AP Physics 1: Unit 5-6 Momentum and SHM Test Review
At time t = 0, a projectile is launched from the top of a cliff at an angle of 30 degrees below the horizontal. Which of the following pairs of graphs best represents the horizontal displacement Δx and the vertical velocity component vvert of the projectile as a function of time t ?
A
A horizontal disk is free to rotate about an axle at its center. The labeled arrows in the figure represent forces of equal magnitude that are exerted on the edge of the disk in the directions shown. Which of the following correctly ranks the magnitude t of the torque about the axle exerted by each force? (A) tA B C D = t = t = t (B) tA D > t > (tB C = t ) (C) (tA B D = t = t ) > tC (D) (tB C = t ) > tD A
B
. The graph shows the force exerted on a ball by the floor as a function of time as the ball bounces off the floor. If the positive direction is upward, which of the following graphs could represent the force exerted on the floor by the ball?
C
On another planet, a ball is in free fall after being released from rest at time t = 0. A graph of the height of the ball above the planet's surface as a function of time t is shown. The acceleration due to gravity on the planet is most nearly (A) 8 m / s2 (B) 16 m / s2 (C) 20 m / s2 (D) 40 m / s2
B
The kinetic energy of the rock when it is at the same height as point D is most nearly (A) 1 mv 2 2 (B) 1 2mgR 2 (C) 1 4mgR 2 (D) 1 2 m v( + 4gR) 2
D
An engineer measures the velocity v of a remote-controlled cart on a straight track at regular time intervals. The data are shown in the graph above. During which of the following time intervals did the cart return to its position at time t = 0 s ?
(C) 7s ≤ t < 10s
At time t = 0 s, an object is moving to the right with a velocity v that can be modeled by the equation v=(4.2 m/s) (- 1.4 m/s2 )t. At what time, if any, does the object change its direction of motion? (A) 0.33 s (B) 3.0 s (C) 5.6 s (D) At no time; the object never changes direction.
B
Two identical blocks A and B are connected by a lightweight rope. Block A is pulled to the right by a constant force F0. The blocks are moving to the right across a rough surface and approach point , where the rough P surface transitions to a surface with negligible friction. How does the tension, T, in the rope connecting the blocks change, if at all, as block A passes point P ? (A) T decreases. (B) T increases. (C) T remains constant. (D) The change in T cannot be determined without knowing the coefficient of friction and the mass of the blocks.
B
The graph shows the acceleration as a function of time for an object that is at rest at time t = 0 s. The distance traveled by the object between 0 and 2 s is most nearly (A) 1 m (B) 2 m (C) 3 m (D) 4 m
C
A block is attached to the end of a string and initially moves at a constant speed in a horizontal circle of constant radius, as shown. The radius is then increased slowly while the speed remains the same. Which of the following graphs best represents the force exerted on the block by the string as a function of the radius?
D
What is the normal force exerted on the rider when passing point D ? (A) 0.2Fg (B) 0.8Fg (C) 1.0Fg (D) 1.2Fg
D
. A force F0 is applied continuously to a box initially at rest on a horizontal surface. The box slides with negligible friction for equal distances d1 and d2, as shown. How does the kinetic energy gained by the block over distance interval d2, ∆ K2, compare to the kinetic energy gained over distance interval d1, ∆ K1, and why? ( A) ∆ K2 1 = ∆ K , because the velocity increases by the same amount over intervals d1 and d2. (B) ∆ K2 1 = ∆ K , because the applied force does the same work on the block over intervals d1 and d2. (C) ∆ K2 1 > ∆ K , because the block is moving faster on average over interval d2. (D) ∆ K2 1 > ∆ K , because the rate of change of kinetic energy is greater over interval d2.
B
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 2.0 s. The magnitude of the change in momentum of the box during this time is most nearly (A) 12 kg · m / s (B) 48 kg · m / s (C) 60 kg · m / s (D) 96 kg · m / s
B
A 2.0 kg disk is able to move on a straight, level track with negligible friction. With the disk initially at rest, a horizontal force is applied to the disk. The force is measured as a function of the disk's displacement, and the data are shown in the graph. When the disk's displacement is 2.0 m, the speed of the disk is most nearly (A) 2.8 m/s (B) 4.0 m/s (C) 5.6 m/s (D) 8.0 m/s
B
A block is set on a table, where there is negligible friction between the block and the table. The block is connected to an identical hanging block by a lightweight string that passes over an ideal pulley as shown. When the blocks are released from rest, the two-block system gains kinetic energy because work is done on the system. Which type of force or forces make a nonzero contribution to the net work done on the two-block system? (A) Gravitational force only (B) Gravitational force and tension only (C) Gravitational force and normal force only (D) Gravitational force, tension, and normal force
B
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? (A) To the left of the launch point (B) At the launch point (C) Between the launch point and point X (D) Between points X and Y
B
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 above 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 = t 1 ? (A) The momentum of the block has decreased to zero at time t 1. (B) The momentum of the block has increased by approximately 1 F0 2 . (C) The momentum of the block has decreased by approximately 1 F t 0 2 . (D) The change in momentum cannot be determined without knowing the distance by which the force probe compressed the block.
B
A student uses a spring scale to exert a horizontal force on a block, pulling the block over a smooth floor. The student repeats the procedure several times, each time pulling the block from rest through a distance of 1.0 m. For which of the following graphs of force as a function of distance will the block be moving the fastest at the end of the 1.0 m ?
B
A wheel with radius 0.33 m and rotational inertia 2.0 kg · m2 spins on an axle with an initial angular speed of 3.0 rad /s. Friction in the axle exerts a torque on the wheel, causing the wheel to stop after 6.0 s. The average torque exerted on the wheel as it slows down has magnitude (A) 0.50 N·m (B) 1.0 N·m (C) 2.0 N·m (D) 3.0 N·m
B
The figures show a cart moving over the top of a hill (Case 1), moving at the bottom of a dip (Case 2), and moving at the top of a vertical loop (Case 3). In each case, the normal force acting on the car is Fn and the weight of the car is Fg. In which case is it always true that Fn g > F , and in which case is it always true that Fn g < F ? Fn > Fg Always: Fn < Fg Always: (A) Case 1 Case 3 (B) Case 2 Case 1 (C) Case 2 Case 3 (D) Case 3 Case 1
B
The graph above represents the position of two identical carts on a straight horizontal track as a function of time. Which of the following statements about the magnitude of the momentum of the two-cart system's center of mass, p com, is true? (A) p is constant from t = 0 s to t = 5 s. com (B) p is smaller after t = 2 s than it is before t = 2 s. com (C) p is larger after t = 2 s than it is before t = 2 s. com (D) p increases at a constant rate from t = 0 s to t = 5 s.
B
Two identical blocks slide along a ramp with negligible friction, as shown. The first block has an initial speed v0 up the ramp while the second has the same initial speed v0 down the ramp. The coordinate system shown defines down the ramp to be the positive x direction. While both blocks are sliding on the ramp, the center of mass velocity of the two-block system is (A) constant and zero (B) constant but not zero (C) increasing in the −x direction (D) increasing in the +x direction
B
Two objects, X and Y, experience external net torques that vary over a period of 5 seconds. Object X has a moment of inertia I0, and Object Y has a moment of inertia 2I0. The average value of the magnitude of the external net torque exerted on Object X from time t = 0 to t = 5 s is tX. Similarly, the average value for Object Y is tY. The magnitudes of the angular momenta L of Objects X and Y versus t are shown in the graph. Which of the following expressions correctly relates tY to tX ? (A) t = 4t Y X (B) t = 2t Y X (C) 2tY = tX (D) 4t = t Y X
B
A cart travels toward the right on a track where friction between the cart and track is negligible. The momentum of the cart as a function of time is modeled in the graph. Which of the following statements are true for the time recorded? Select two answers. (A) The change in momentum of the cart is nearly equal to 1.9 kg · m / s. (B) The impulse delivered to the cart is nearly equal to 0.75 kg · m / s. (C) The net external force exerted on the cart is nearly equal to 0.15 N. (D) The work done on the cart is nearly equal to 1.5 J.
B, C
A block slides down an inclined plane in a classroom. Which of the following pieces of information are needed to determine whether the velocity of the block will be constant? Select two answers. (A) The mass of the block (B) The angle of the inclined plane (C) The acceleration due to gravity in the classroom (D) The coefficient of kinetic friction between the block and the inclined plane
B, D
Four forces are exerted on a disk of radius R that is free to spin about its center, as shown above. The magnitudes are proportional to the length of the force vectors, where F1 4 = F , F2 3 = F , and F1 2 = 2F . Which two forces combine to exert zero net torque on the disk? Select two answers. (A) F1 (B) F2 (C) F3 (D) F4
B, D
3. The figure shows three cases where two spheres are touching and attract each other with the gravitational force. The radii of the spheres in each case are shown. All of the spheres are made of material with the same density. Which of the following correctly ranks these cases based on the gravitational force between the spheres? (A) (A = B) > C (B) A > C > B (C) B > C > A (D) C > (A = B)
C
3. The wheel on a vehicle has a rotational inertia of 2 2 . 0 kg · m . 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? (A) 12 kg · m2 / s (B) 2 16 kg · m / s (C) 2 20 kg · m / s (D) 32 kg · m2 / s
C
A rubber ball with mass 0.20 kg is dropped vertically from a height of 1.5 m above a floor. The ball bounces off of the floor, and during the bounce 0.60 J of energy is dissipated. What is the maximum height of the ball after the bounce? (A) 0.30 m (B) 0.90 m (C) 1.2 m (D) 1.5 m
C
The motion of an object is shown in the velocity-time graph. Which best describes the motion of the object? (A) The object is either speeding up or slowing down the entire time. (B) The object starts and finishes at the same position. (C) The object travels in the same direction for the entire time. (D) The object undergoes positive acceleration the entire time
C
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 reaches the floor first? (A) The red sphere (B) The blue sphere (C) The sphere with the greater mass (D) Neither; the spheres reach the floor at the same time.
D
A block is set on a rough horizontal table where frictional forces are not negligible. The block is pushed against a horizontal spring, and it is released at time t = 0. The spring pushes the block across the table. At time t = t 1, the block leaves the table. The block strikes the ground at time t = t2. Which of the following describes the change in mechanical energy of the block-spring system for times ?
(B) Increase, Decreases
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 above, 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?
(C) Increase, No Effect
A box of mass m is released from rest and accelerates down a ramp that is at an angle q to the horizontal, as shown. The coefficient of kinetic friction between the box and the ramp is m. As the box is sliding down the ramp, how are the magnitudes of the horizontal and vertical components of the box's velocity changing, if at all? Horizontal Component: Vertical Component: (A) Not changing Not changing (B) Not changing Increasing (C) Increasing Not changing (D) Increasing Increasing
(D)
. 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? (A) F < mg (B) F = mg (C) F > mg (D) F can be greater than or less than mg, depending on the speed of the elevator.
A
A block of mass m travels with speed v0 to the right on a horizontal surface with negligible friction toward a sphere of mass 2m hanging at rest from a light cord, as shown above. The block collides elastically with the sphere. Which of the following correctly describes the speed and direction of the block and the speed of the sphere a short time after the collision?
A
A cart of mass m is moving with negligible friction along a track with known speed v1 to the right. It collides with and sticks to a cart of mass 4m moving with known speed v2 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? (A) Only conservation of momentum, because the momentum lost by one cart is gained by the other and there is only one unknown quantity. (B) Both conservation of mechanical energy and conservation of momentum, because both principles apply in any collision. (C) Both conservation of mechanical energy and conservation of momentum, because neither cart changes direction. (D) Either conservation of momentum or conservation of mechanical energy, because only one equation is required to solve for the one unknown variable.
A
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? (A) The sum of the kinetic energy and the gravitational potential energy changes by an amount equal to the energy dissipated by friction. (B) The gravitational potential energy decreases and the kinetic energy is constant. (C) The decrease in the gravitational potential energy is equal to the increase in kinetic energy. (D) The gravitational potential energy and the kinetic energy must both decrease.
A
Block A is set on a rough horizontal table and is connected to a horizontal spring that is fixed to a wall, as shown. Block A is then also connected to hanging block B by a lightweight string that passes over an ideal pulley, as shown. The friction force exerted on block A by the table is not negligible. The blocks are initially held at rest so that the spring is not stretched. When the blocks are released, hanging block B moves downward and block A on the table moves to the right until the system comes again to rest. Let E1 be the mechanical energy of the blocks-spring system, and let E2 be the mechanical energy of the blocks-spring-Earth system. How do these two energies change from when the blocks are held at rest to when the blocks come to rest again? (A) Increases Decreases (B) Decreases Increases (C) Remains constant Decreases (D) Remains constant Remains constant
A
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 above. 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 (A) 2.4 m / s (B) 3.2 m / s (C) 3.8 m / s (D) 6.0 m / s
A
Carts 1 and 2 are initially moving toward each other, as shown in the top figure. The carts collide and afterward are both moving to the right, as shown in the bottom figure. If the positive direction is to the right, which of the following best represents the force exerted on each cart by the other during the collision as a function of time?
A
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 1: Trial 2: (A) Does not change Does not change (B) Does not change Decreases (C) Decreases Does not change (D) Decreases Decreases
A
On Earth, when a box slides across a horizontal board, the board exerts a frictional force of magnitude F0 on the box. The board and the box are moved to a planet with twice the radius but one-third the mass of Earth. When the box slides across the board, the frictional force exerted by the board on the box is now (A) 1 F0 12 (B) 1 F0 6 (C) 2 F0 3 (D) F0
A
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 above, and calculate final kinetic energy and momentum. Which cart has a greater kinetic energy at the end of the push? (A) The 1 kg cart (B) The 2 kg cart (C) Both carts have the same amount of kinetic energy. (D) The relationship cannot be determined without knowing the distance each cart moved as the force was being applied.
A
Two identical spaceships are moving through space both with speed v0. Both spaceships experience a net force of magnitude F0 over the same time interval. For spaceship 1, the net force acts in the same direction as the spaceship is moving; for spaceship 2, the net force is directed opposite to the spaceship's motion, causing spaceship 2 to slow down but not stop. For which spaceship, if either, does the kinetic energy change by a greater magnitude, and why? (A) Spaceship 1 will have a greater change in kinetic energy because the distance traveled is greater than that of spaceship 2. (B) Spaceship 2 will have a greater change in kinetic energy because the force slows down the spaceship. (C) Spaceship 1 and 2 have the same change in kinetic energy because the time and the force are the same. (D) Spaceship 1 and 2 have the same change in kinetic energy because the net work done on each has the same magnitude.
A
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. (A) The length of the skid marks (B) The contact area of each tire with the track (C) The coefficient of static friction between the tires and the track (D) The coefficient of kinetic friction between the tires and the track
A, C
An object is moving along a straight, flat section of track. The net force acting on the object as a function of position is shown in the graph, where the positive direction is in the direction of motion of the object. Assuming the object moves from position x = 0 to x = 7d0 without stopping or moving backward, which of the following statements about its motion are correct? Select two answers. (A) The object has its greatest kinetic energy at position 5d0. (B) The kinetic energy of the object at position d0 is greater than 2F d00 . (C) The object has the same kinetic energy at position d0 that it has at position 7d0. (D) The kinetic energy of the object is not changing when it is between positions d and d 0 3 0.
A, C
. An object hangs in equilibrium from a spring, as shown above. 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 U stored in the spring when the object is at each of the three positions? (A) UZ > (UX = UY) (B) UY > (UX = UZ) (C) UY X Z > U > U (D) UY Z X
B
. 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 ? (A) vA / 9 (B) vA /3 (C) 3vA (D) 9vA
B
1. The figure above shows a uniform meterstick that is set on a fulcrum at its center. A force of magnitude 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 2F be exerted on the meterstick to keep the meterstick in equilibrium? (A) A (B) B (C) C (D) D
B
2. A bicycle wheel of known rotational inertia is free to rotate about its central axis. With the wheel initially at rest, a student wraps a string around the wheel and pulls the string with a spring scale, causing the wheel to rotate. The student records the tension in the string and the time for which the string was pulled. Without measuring the wheel's final angular speed, can the student find the magnitude of the wheel's final angular momentum, and what is a correct explanation? (A) Yes. The student has sufficient information already. (B) Yes. The student also needs to measure the wheel's radius to calculate the torque exerted on the wheel. (C) No. Angular momentum can only be found by measuring rotational inertia and angular speed. (D) No. Measuring the radius would allow the student to calculate the torque, not the angular momentum.
B
A vertical spring launcher is attached to the top of a block and a ball is placed in the launcher, as shown in the figure. While the block slides at constant speed to the right across a horizontal surface with negligible friction between the block and the surface, the ball is launched upward. When the ball reaches its maximum height, what will be the position of the ball relative to the spring launcher? (A) Above and to the right of the spring launcher (B) Directly above the spring launcher (C) Above and to the left of the spring launcher (D) The relative position of the ball depends on the horizontal speed of the block.
B
At time t = 0, a cart is at x =10 m and has a velocity of 3 m/s in the −x-direction. The cart has a constant acceleration in the +x-direction with magnitude 2 2 3 m/s < < a 6 m/s . Which of the following gives the possible range of the position of the cart at t =1 s ? (A) 4 m < < x 5.5 m (B) 8.5 m < < x 10 m (C) 11.5 m < < x 13 m (D) 14.5 m < < x 16 m
B
Blocks 1 and 2 are connected by a light string that passes over a pulley with negligible mass and friction, as shown in the figure. Block 1 is on a table covered with two different materials, A and B. The two-block system is released from rest, and the speed of block 1 begins to increase. When block 1 reaches material B, its speed increases at a greater rate. Which of the following correctly compares the coefficient of kinetic friction m between block 1 and the two materials and describes the change in the magnitude of the net force on block 2 as block 1 slides from material A to material B? (A) mA > mB Decreases (B) mA > mB Increases (C) mA < mB Increases (D) mA < mB Decreases
B
In a classroom at time t = 0, a sphere is thrown upward at a 45° angle to the horizontal. At time t 1, while the sphere is still rising, it bounces off the ceiling elastically and with no friction. Which of the following pairs of graphs could represent the sphere's horizontal velocity and vertical velocity as functions of time t ?
B
A solid disk whose plane is parallel to the ground spins with an initial angular speed w0. Three identical blocks are dropped onto the disk at locations A, B, and C, one at a time, not necessarily in that order. Each block instantaneously sticks to the surface of the disk, slowing the disk's rotation. Based on the data presented in the graph, which of the following lists the points in the order in which the blocks are dropped onto the disk? (A) A, B, C (B) B, C, A (C) C, A, B (D) B, A, C The blocks are now dropped in the reverse order and the final angular speed of the disk is w2. How does w2 compare to w1, the final angular speed shown on the graph from the initial experiment? (A) w2 1 < w (B) w2 1 = w (C) w2 1 > w (D) The final angular speed cannot be compared without knowing the distances from the disk's center to points A, B, and C.
B, D
A block of mass 2.0 kg, starting from rest, is pushed with a constant force across a horizontal track. The position of the block as a function of time is recorded, and the data are shown in the table. What is the magnitude of the change in momentum of the block between zero and 4.0 seconds? (A) 0.8 kg·m/s (B) 1.2 kg·m/s (C) 1.6 kg·m/s (D) 3.2 kg·m/s
C
A box experiences a varying net force that changes its velocity. The graph shows the velocity of the box as a function of time. Which of the following correctly describes the net work, Wnet, done on the box for the given intervals of time? Between 0 and t_1: Between 1_t and t_2: Between t2 and t3: (A) W > 0 net W 0 net = W 0 net < (B) W 0 net = W > 0 net W > 0 net (C) W 0 net = W 0 net = W 0 net < (D) W > 0 net W > 0 net W > 0
C
A launcher with mass m1 is suspended from the ceiling by a string, as shown. A block with mass m2 1 < m is launched horizontally. At the moment of launch, the block has unknown speed v2 and the launcher has unknown speed v1 in the opposite direction. Which of the following is a true statement about the forces exerted between the launcher and block? (A) The launcher exerts a greater force on the block than the block exerts on the launcher. (B) The block exerts a greater force on the launcher than the launcher exerts on the block. (C) The block and the launcher exert forces of equal magnitude on each other. (D) The relative magnitude of the force exerted on the spring by the block and launcher cannot be determined without knowing v1 and v2.
C
A platform is initially rotating on smooth ice with negligible friction, as shown at left in the figure. A stationary disk is dropped directly onto the center of the platform. A short time later, the disk and platform rotate together at the same angular velocity, as shown at right in the figure. How does the angular momentum of only the platform change, if at all, after the disk drops? What is a justification for your answer? (A) It decreases. The top disk exerts a torque on the platform. (B) It decreases. The potential energy of the platform-disk-Earth system decreases when the disk drops. (C) It stays the same. Angular momentum is a conserved quantity. (D) It stays the same. The torques that the disk and platform exert on each other are equal in magnitude but in opposite directions.
C
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 above. How does the momentum of the cart change during the time interval 0 s to 20 s ? (A) The momentum increases in magnitude during the entire time interval. (B) The momentum decreases in magnitude during the entire time interval. (C) The momentum increases in magnitude at first, then decreases and reverses direction. (D) The momentum increases in magnitude at first, then decreases without reversing direction.
C
A toy doll and a toy robot are standing on a frictionless surface facing each other. The doll has a mass of 0.20 kg, and the robot has a mass of 0.30 kg. The robot pushes on the doll with a force of 0.30 N. The magnitude of the acceleration of the robot is (A) zero (B) 0.60 m/s2 (C) 1.0 m/s2 (D) 1.5 m/s2
C
An object is initially at rest. A varying force is applied to the object as shown in the graph. Which of the following correctly explains the momentum of the object at time t = 7 s ? (A) The final momentum of the object is negative because the slope of the graph is negative the entire time from t = 0 s to t = 7 s. (B) The final momentum of the object is positive because the maximum magnitude of the force in the positive direction is twice the maximum magnitude of the force in the negative direction. (C) The final momentum of the object is negative because the magnitude of the area bounded by the graph and the horizontal axis is less from t = 0 s to t = 2 s than from t = 2 s to t = 7 s. (D) The final momentum of the object is positive because the average magnitude of the force is higher from t = 0 s to t = 2 s than the average magnitude of the force from t = 2 s to t = 7 s.
C
Three blocks are pushed along a rough surface by a force with magnitude P, as shown above. FC is the magnitude of the contact force between blocks 2 and 3, and Ff, FN, and FG are the magnitudes of the friction, normal, and gravitational forces on block 3, respectively. Which of the following is a correct free-body diagram for block 3 ?
C
Two identical blocks are connected by a lightweight string that passes over a lightweight pulley that can rotate about its axle with negligible friction. The two-block system is released from rest and the blocks accelerate. Which of the following correctly relates the potential energy gained by the block 1-Earth system ∆ U1 to the potential energy lost by the block 2-Earth system ∆ U2 and provides correct evidence? (A) ∆ U1 2 = ∆ U , because both blocks travel the same distance. (B) ∆ U1 2 = ∆ U , because both blocks gain the same amount of kinetic energy. (C) ∆ U1 2 < ∆ U , because the two-block system gains kinetic energy. (D) ∆ U1 2 < ∆ U , because the tension exerted on block 1 by the string is less than the tension exerted on block 2 by the string.
C
. A student is asked to move a box from ground level to the top of a loading dock platform, as shown in the figures above. 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? (A) Lifting the box straight up, because it requires a larger applied force to lift it straight up (B) Pushing the box up the incline, because the force is applied for a longer distance (C) Lifting the box straight up, because the incline acts as a simple machine and reduces the force required (D) 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
D
A box of mass m slides up a ramp with initial velocity +v0. The kinetic friction force on the box has magnitude f . Which of the following is a correct equation that could be used to determine the acceleration a of the box? (A) −f = ma (B) mg sin q − f = ma (C) f − mg sin q = ma (D) − −f mg sin q = ma
D
An amusement park ride consists of a large vertical wheel of radius R that rotates counterclockwise on a horizontal axis through its center, as shown above. The cars on the wheel move at a constant speed v. Points A and D represent the position of a car at the highest and lowest point of the ride, respectively. A person of weight Fg sits upright on a seat in one of the cars. As the seat passes point A, the seat exerts a normal force with magnitude 0.8Fg on the person. While passing point A, the person releases a small rock of mass m, which falls to the ground without hitting anything. Which of the following best describes the passenger's linear and angular velocity while passing point A ? Linear Velocity: Angular Velocity: (A) Constant Changing (B) Constant Constant (C) Changing Changing (D) Changing Constant
D
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? (A) 10 3 N, directed northwest (B) 10 3N, directed southeast (C) 10 2N, directed northwest (D) 10 2N, directed southeast
D
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 free-body diagrams could represent the forces exerted on the object?
D
In Figure 1, cart Y is connected to cart X by a tight string and is also connected to the hanging block of mass m0 by a light string that passes over a pulley. Figure 2 shows a system that is identical except for one change: cart Y and X are connected by a spring at its equilibrium length. Both systems are released from rest. Is the hanging block's acceleration as a function of time the same in both systems, and why or why not? (A) Yes, because the net external force exerted on both systems is the same. (B) Yes, because the tension in the string connecting the block to cart Y is determined by the masses of cart Y and the block. (C) No, because the net external force exerted on each system is different. (D) No, because the tension in the string connected to the block is constant in one system but not in the other.
D
Sphere 1 of mass m and sphere 2 of mass 2m hang from light strings. Sphere 1 is pulled back, as shown above, and released from rest. Sphere 1 has kinetic energy Ki immediately before colliding with sphere 2. The two spheres stick together and move horizontally for an instant after the collision. During the collision, what is the change in the kinetic energy ΔK of the two-sphere system? (A) 0 (B) -K/3 (C) − K/2 D) -2K/3
D
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 above. 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? (A) M and v only (B) M , v, and h (C) R and h (D) R, M , and v
D
Three blocks, A, B, and C, are pushed by a constant force F that is applied on block A as shown. There is negligible friction between the blocks and the surface. When a small object is attached to the top of block B, the normal force between blocks A and B is FAB and the normal force between blocks B and C is FBC. How will the values of FAB and FBC change if the small object is moved to the top of block C and the experiment is repeated? F_AB: F_BC: (A) Increases Stays the same (B) Decreases Increases (C) Stays the same Decreases (D) Stays the same Increases
D
Three spheres, with masses indicated above, 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 above. What is the new gravitational potential energy of the three-sphere system? (A) −Gm^2/r (B) -2Gm^2/r (C) -4Gm^2/r (D) -5Gm^2/r
D
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? (A) The force exerted by A on B will be twice as great as the force exerted by B on A, because A has twice the mass of B. (B) The force exerted by A on B will be half as great as the force exerted by B on A, because A has half the speed of B. (C) The forces exerted by each object on the other are the same, because the product of mass and speed is the same for both objects. (D) The forces exerted by each object on the other are the same, because interacting objects cannot exert forces of different magnitude on each other.
D
