/2?
Its kinetic energy is half of its initial kinetic energy.
A purse sits on the passenger seat of a car making a left turn at a steady speed. Based on this information, which is a possible direction for the purse's acceleration according to the pictured reference frame looking down at the car during the start of the turn?
Left
13. A ball falls straight down through the air under the influence of gravity. There is a retarding force F on the ball with magnitude given by F = bv, where v is the speed of the ball and b is a positive constant. The ball reaches a terminal velocity after a time t. The magnitude of the acceleration at time t/2 is
Less than 10 m/s/s
42. A simple pendulum consists of a sphere tied to the end of a string of negligible mass. The sphere is pulled back until the string is horizontal and then released from rest. Assume gravitational potential energy is zero when the sphere is at its lowest point. What angle will the string make with the horizontal when the kinetic energy and the potential energy of the sphere-Earth system are equal?
Less than 45 degrees
45. Two pucks are firmly attached by a stretched spring and are initially held at rest on a frictionless surface. The pucks are then released simultaneously. If puck I has three times the mass of puck II, which of the following quantities is the same for both pucks as the spring pulls the two pucks toward each other?
Magnitude of momentum
Three identical spherical weights all begin at an identical height above the ground with no initial vertical velocity. Weight A is dropped straight downwards. Weight B slides down a frictionless ramp. Weight C is thrown out horizontally and takes a parabolic path to the ground, striking exactly at the base of the ramp. The initial positions and velocity vectors for each object are given below. What other information would you need in order to determine which object has the greatest displacement at the moment when each strikes the ground?
No other information is needed, B and C tie, then A
50. A ball is tossed straight up from the surface of a small, spherical asteroid with no atmosphere. The ball rises to a height equal to the asteroid's radius and then falls straight down toward the surface of the asteroid. What forces, if any, act on the ball while it is on the way up?
Only a decreasing gravitational force that acts downward
An ant is walking on a piece of paper along the x-axis of a graph. It is initially moving quickly from the positive side of the graph towards the negative side. The ant crosses the origin, slows down, and then stops. Just before it comes to rest, which of the following correctly shows the signs of the position, velocity, and acceleration ?
Position (-), Velocity (-), Acceleration (+)
A man throws three different balls (P, Q, and R) into the air. Ball P has a mass of m, and is thrown at an initial speed of v. Ball Q has a mass of 2m, and is thrown at an initial speed of 2v. Ball R has a mass of 3m, and is thrown at an initial speed of 3v. Which of the following is the correct ranking for the maximum height of the balls?
R > Q > P
24. Steel sphere A of mass M is moving along a horizontal surface with constant speed v. Identical steel sphere B is at rest and hangs on a string of length R attached to a support at point P, as shown in the figure below. The spheres collide, and as a result sphere A stops and sphere B swings a vertical height h before coming momentarily to rest. Knowing values for which of the following will allow determination of the angular impulse on sphere B with respect to P due to the collision?
R, M, and v
An ant walks clockwise along the outer edge of a clock from the 6 to 12. What is the direction of the ant's average change in velocity?
Right
The block shown is suspended by three ropes. The first rope goes straight up, the second is straight to the left, and the final rope is at a diagonal, as shown. Which of the following equations or inequalities relating the magnitudes of the forces shown is correct?
T2 < T3
A geosynchronous (one that makes a full rotation every 24 hours) satellite orbits the earth at 35,786 km above the surface of the earth and has a mass of 850 kg. Which of the following values would you need to find the force of gravity the satellite exerts on the earth?
The diameter of the earth
37. A 4 kg object moving to the left collides with and sticks to a 3 kg object moving to the right. Which of the following is true of the motion of the combined objects immediately after the collision?
The final behavior of the two objects can not be determined without information about their pre-collision speeds.
45. A man stands on the surface of a planet of uniform density with radius R. He then moves into a deep hole of depth R/2. How does the magnitude of the total force of gravity compare here, within the planet, to the magnitude of the total force of gravity on the surface?
The force is less than the original value
A pick-up truck has a large box sitting in the center of the truck bed. The box is not in contact with any of the sides of the truck. The turck begins to accelerate up a hill and the box remains at rest relative to the truck. What force is responsible for the box's increase in speed up the hill?
The force of static friction of the truck on the box
22. Two objects, A and B, move toward one another. Object A has twice the mass and half the speed of object B. Which of the following describes the forces the objects exert on each other when they collide and provides the best explanation?
The forces exerted by each object on the other are the same, because interacting objects cannot exert forces of different magnitude on each other.
An experimenter uses the apparatus shown to pull a block across a rough surface and creates a graph of the acceleration of the block versus the applied force measured with the spring scale. Which of the following quantities would represent the slope of the graph shown?
The inverse of the mass of the block, 1/m
29. A satellite in a circular orbit around Earth is initially not rotating with respect to its center of mass. Two identical thrusters on opposite sides of the satellite fire in opposite directions over the same 10-minute time interval, as shown below,and then turn off. How does the firing of the thrusters affect the mechanical energy of the satellite-Earth system and the shape of the satellite's orbit, if at all?
The mechanical energy increases but there in no change in the shape of the orbit
17. A soft foam block of mass m slides without friction in the positive x-direction with speed v. At time t = 0, a student briefly pushes the block with a force probe in the positive x-direction. The graph below shows the force probe's measurements as a function of time during the push. Which of the following statements is true about the block's momentum between t = 0 and t = t₁?
The momentum of the block has increased by approximately ½F₀t₁
42. A block on a horizontal frictionless plane is attached to a spring, as shown. The block oscillates along the x‑axis with amplitude A. Which of the following statements about energy is correct?
The potential energy of the spring is at a minimum at x = 0.
A pair of students design an experiment to find the acceleration of a toy car. They measure the velocity of the car versus the time and graph the velocity versus the time of the car, they could find the acceleration using:
The slope of the graph
6. A student sets an object attached to a spring into oscillatory motion and uses a position sensor to record the displacement of the object from equilibrium as a function of time. A portion of the recorded data is shown in the figure below. The speed of the object at time t=0.65s is the most nearly equal to which of the following?
The slope of the tangent to the best-fit sinusoidal curve at 0.65s
A man on a bike at a constant speed runs over a piece of gum which sticks to the tire. The initial acceleration of the gum as the tire begins to lift the gum is:
Upwards
5. Is it possible for an object's velocity to increase while its acceleration decreases?
Yes, an example would be a falling object in the presence of air resistance
It is known that a lab cart is moving east at 25 cm/s at time t1 = 0.10 s, and then moving east at 15 cm/s at time t2 = 0.20 s. Is this enough information to determine the direction of the average acceleration acting on the lab cart between time t1 and time t2?
Yes, since we know the cart is slowing down we can assume the acceleration must be to the west
41. A stone disk is sliding on frictionless ice to the west with speed v, as shown in the figure below. As the disk slides by, a child uses a rubber mallet to hit the disk at point X, exerting a force directly toward the center of the disk. The child hits point X every half second for about 10 s, changing the trajectory of the disk but not causing it to rotate. Which of the following most closely approximates the path of the disk while the child is hitting it?
a parabolic path
Two arrows are launched at the same time with the same speed. Arrow A at an angle greater than 45 degrees, and arrow B at an angle less than 45 degrees. Both land at the same spot on the ground. Which arrow arrives first? Assume air resistance is negligible.
arrow B arrives first
Two identical carts are travelling down a sloped track. Cart A starts behind Cart B but Cart A has a greater initial velocity. At the 5 second mark they collide. Which of the following graphs could represent this motion?
equal slopes where a starts at a higher y value
According to the position versus time graph, rank the average speed during the labeled time interval. Each dotted line represents an equal time interval.
p = r = s > q
Three asteroids of identical mass are placed near each other as shown. The distance between the center of mass of asteroid a1 and a2 is D. The distance between the center of mass of a2 and a3 is 2D. Rank the magnitude of net force acting on each asteroid.
ΣF1 > ΣF2 > ΣF3
12. Two charged conducting spheres are separated by a distance d, as shown in the figure below. One sphere has charge +5Q, the other has charge -Q, and the diameter of each sphere is much smaller than d. Each sphere exerts a force of magnitude F on the other. The spheres are brought together and touch briefly. After touching, the left sphere has charge +2Q. The spheres are then returned to their original locations. What is the magnitude of the new force between the spheres?
⅘ F
31. A ball of mass m is initially rolling across a level surface at velocity v when it hits a wall and bounces off, rolling v/2 in the opposite direction. How much energy does the ball lose during the collision?
⅜mv²
34. In trial 1 of an experiment, a cart moves with speed v₀ on a frictionless, horizontal track and collides elastically with another cart that is initially at rest. In trial 2, the setup is identical except that the carts stick together during the collision. How does the speed of the two-cart system's center of mass change, if at all, during the collision in each trial?
(Trial One) Does not change (Trial Two)Does not change
28. Three identical rocks are launched with identical speeds from the top of a platform of height h0. The rocks are launched in the directions indicated below. Rock 1, of mass m, reaches a maximum height hmax after being launched. During the time between the instant rock 1 is launched from height h0 and the instant it returns to height h0 , the work done on the rock by the gravitational force is
0
32. A 2 kg ball is attached to a 0.80 m string and whirled in a horizontal circle at a constant speed of 6 m/s. The work done on the ball during each revolution is:
0J
8. A student sets an object attached to a spring into oscillatory motion and uses a position sensor to record the displacement of the object from equilibrium as a function of time. A portion of the recorded data is shown in the figure below. The frequency of oscillation is most nearly
2.0 Hz
18. The motion of a circus clown on a unicycle moving in a straight line is shown in the graph below. What would be the acceleration of the clown at 5 s?
2.0 m/s/s
13. The wheel on a vehicle has a rotational inertia of 2.0 kg*m². At the instant the wheel has a counterclockwise angular velocity of 6.0 rad/s, an average counterclockwise torque of 5.0 N*m is applied, and continues for 4.0 s. What is the change in angular momentum of the wheel?
20 kg*m²
2. A car of mass m, traveling at speed v, stops in time t when maximum braking force is applied. Assuming the braking force is independent of mass, what time would be required to stop a car of mass 2m traveling at speed v?
2t
36. The graph below shows the force exerted by a spring as a function of the length of the spring. A block on a frictionless table is pushed against the spring that is fastened to a wall. The spring is compressed until its length is 20 cm. The block is then released. Which of the following values is closest to the kinetic energy with which the block leaves the spring?
3 J
2. A 12 kg box sliding on a horizontal floor has an initial speed of 4.0 m/s. The coefficient of friction between the box and the floor is 0.20. The box moves a distance of 4.0 m in 2.0s. The magnitude of the change in momentum of the box during this time is most nearly
48 kg・m/s
22. The motion of a circus clown on a unicycle moving in a straight line is shown in the graph below. After 12 seconds, how far is the clown from her original starting point?
74 m
31. The figure below shows a uniform meterstick that is set on a fulcrum at its center. A force of magnitude F toward the bottom of the page is exerted on the meterstick at the position shown. At which of the labeled positions must an UPWARD force of magnitude ½F be exerted on the meterstick to keep the meterstick in equilibrium?
A
1. The 10.0 kg box shown in the figure to the right is sliding to the right along the floor. A horizontal force of 10.0 N is being applied towards the right. The coefficient of kinetic friction between the box and the floor is 0.20. The box is moving with:
Acceleration to the left
Consider the motion of an object given by the position vs. time graph shown. For what time(s) is the speed of the object greatest?
At 4 seconds
15. A projectile fired into the air explodes and splits into two halves of equal mass that hit the ground at the same time. If the projectile had not exploded, it would have landed at point X, which is a distance R to the right of the launch point. After the explosion, one of the halves lands at point Y, which is a distance 2R to the right of the launch point. If air resistance is negligible, where did the other half land?
At the launch point
47. Two lab carts have the same mass and are free to move on a horizontal track. The carts' wheels have negligible mass. Cart 1 travels to the right at 1.0 m/s and collides with cart 2, which is initially at rest, as shown at left below. Cart 2 has a compressed spring-loaded plunger with a non-negligible amount of stored energy. During the collision, the spring-loaded plunger pops out, staying in contact with cart 1 for 0.10 s as the spring decompresses. Negligible mechanical energy dissipates during the collision. Taking rightward as positive, the carts' velocities after the collision could be which of the following? Select two answers.
Cart 1: -0.5 m/s, Cart 2: 1.5 m/s Cart 1: -1.0 m/s, Cart 2: 2.0 m/s
14. A ball is tossed straight up from the surface of a small, spherical asteroid with no atmosphere. The ball rises to a height equal to the asteroid's radius and then falls straight down toward the surface of the asteroid. The acceleration of the ball at the top of its path is:
Equal to one-fourth the acceleration at the surface of the asteroid
A father throws a ball to his daughter as shown. Rank the magnitude of the acceleration at each labeled moment. Assume air resistance is negligible.
F = G = H
40. Block A and block B move toward each other on a level frictionless track. Block A has mass m and velocity +v . Block B has mass 2m and velocity -v . The blocks collide, and during the collision the magnitude of the net force exerted on block A is F. What is the magnitude of the net force exerted on block B, and why does it have that value?
F, because the net force is equal to the mutual contact force between the blocks.
33. A worker in a factory pushes a crate with some applied force, causing the crate to slide. After the worker stops their push, the crate continues to slide some distance before coming to rest due to friction with the factory floor. Which of the following describes the interval for which the net work on the crate is zero?
From the time the worker begins pushing until the crate comes to rest
38. Tiny drops of oil that have different amounts of electric charge produced by a random process are sprayed into a region between a positively and a negatively charged plate. The charge on each drop is determined by analyzing the effect of the electric force on the drop's motion. Two graphs of the number of drops as a function of the charge on each drop, where e is the charge of an electron, are shown below. Which graph shows the most likely result after repeating the experiment many times, and why?
Graph 1, because it shows that within experimental error charge only exists in multiples of e
7. 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. The sum of the forces on the object is zero in which cases?
I and II only
24. The figure to the below shows a rough semicircular track whose ends are at a vertical height h. A block placed at point P at one end of the track is released from rest and slides past the bottom of the track. Which of the following is true of the height to which the block rises on the other side of the track?
It is between zero and h; the exact height depends on how much energy is lost to friction
50. Some bicycle brakes work by pressing rubber pads against the rim of the wheel. To test newly designed brakes, bicycle engineers mount a wheel of known rotational inertia on a low-friction axle, as shown below. The engineers spin the wheel with known initial angular speed and then apply the brakes with a constant force. Which of the following procedures would enable the engineers to find the torque exerted by the brakes on the wheel? Select two answers.
Measuring how much time the wheel takes to come to rest Measuring how many rotations the wheel completes while coming to rest
41. Two objects, P and Q, have the same momentum. Q can have more kinetic energy than P if it has
More speed than P
11. A student is asked to move a box from ground level to the top of a loading dock platform, as shown in the figures below. In Figure 1, the student pushes the box up an incline with negligible friction. In Figure 2, the student lifts the box straight up from ground level to the loading dock platform. In which case does the student do more work on the box, and why?
Neither method, because the work is the same in both cases, since using the ramp decreases the force by the same factor that it increases the distance
1. A blue sphere and a red sphere with the same diameter are released from rest at the top of a ramp. The red sphere takes a longer time to reach the bottom of the ramp. The spheres are then rolled off a horizontal table at the same time with the same speed and fall freely to the floor. Which sphere reached the floor first?
Neither; the spheres reach the floor at the same time.
28. A cart of mass m is moving with negligible friction along a track with known speed 1v to the right. It collides with and sticks to a cart of mass 4m moving with known speed 2v to the right. Which of the two principles, conservation of momentum and conservation of mechanical energy, must be applied to determine the final speed of the carts, and why?
Only conservation of momentum, because the momentum lost by one cart is gained by the other and there is only one unknown quantity.
4. A spring‑loaded gun can fire a projectile to a height h if it is fired straight up. If the same gun is pointed at an angle of 45° it will:
Reach a lower height that originally because it has less velocity in the y-direction
9. An object has 4 forces acting on it. One force going north is 20 N, the next force is 5 N west, and 10 N to the south. What is the direction of the final force if the object is accelerating due east?
Southeast
21. Two artificial satellites, 1 and 2, are put into circular orbit at the same altitude below Earth's surface. The mass of satellite 2 is twice the mass of satellite 1. If the period of satellite 1 is T, what is the period of satellite 2?
T
48. Two frictionless lab carts start from rest and are pushed along a level surface by a constant force. Students measure the magnitude and duration of the force on each cart, as shown in the partially completed data table below, and calculate final kinetic energy and momentum. Which cart has a greater kinetic energy at the end of the push?
The 1 kg
A student is informed that the acceleration versus time graph of an ice block was plotted after it had been pushed to the right. If motion to the right is defined as positive, which of the following statements uses the motion graph to correctly describe the current linear motion of the ice block?
The block is going to the right and slowing down
A horse accelerates at a constant rate from rest covering 100 meters. What other information is needed to discover the horse's acceleration?
The final velocity of the horse
48. A test car and its driver, with a combined mass of 600 kg, are moving along a straight, horizontal track when a malfunction causes the tires to stop rotating. The car skids to a halt with constant acceleration, leaving skid marks on the road during the whole time it skids. Which two of the following measurements, taken together, would allow engineers to find the total mechanical energy dissipated during the skid? Select two answers.
The length of the skid marks The coefficient of kinetic friction between the tires and the track
Which of the following variables could be changed without affecting the orbital period of the satellite?
The mass of the spacecraft
39. A sphere of mass m₁, which is attached to a spring, is displaced downward from its equilibrium position as shown below and released from rest. A sphere of mass m₂, which is suspended from a string of length L, is displaced to the right as shown below right and released from rest so that it swings as a simple pendulum with small amplitude. Assume that both spheres undergo simple harmonic motion. Which of the following is true for both spheres?
The maximum kinetic energy is obtained as the sphere passes through its equilibrium position.
5. A sled slides down a hill with friction between the sled and hill but negligible air resistance. Which of the following must be correct about the resulting change in energy of the sled-earth system.
The sum of the kinetic energy and the gravitational potential energy changes by the amount equal to the energy dissipated by friction.
8. A uniform rigid bar of weight W is supported in a horizontal orientation as shown below by a rope that makes a 30° angle with the horizontal. The force exerted on the bar at point O, where a nail acts as the pivot, is best represented by a vector whose direction is which of the following?
Up and right
A car drives at a constant speed through a dip as shown. At the bottom of the dip, what is the direction of the acceleration of the car?
Upwards
43. A negatively charged rod is placed in a small container filled with air that is electrically neutral.The container is then sealed. Fifteen seconds later, measurements reveal that the air inside the container has a net negative charge. What is the primary reason that the air becomes negatively charged?
When air molecules bounce off the rod, negative charge transfers from the rod to some of those molecules.
The motion of a spaceship can be described with acceleration and velocity vectors. Which combination of vectors would lead to an initial increase in speed AND a change in direction? Assume the angular relationship between the directions of the two vectors are kept constant.
acute angle
26. An object is dropped from rest from a certain height. Air resistance is negligible. After falling a distance d, the object's kinetic energy is proportional to which of the following?
d
15. A block of mass 3m can move without friction on a horizontal table. This block is attached to another block of mass m by a cord that passes over a frictionless pulley, as shown below. If the masses of the cord and the pulley are negligible, what is the magnitude of the acceleration of the descending block?
g/4
12. A plane 5 meters in length is inclined at an angle of 37°, as shown below. A block of weight 20 N is placed at the top of the plane and allowed to slide down. The magnitude of the normal force exerted on the block by the plane is
greater than zero but less than 20 N
43. A sphere of mass m₁, which is attached to a spring, is displaced downward from its equilibrium position as shown below and released from rest. A sphere of mass m₂, which is suspended from a string of length L, is displaced to the right as shown below right and released from rest so that it swings as a simple pendulum with small amplitude. Assume that both spheres undergo simple harmonic motion. If both spheres have the same period of oscillation, which of the following is an expression for the spring constant?
m₁g / L
16. From the top of a high cliff, a ball is thrown horizontally with initial speed v₀. Which of the following graphs best represents the ball's kinetic energy K as a function of time t?
starts at 0, exponential graph increasing
33. Two satellites are in circular orbits around Earth. Satellite A has speed vA . Satellite B has an orbital radius nine times that of satellite A. What is the speed of satellite B ?
vA/3
30. A rock is lifted for a certain time by a force F that is greater in magnitude than the rock's weight W. The change in kinetic energy of the rock during this time is equal to the
work done by the net force (F - W)
25. A pendulum consists of a ball of mass m suspended at the end of a massless cord. The pendulum is drawn up to a height of h. At the low point of its swing, the speed of the pendulum ball is:
√(2gh)
47. A stationary object explodes, breaking into three pieces of masses m, m, and 3m. The two pieces of mass m move off at right angles to each other with the same magnitude of momentum mV, as shown in the diagram below. What are the magnitude and direction of the velocity of the piece having mass 3m?
√2v/3 , ↙
23. A child pushes horizontally on a box of mass m which moves with constant speed v across a horizontal floor. The coefficient of friction between the box and the floor is 𝜇. At what rate does the child do work on the box?
𝜇mgv
