AP Physics Final Exam Question Bank and Answer

A simple pendulum consisting of a small object of mass m attached to a string of length l has a period T. A pendulum with which of the following combinations of object mass and string length will also have period T ?

(A. Answer in Picture)

A pendulum consisting of a sphere suspended from a light string is oscillating with a small angle with respect to the vertical. The sphere is then replaced with a new sphere of the same size but greater density and is set into oscillation with the same angle. How do the period, maximum kinetic energy, and maximum acceleration of the new pendulum compare to those of the original pendulum?

(D. Answer in the Picture)

An object slides across a horizontal surface such that it slows down due to the force of friction that is exerted on the object. The object and the direction of its displacement are shown in the figure. Which of the following free-body diagrams could represent the forces that are exerted on the object?

A.

An object of mass M hangs from a string that is looped around a pulley of negligible friction, as shown. The pulley has a mass 0.5M. The object is released from rest and it falls to the floor at time t1. Which of the following pairs of graphs best represents the angular speed as a function of time for the pulley and the vertical speed as a function of time for the falling object for a short time after it is released from rest?

A. (You know the two graphs)

A block of mass 0.4kg on a horizontal surface is attached to a horizontal spring of negligible mass. The other end of the spring is attached to a wall, and there is negligible friction between the block and the horizontal surface. The block-spring system then experiences simple harmonic motion as described by the graph. The maximum spring potential energy of the block-spring system is most nearly

A. 0.2 J

A toy cannon of mass 1.0 kg is initially at rest on a horizontal surface when it launches a 0.05 kg projectile with a velocity of 10 m/s at an angle of 60° above the horizontal. What is the speed of the 1.0 kg cannon immediately after the projectile is released, assuming that friction is negligible?

A. 0.25 m/s

The free body diagram shown above is for a 5 kg box on a rough surface being pulled to the right at a constant speed by a string that is at an angle of 30°above the horizontal. The coefficient of kinetic friction between the box and the surface is 0.30. The tension in this string is most nearly

A. 14.47N

The table shows experimental data of the magnitude of four forces exerted on a 2kg object as it slides across a horizontal surface. Which of the following could represent the magnitude of the net force that is exerted on the object? Select two answers.

A. 6N B. 10N

A net force is applied to the edge of a disk that has a diameter of 0.5m. The disk is initially at rest. A graph of the net force as a function of time for the edge of the disk is shown. The net force is applied tangent to the edge of the disk. How can a student use the graph to determine the change in angular momentum of the disk after 8s? Justify your selection.

A. Determine the vertical intercept, multiply the result by 0.25m, and then multiply that result by 8s. This procedure can be used because ΔL=τΔt with τ=rF.

A student must determine a nonzero change in momentum of an object for a specific interval of time. Which of the following experiments could the student conduct? Select two answers.

A. Drop a ball of known mass above a motion detector, and record the final speed of the ball before it reaches the motion sensor. D. Give a block of known mass an initial velocity so that it slides across a rough surface in front of a motion detector, slows down, and eventually stops. Use the motion detector to record the initial velocity of the block.

A disk of radius R=0.5cm rests on a flat, horizontal surface such that frictional forces are considered to be negligible. Three forces of unknown magnitude are exerted on the edge of the disk, as shown in the figure. Which of the following lists the essential measuring devices that, when used together, are needed to determine the change in angular momentum of the disk after a known time of 5.0s?

A. Force Probe and Protractor

A rocket is continuously firing its engines as it accelerates away from Earth. For the first kilometer of its ascent, the mass of fuel ejected is small compared to the mass of the rocket. For this distance, which of the following indicates the changes, if any, in the kinetic energy of the rocket, the gravitational potential energy of the Earth-rocket system, and the mechanical energy of the Earth-rocket system?

A. Increasing, Increasing, Increasing

An object is released from a large height above the ground and takes a very long time to reach the ground. The only forces exerted on the object are the force of Earth's gravity and the force of friction exerted by Earth's atmosphere as the object falls. A graph of the object's speed V as a function of time T is shown above. Which of the following claims best describes the force of friction exerted on the object?

A. It is initially zero and increases until it is equal to the force of gravity.

A block on a horizontal surface is attached to a horizontal spring of negligible mass and spring constant k0. The other end of the spring is attached to a wall. When the spring is unstretched, the block is located at x=0m, as shown in Figure 1. The block is then pulled to x=0.3m and released from rest so that the block-spring system oscillates between x=−0.3m and x=0.3m. A student creates the graph shown in Figure 2, which shows the kinetic energy of the block-spring system as a function of the block's position. Which of the following mathematical routines can a student use, if at all, to determine the approximate change in the spring potential energy of the block-spring system when the block is moved from a position of x=0.00m to x=0.02m ?

A. Subtract the kinetic energy of the block at x=0.02m from the kinetic energy of the block at x=0.00m.

A block of mass M on a horizontal surface is attached to a horizontal spring of negligible mass. The other end of the spring is attached to a wall, and there is negligible friction between the block and the horizontal surface. When the block is pulled to a position beyond the spring's natural length and released from rest, the block experiences simple harmonic motion. A graph of the force exerted on the spring as a function of the block's position is shown. A student collects data such that the force that the spring exerts on the block for every 0.25s is plotted on the graph that is shown. Which two of the following claims is correct about the block-spring system during the time in which data were collected? Select two answers.

A. The block has its maximum acceleration at all times 0.5n, where n is a zero or a whole number. B. The block has maximum spring potential energy at all times 0.5n, where n is a zero or a whole number.

A block of mass 0.10kgis attached and secured to one end of a spring with spring constant 50Nm. The other end of the spring is secured to a wall. The block is pushed against the spring, which compresses the spring to a position of x=−0.04m. When uncompressed, the end of the spring that is attached to the block is at a position of x=0.00m. The block-spring system is then released from rest, and the block travels along a horizontal, rough track. A motion sensor is placed so that it measures the velocity of the object as it slides along the track. A graph of total mechanical energy of the block-spring system as a function of position is shown. Which of the following statements about the block-spring system are true? Select two answers.

A. The force exerted on the block by the spring at x=−0.02m is 1 N. D. The work done by friction as the block travels from x =−0.04m to x= −0.02m is 0.010J.

An object travels down a ramp at a constant acceleration. The object experiences a force of friction and a gravitational force. Which of the following could be true about the motion of the object?

A. The force of friction between the surface and the object is less than the component of the gravitational force that is parallel to the ramp.

A ball is moved from Earth to a planet that has a gravitational acceleration that is double that of Earth. How does the gravitational force on the ball when it is on the new planet compare to the gravitational force on the ball when it is on Earth?

A. The gravitational force on the ball when it is on the new planet is double the force on the ball when it is on Earth.

A sphere of mass m1, which is attached to a spring, is displaced downward from its equilibrium position as shown above left 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 above 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?

A. The maximum kinetic energy is attained as the sphere passes through its equilibrium position.

A uniform rod is at rest on a horizontal surface. A student may launch a sphere of clay toward the rod along one of the three paths shown in the figure. Path X and path Z are directed toward the center of mass of the rod. In each case, the sphere of clay is launched with the same linear speed and sticks to the rod. In each case, the time of collision between the sphere of clay and the rod is time t0. A pivot is fixed to the end of the rod, representing the point at which the rod or clay-rod system may rotate. Frictional forces are considered to be negligible. Consider the situation in which three identical spheres of clay are launched simultaneously, one along each possible path. All three spheres of clay are launched with the same initial linear speed and collide with the rod at the same time. The time of collision with the rod for each sphere is time t0. Which of the following predictions is correct about the motion of the system containing the rod and all three spheres of clay immediately after the collision?

A. The system will rotate in the clockwise direction with a constant angular speed.

A disk is fixed to a horizontal axle that extends between two supports, as shown in the figure. Frictional forces between the axle and the supports is not negligible. At time ts, the disk rotates about the center axle with an initial angular speed wd. A student measures the angular displacement Δθ0 of a point on the edge of the disk from time ts until the disk no longer rotates. The angular acceleration of the disk is determined to be αdαd, and this value remains constant. Based on the data, if possible, how could the student predict the angular displacement of a point on the edge of the disk from time ts until the disk no longer rotates if the initial angular speed is increased to 2ωd ? Justify your selection.

A. Use the equation ω2=ω20+2α(θ−θ0), because the disk comes to rest, ω0=2ωd, and α=αd. Solve for θ−θ0.

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?

D. 1/2 mv20 +mgh

In an experiment, one end of a light string is attached and wrapped around a pulley of diameter 0.5⁢ m. The other end of the string is connected to a block of mass 0.5 kg. The block is released from rest, and the pulley begins to spin in the counterclockwise direction, as shown in Figure 1. Students collect the necessary data to create the graph of the magnitude of the angular momentum of the pulley as a function of time shown in Figure 2. The students state that the graph shows that the net torque exerted on the pulley is constant. Do the data from the graph support the students' statement? Justify your selection.

A. Yes, because the slope of the best-fit line is constant.

During an experiment, students collect data about the angular momentum of a rigid, uniform spinning wheel about an axle as a function of time, which was used to create the graph that is shown. A frictional torque is exerted on the wheel. A student makes the following statement about the data. "The frictional torque exerted on the wheel is independent of the wheel's angular speed." Does the data from the graph support the student's statement? Justify your selection.

A. Yes, because the slope of the line is constant.

A block of mass 0.5kg on a horizontal surface is attached to a horizontal spring of negligible mass and spring constant 50N/m. The other end of the spring is attached to a wall, and there is negligible friction between the block and the horizontal surface. When the spring is unstretched, the block is located at x=0m. The block is then pulled to x=0.3m and released from rest so that the block-spring system oscillates between x=−0.3m and x=0.3m. What is the magnitude of the acceleration of the block and the direction of the net force exerted on the block when it is located at x=0.3m?

B. (30m/s Negative)

A block of mass M on a horizontal surface is attached to a horizontal spring of negligible mass. The other end of the spring is attached to a wall, and there is negligible friction between the block and the horizontal surface. The object is displaced from the object-spring's equilibrium position and released from rest so that the system oscillates. A student collects data about the object's horizontal displacement x, velocity vx, acceleration ax, and the net force Fx exerted on the object as the object oscillates. Which of the following graphs, with appropriate evidence, could the student be able to create from the data to explain that the object undergoes simple harmonic motion?

B. (Answer In Picture)

An object initially at rest falls from a height H until it reaches the ground. Two of the following energy bar charts represent the kinetic energy K and gravitational potential energy Ug of the object-Earth system at two positions. The first position is when the object is initially released, and the second position is when the object is halfway between its release point and the ground. Which two charts could represent the mechanical energy of the object-Earth system? Select two answers.

B. (Answer is Picture)

The figure above shows the net force exerted on an object as a function of the position of the object. The object starts from rest at position x = 0 m and acquires a speed of 3.0 m / s after traveling a distance of 0.090 m. What is the mass of the object?

B. 0.030 kg

A block of mass M on a horizontal surface is attached to a horizontal spring of negligible mass and spring constant 20N/m. The other end of the spring is attached to a wall, and there is negligible friction between the block and the horizontal surface. When the block is pulled to a position beyond the spring's natural length and released from rest, the block experiences simple harmonic motion. A graph of the force exerted on the spring as a function of the block's position is shown. What is the spring potential energy stored in the spring-block system at position B?

B. 0.4 J

A block of mass M is launched by a spring of negligible mass along a horizontal surface of negligible friction. The spring constant of the spring is k. The spring is initially compressed a distance x0. The block is released from rest. Some time after the block is released and travels in the direction shown in the figure, the spring compression is xf. Which of the following mathematical calculations can a student use to determine the speed Vf of the block at this new position?

B. 1/2kx20=1/2kx2f+1/2mv2f. Solve for vf.

A rod may freely rotate about an axis that is perpendicular to the rod and is along the plane of the page. The rod is divided into four sections of equal length of 0.2m each, and four forces are exerted on the rod, as shown in the figure. Frictional forces are considered to be negligible. Which of the following correctly describes an additional torque that must be applied in order to keep the rod from rotating?

B. 18N⋅m counterclockwise

A block on a horizontal surface is attached to a horizontal spring of negligible mass, as shown in Figure 1. The other end of the spring is attached to a wall, and there is negligible friction between the block and the horizontal surface. A group of students wants to investigate how stretching the spring within the block-spring system influences the motion of the system. For each trial of an experiment, the spring is stretched a variable distance Δx from its natural spring length, as shown in Figure 2, and blocks of different mass may be used. The block is then released from rest, and the system is allowed to oscillate. Figure 3 shows the horizontal position of the block as a function of time for one trial of the experiment. At which of the following times does the spring exert its maximum force on the block?

B. 2.0s

A student attaches a 0.6kg block to a vertical spring so that the block-spring system will oscillate if the block-spring system released from rest at a vertical position that is not the system's equilibrium position. The student measures the velocity of the block as a function of time as the system oscillates, as shown in the graph. The spring constant of the spring is most nearly

B. 2.6 N/m

A block on a horizontal surface is attached to a horizontal spring of negligible mass, as shown in Figure 1. The other end of the spring is attached to a wall, and there is negligible friction between the block and the horizontal surface. A group of students wants to investigate how stretching the spring within the block-spring system influences the motion of the system. For each trial of an experiment, the spring is stretched a variable distance Δx from its natural spring length, as shown in Figure 2, and blocks of different mass may be used. The block is then released from rest, and the system is allowed to oscillate. Figure 3 shows the horizontal position of the block as a function of time for one trial of the experiment. In one experiment, the students allow the block to oscillate after stretching the spring a distance A. If the potential energy stored in the spring is U0, then what is the change in kinetic energy of the block after it is released from rest and has traveled a distance of A/2 ?

B. 3/4 Uo

During an experiment a student records the net horizontal force exerted on an object moving in a straight line along a horizontal frictionless track. The graph above shows the force as a function of time. Of the following, which is the best approximation of the magnitude of the change in momentum of the object between 0 s and 4 s?

B. 30 kg ⋅ m/s

An Atwood's machine is set up by suspending two blocks connected by a string of negligible mass over a pulley, as shown above. The blocks are initially held at rest and then released at time t0=0 s. The speed of the 3 kg block at time t1=2.0s is most nearly

B. 4.0m/s

In experiment 1, a block of mass M is attached to the end of vertical spring of spring constant k0 with its free end at vertical position L0, as shown in Figure 1. The mass of the spring is considered to be negligible. When the block is attached to the spring and is at rest at the block-spring's equilibrium position, the spring is stretched so that its end is at a new position L1, as shown in Figure 2. The block is then pulled down to a new vertical position L2 and then released from rest so that the block-spring system oscillates. Assume that the reference line for zero gravitational potential energy of the system is at the lowest point in the system's vertical displacement from equilibrium. The experiment is assumed to be performed near Earth's surface. A student is asked to perform experiment 1, but with a spring of an unknown spring constant. The student performs four trials of the experiment with blocks of different mass and collects the data that are shown in the table. How should the student graphically analyze the data in order to determine the spring constant of the spring?

B. Create a graph with the period of oscillation plotted on the vertical axis and the square root of the mass of the block plotted on the horizontal axis. Use the slope of the best-fit line to determine the spring constant.

A point on the edge of a disk rotates around the center of the disk with an initial angular velocity of 3rad/s clockwise. The graph shows the point's angular acceleration as a function of time. The positive direction is considered to be counterclockwise. All frictional forces are considered to be negligible. How can the graph be used to determine the angular speed of the disk after 2s? Justify your selection.

B. Determine the area bound by the line and the horizontal axis from 0s to 2s , because this area represents the change in the angular velocity of the point on disk.

A student is conducting an experiment to analyze the mechanical energy of a block-spring system. The student places a block of mass 2kg on a horizontal surface and attaches the block to a horizontal spring of negligible mass and spring constant 100N/m, as shown in the figure. There is negligible friction between the block and the horizontal surface. The other end of the spring is attached to a wall. The block-spring system is initially at the spring's equilibrium position. Based on data collected from the experiment, the student creates the graph that shows the force exerted on the spring as a function of the distance the spring is compressed. How can the student use the data to experimentally determine the work done on the spring by the block?

B. Determine the area bound by the line of best fit through the data and the horizontal axis from 0.0 m to 1.0 m.

A group of students must conduct an experiment to determine how the location of an applied force on a classroom door affects the rotational motion of the door. The rotational inertia of the door about its hinges is known. The initial angular velocity of the door is zero. The students conduct the experiment and gather data about the net torque exerted on the door and angular acceleration of the door for several trials. They create a graph of the door's angular acceleration as a function of the net torque and sketch a best-fit line through the data. How can the students analyze the data to determine the rotational inertia of the door about its hinges?

B. Determine the inverse of the slope of the best-fit line.

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 momentum of the object is increasing in which of the cases?

B. III only

A student must use an object attached to a string to graphically determine the gravitational field strength near Earth's surface. The student attaches the free end of the string to the ceiling and pulls the object-string system so that the string makes an angle of 5 degrees from the object's vertical hanging position. The student then releases the object from rest and uses a stopwatch to measure the time it takes for the object to make one complete oscillation. Which of the following is the next step that will allow the student to determine the gravitational field strength?

B. Repeat the experiment by changing the length of the string for multiple trials.

A student attaches a block to a vertical spring so that the block-spring system will oscillate if the block-spring system is released from rest at a vertical position that is not the system's equilibrium position. Which of the following measuring tools, when used together, can be used to determine the spring constant of the spring? Select two answers.

B. Stopwatch C. Electronic Balance

The system shown above consists of two identical blocks that are suspended using four cords, each of a different length. Which of the following claims are true about the magnitudes of the tensions in the cords? Select two answers.

B. T1 cos30°=T2 cos60° C. T3>T4

The surface of an incline is coated with an experimental substance that is intended to reduce the frictional force between a block and the surface of the incline. A 2 kg block is placed at the top of the incline at a height of 1.8 m, as shown in the figure. After the block is released from rest, the block slides down the incline and a motion detector at the bottom of the incline measures the block's speed as 5.8m/s after the block is no longer on the incline. Which of the following claims is correct about the experimental substance?

B. The experimental substance did not reduce all the frictional force because some of the gravitational potential energy of the Earth-block system at the top of the incline was converted into nonmechanical energy.

A block of mass M hangs at rest at the bottom of a stationary spring that stretches a distance A from the spring's unstretched length. The block is then pulled down an additional distance AA so the spring is stretched a distance 2A , as shown in the figure. The block is released from rest, and the center of mass of the block vertically oscillates a displacement of 2A from its lowest position to its highest position. The lowest vertical position of the block's center of mass is the location at which the gravitational potential energy of the block-spring-Earth system is zero. Which two of the following claims are correct about the mechanical energy of the system? Select two answers.

B. The kinetic energy of the block is at its maximum when the spring is stretched a distance A from its unstretched length. C. The potential energy of the system is at its maximum when spring is stretched a distance 2A from its unstretched length.

A block of mass M is at rest on a ramp that is inclined at an angle θ with respect to the horizontal. Frictional forces are considered to be nonnegligible. The block is pushed against a spring and then held in place. The spring is compressed a distance of x1, and the spring is not secured to the block. The block is then released from rest, travels up the incline, and comes to rest after traveling a distance D, as shown above. Which of the following claims correctly describes the energy of the system under consideration from when the block compressed the spring and when the block has traveled a distance D along the incline? Select two answers.

B. The mechanical energy of the system consisting of the block does not change. C. The mechanical energy of the system consisting of the block and Earth increases by more than zero but less than 1/2kx21.

The gravitational field strength near Jupiter's surface is nearly 2.53 times greater than the gravitational field strength near Earth's surface. Which of the following claims is correct about the period of a pendulum if it oscillates near Jupiter's surface and near Earth's surface?

B. The period of the pendulum will be greater on Earth.

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 above. The frequency of oscillation is most nearly

D. 2.0 Hz

A person applies an impulse of 5.0 kg∙m/s to a box in order to set it in motion. If the person is in contact with the box for 0.25 s, what is the average force exerted by the person on the box?

D. 20.0N

A block of mass 1.0kg on a horizontal surface is attached to a horizontal spring of negligible mass and spring constant 100N/m. The other end of the spring is attached to a wall, and there is negligible friction between the block and the horizontal surface. When the spring is unstretched, the block is located at x=0m. The block is then pulled to x=0.5m and released from rest so that the block-spring system oscillates between x=−0.5m and x=0.5m, as shown in the figure. Which of the following descriptions about the system are correct? Select two answers.

B. The spring potential energy of the system at x=0.25m is nearly 3.13 J. D. The sum of the spring potential energy of the system and the kinetic energy of the block at x=0.4m is nearly 12.5J.

A student predicts that a block sliding down a ramp inclined at 45 degrees should have an acceleration of approximately 7 m/s2. The block is released from rest, and the student measures the distance the block travels and the time it takes to travel that distance. The student determines that the block's acceleration is only 5.5 m/s2. Which of the following is the most likely reason for the difference between the predicted and calculated accelerations?

B. The student's model used to make the prediction did not account for all of the forces that are exerted on the block.

A student attaches a block to a vertical spring so that the block-spring system will oscillate in simple harmonic motion if the system is released from rest at a vertical position that is not the system's equilibrium position. Which of the following explanations is correct about why the system oscillates in simple harmonic motion about the block-spring system's equilibrium position?

B. The system oscillates in simple harmonic motion because the block's acceleration is directly proportional to and opposite in direction to the block's displacement from the system's equilibrium position.

Students work together during an experiment about Newton's laws. The students use a setup that consists of a cart of known mass connected to one end of a string that is looped over a pulley of negligible friction, with its other end connected to a hanging mass. The cart is initially at rest on a horizontal surface and rolls without slipping when released. The inertia of the cart's wheels is negligible. Students have access to common laboratory equipment to make measurements of components of the system. The students double the mass that hangs from the string. They also replace the original cart with a new cart that has double the mass. By doubling both masses, how will the tension in the string and the acceleration of the cart change?

B. The tension will double, but the acceleration will stay the same.

Three different experiments are conducted that pertain to the oscillatory motion of a pendulum. For each experiment, the length of the pendulum and the mass of the pendulum are indicated. In all experiments, the pendulum is released from the same angle with respect to the vertical. The pendulum in Experiment 2 is released from rest at an angle of θ0 with respect to the vertical. What is the magnitude of the change in kinetic energy of the pendulum from its lowest point to the highest point along its arc?

D. 2Mg(L−Lcosθ0)

A uniform rod is at rest on a horizontal surface. A student may launch a sphere of clay toward the rod along one of the three paths shown in the figure. Path X and path Z are directed toward the center of mass of the rod. In each case, the sphere of clay is launched with the same linear speed and sticks to the rod. In each case, the time of collision between the sphere of clay and the rod is time t0. A pivot is fixed to the end of the rod, representing the point at which the rod or clay-rod system may rotate. Frictional forces are considered to be negligible. A sphere of clay travels toward the rod along path Z. A student must predict what will happen to the linear momentum and the angular momentum of the rod-sphere system as a result of the collision. Which of the following correctly predicts the change, if any, of these quantities?

C. (Decreases, No Change)

A point on a disk rotates around the center axle of the disk. The table shows the angular speed of the point as a function of time. Which of the following graphs could represent the angular position of the point as a function of time?

C. (Downward Curve)

A group of students must study the oscillatory motion of a pendulum. One end of a light string is attached to the ceiling, and the other end of the string is attached to a mass hanger so that small disks of various masses may be stacked on the hanger, as shown in the figure. Students are provided with data in which an experiment was conducted to determine the relationship between the length of the pendulum and the period of oscillation. The data include a pendulum of length 0.5m, for which it took 81s for the pendulum bob to oscillate 10 times. However, the experiment was conducted at a location that is not near Earth's surface. The gravitational field strength where the experiment was conducted is most nearly

C. 0.30 N/kg

A student attaches a block to a horizontal spring so that the block-spring system will oscillate if the block-spring system released from rest at a horizontal position that is not the system's equilibrium position. The student creates a graph of the block-spring system's kinetic energy as a function of time, as shown. The spring potential energy of the block-spring system at 5.0s is most nearly

C. 0.73 J

A cart of mass 2.0kg on a horizontal surface is attached to a horizontal spring of negligible mass. A 1.0kg block is secured on top of the of the 2.0kg cart. The other end of the spring is attached to a wall, and there is negligible friction between the cart-block-spring system and the horizontal surface. The cart-block-spring system then experiences simple harmonic motion as described by the graph that shows the velocity of the cart-block system as a function of time. The maximum spring potential energy of the cart-block-spring system is most nearly

C. 0.96 J

The graph above shows velocity v as a function of time t for a 0.50 kg object traveling along a straight line. The graph has three segments labeled 1, 2, and 3. A rope exerts a constant force of magnitude FT on the object along its direction of motion the whole time. During segment 2 only, a frictional force of magnitude Ff is also exerted on the object. For another identical object initially at rest, no frictional force is exerted during segment 2 (between t = 2 s and t = 4 s). A rope exerts the same constant force of magnitude FT as in the previous scenario. What is the change in the object's kinetic energy during segment 2?

C. 12.0 J

A ball of mass 0.4 kg is initially at rest on the ground. It is kicked and leaves the kicker's foot with a speed of 5.0 m/s in a direction 60° above the horizontal. The magnitude of the impulse imparted by the ball to the foot is most nearly

C. 2 N▪s

A 0.5 kg pendulum bob is raised to 1.0 m above the floor, as shown in the figure above. The bob is then released from rest. When the bob is 0.8 m above the floor, its speed is most nearly

C. 2 m/s

A rod is initially at rest on a rough horizontal surface. Three forces are exerted on the rod with the magnitudes and directions shown in the figure. The force exerted in the center of the rod is an equidistant 0.5m from both ends of the rod. If friction between the rod and the table prevents the rod from rotating, what is the magnitude of the torque exerted on the rod about its center from frictional forces?

C. 20 N*M

A block on a horizontal surface is attached to a horizontal spring of negligible mass and spring constant 30N/m. The other end of the spring is attached to a wall, and there is negligible friction between the block and the horizontal surface. The block-spring system experiences simple harmonic motion, as shown in the graph. What is the change in spring potential energy of the block-spring system from when the block is released to when the block has its greatest speed?

C. 240 J

A point on the edge of a disk rotates around the center of the disk with an initial angular velocity of 3rad/s clockwise. The graph shows the point's angular acceleration as a function of time. The positive direction is considered to be counterclockwise. All frictional forces are considered to be negligible. What is the angular displacement of the point after 10s?

C. 270 radians

In experiment 1, a block of mass M is attached to the end of vertical spring of spring constant k0 with its free end at vertical position L0, as shown in Figure 1. The mass of the spring is considered to be negligible. When the block is attached to the spring and is at rest at the block-spring's equilibrium position, the spring is stretched so that its end is at a new position L1, as shown in Figure 2. The block is then pulled down to a new vertical position L2 and then released from rest so that the block-spring system oscillates. Assume that the reference line for zero gravitational potential energy of the system is at the lowest point in the system's vertical displacement from equilibrium. The experiment is assumed to be performed near Earth's surface. What is the magnitude of the change in potential energy of the block-spring system when it travels from its lowest vertical position to its highest vertical position?

C. 2kgL1L2

An object of mass 10 kg is released from rest above the surface of a planet such that the object's speed as a function of time is shown by the graph above. The force due to gravity exerted on the object is most nearly

C. 35N

A block of mass 0.5kg on a horizontal surface is attached to a horizontal spring of negligible mass and spring constant 50N/m. The other end of the spring is attached to a wall, and there is negligible friction between the block and the horizontal surface. When the spring is unstretched, the block is located at x=0.0 m. The block is then pulled to x=0.5 m and released from rest so that the block-spring system oscillates between x=−0.5 m and x=0.5 m, as shown in figure 1. A free-body diagram of the object at a particular location is shown in figure 2. Based on the free-body diagram, at which of the following locations could the block be?

C. Between positions x=0.0 m and x=0.5 m

A block on a horizontal surface is attached to a horizontal spring of negligible mass, as shown in Figure 1. The other end of the spring is attached to a wall, and there is negligible friction between the block and the horizontal surface. A group of students wants to investigate how stretching the spring within the block-spring system influences the motion of the system. For each trial of an experiment, the spring is stretched a variable distance Δx from its natural spring length, as shown in Figure 2, and blocks of different mass may be used. The block is then released from rest, and the system is allowed to oscillate. Figure 3 shows the horizontal position of the block as a function of time for one trial of the experiment. The students must conduct an experiment to determine the magnitude of the force exerted on the block when the block is at a position of A/2, where A is the amplitude of oscillation for the block-spring system. For each trial, the students attach blocks of different mass mm to the spring, stretch the spring a known distance A, release the system from rest, measure the period of oscillation T, and then measure the maximum velocity vv of the system. How should students use a graph to determine the magnitude of the force under consideration?

C. Determine the magnitude of the slope of the best-fit line of T^2 as a function of m. Multiply the result by A/2.

An object is in simple harmonic motion. Of the following quantities related to the object, which set of three can have maximum magnitudes at the same instant of time? I. Displacement II. Velocity III. Acceleration IV. Kinetic energy V. Potential energy

C. I, III, and V

Student Y is at rest while sitting on a swing. Student X stands behind student Y and provides an initial applied force on student Y. Student Y's position on the swing then oscillates. Which of the following claims is correct about student Y?

C. If student X applies a greater force on student Y, the total mechanical energy of the student Y-Earth system will increase compared to the original situation.

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?

C. K/2

Which of the following is true of the conservation of momentum and kinetic energy?

C. Kinetic energy is conserved only in elastic collisions.

A student conducts an experiment to test the relationship between the net torque exerted on an object and the change in angular momentum of the object. A variable net torque is exerted on the object to make it rotate about its internal axis. Data from the experiment are used to construct a graph of the net torque exerted on the object as a function of time, as shown in Figure 1. A graph is also created of the angular momentum of the object as a function of time, as shown in Figure 2. Which of the following statements about the change in the object's angular momentum for a given time interval is correct? Justify your selection.

C. The change in the object's angular momentum for a given time interval does not remain the same throughout the experiment. This is because the slope of the best-fit line in Figure 1 is a nonzero constant.

A conveyor belt ramp of length 7m is inclined at 20°with respect to the horizontal and is used to move objects from one location to another location. When an object is placed on the conveyor belt, the object travels up the incline with a constant speed of 1.5 m/s. A motor is used to keep the conveyor belt moving. The mass of the objects that are placed on the conveyor belt are varied. For the system that only includes the object, which of the following claims best describes what happens to the mechanical energy of the system while the object is moving from the bottom of the ramp to the top of the ramp?

C. The mechanical energy of the object is constant because the kinetic energy of the object is constant.

In an experiment, one end of a string is attached to an object of mass M, and the other end of the string is secured so that the object is at rest as it hangs from the string. When the object is raised to a height above its lowest point, the object undergoes simple harmonic motion. Data collected from the experiment is graphed and linearized, as shown. What information from the graph can be used to determine the acceleration due to gravity for an object that is released from rest near Earth's surface and allowed to fall to the ground?

C. The slope of the graph represents the quantity 4π^2/g.

An inclined track is secured to a table. The height of the highest point of the track above the tabletop is h1. The height from the tabletop to the floor is h2. A block of mass M is released from rest and slides down the track such that all frictional forces are considered to be negligible. The block leaves the track horizontally and strikes the ground at a distance D from the edge of the track as shown. Which of the following statements is correct about the scenario? Select two answers.

C. The total mechanical energy of the system containing only the block increases from the moment of release to the moment it strikes the ground. D. The total mechanical energy of the block-Earth system remains constant.

The two blocks of masses M and 2M shown above initially travel at the same speed v but in opposite directions. They collide and stick together. How much mechanical energy is lost to other forms of energy during the collision?

D. 4/3 Mv^2

A block on a horizontal surface is placed in contact with a light spring with spring constant k, as shown in Figure 1. When the block is moved to the left so that the spring is compressed a distance D from its equilibrium length, the potential energy stored in the spring-block system is Em. When a second block of mass 2m is placed on the same surface and the spring is compressed a distance 2d, as shown in Figure 2, how much potential energy is stored in the spring compared to the original potential energy Em? All frictional forces are considered to be negligible.

D. 4Em

A block on a horizontal surface is attached to a horizontal spring of spring constant 50N/m. The other end of the spring is attached to a wall. The block is initially at the equilibrium position of the block-spring system, as shown in the figure. The block is then moved to a position of x=60cm and released from rest so that the system oscillates. A student predicts the kinetic energy of the block-spring system as a function of the block's horizontal position as shown in Graph 1. When an experiment is conducted, the block does not make a complete oscillation because frictional forces were not considered in the student's prediction. Data is collected about the actual kinetic energy of the block-spring system as a function of the block's horizontal position and is used to create Graph 2. How can the student use one or both graphs to determine how much mechanical energy is converted to nonmechanical energy from the instant the block is released from rest to the instant that the block is no longer in motion?

C. Use Graph 2 to determine the spring potential energy stored in the system at the instant the block is no longer in motion. Subtract this value from the maximum predicted kinetic energy of the block that can be determined from Graph 1.

A uniform rod is at rest on a horizontal surface. A student may launch a sphere of clay toward the rod along one of the three paths shown in the figure. Path X and path Z are directed toward the center of mass of the rod. In each case, the sphere of clay is launched with the same linear speed and sticks to the rod. In each case, the time of collision between the sphere of clay and the rod is time t0. A pivot is fixed to the end of the rod, representing the point at which the rod or clay-rod system may rotate. Frictional forces are considered to be negligible. Consider the case in which the sphere of clay is launched along path Y. The sphere of clay is launched with a speed v0 and collides with the rod a distance ll away from the pivot. The length of the rod is L. The rotational inertia of the rod about the joint is IR, and the mass of the sphere of clay is mc. The sphere of clay is considered to be a point mass. What is the angular speed ωf of the clay-rod system immediately after the collision?

C. ωf=mcv0l/mcl^2+IR

A 2kg object is released from rest near and above Earth's surface such that the object-Earth system's gravitational potential energy as a function of time is shown in the graph. Which of the following graphs represents the kinetic energy of the object as a function of time? Assume all frictional forces are considered to be negligible.

D. (Upward Sloping Graph)

A point on the edge of a disk rotates around the center of the disk with an initial angular velocity of 3rad/s clockwise. The graph shows the point's angular acceleration as a function of time. The positive direction is considered to be counterclockwise. All frictional forces are considered to be negligible. Which of the following graphs qualitatively represents the angular velocity ω of the point on the disk as a function of time t between 0s to 2s?

D. (Upward Sloping graph but starts negative)

A group of students must conduct an experiment to determine how the location of an applied force on a classroom door affects the rotational motion of the door. The rotational inertia of the door about its hinges is known. The initial angular velocity of the door is zero. Which of the following lists what measuring devices the students need and the measurements they should take to collect the necessary data to test the relationship between a torque exerted on the door and the change in angular velocity of that object about the hinges of the door? Justify your selection.

D. A stopwatch to measure the time interval during which the force is applied, a force probe to measure the applied force on the door, a protractor to measure the angular displacement of the door, and a meterstick to measure the radial distance from the door's hinges to the location where the force is applied.

Two blocks are connected to identical ideal springs and are oscillating on a horizontal frictionless surface. Block A has mass m, and its motion is represented by the graph of position as a function of time shown above on the left. Block B's motion is represented above on the right. Which of the following statements comparing block B to block A is correct?

D. Because block B has more mass, its acceleration is smaller than that of block A at any given displacement from the equilibrium position.

Block 1 of mass m1 and block 2 of mass m2 are sliding along the same line on a horizontal frictionless surface when they collide at time tc. The graph above shows the velocities of the blocks as a function of time. Which block has the greater mass, and what information indicates this?

D. Block 2, because the final velocity is closer to the initial velocity of block 2 than it is to the initial velocity of block 1.

An experiment is conducted such that an applied force is exerted on a 2kg object as it travels across a horizontal surface. A graph of the net force exerted on the object as a function of the object's distance traveled is shown. How could a student use the graph to determine the work done by the applied force?

D. Calculate the area bound by the line of best fit and the horizontal axis from 0m to 3m.

A net torque is applied to the edge of a spinning object as it rotates about its internal axis. The table shows the net torque exerted on the object at different instants in time. How can a student use the data table to determine the change in angular momentum of the object from 0s to 6s? Justify your selection.

D. Create a graph of net torque as a function of time and graph four points of data by using the table. Determine the area bound by the curve and the horizontal axis from 0s to 6s, because the shape of the curve on the graph will be a right triangle and the area can be directly determined.

A group of students must study the oscillatory motion of a pendulum. One end of a light string is attached to the ceiling, and the other end of the string is attached to a mass hanger so that small disks of various masses may be stacked on the hanger, as shown in the figure. The students perform four experiments, as described. Experiment 1: Determine the relationship between the mass of the pendulum and the period of oscillation. Experiment 2: Determine the relationship between the displacement of the pendulum and the period of oscillation. Experiment 3: Determine the relationship between the period of oscillation and the length of the pendulum. Experiment 4: Determine the relationship between the vertical release height of the hanger-disk system and its speed at the lowest point of its arc. The students collect data to create the graph that is shown, but the horizontal and vertical axes are not labeled. Which experiments could be represented by the graph?

D. Experiment 3 and Experiment 4

A 4.0 kg cube is placed in a container of water. A student observes that the cube floats. The net force exerted on the cube F represents the sum of the force due to gravity and the force exerted on the cube by the water. A force probe is used to measure F as a function of the cube's distance y from the bottom of the container. The graph shows F as a function of y, where the positive direction is upward. Which of the following statements is correct about the motion of the cube if it is released from rest at a vertical position of y=0.05m?

D. The cube will oscillate between y=0.05 m and y=0.09 m.

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?

D. The motion cannot be determined without knowing the speeds of the objects before the collision.

Student X attaches an object of mass M to the end of a string of length L so that a pendulum is constructed. Student Y attaches an object of mass M to a string of length 4L to construct a second pendulum. Which of the following claims correctly compares the period of Student X's pendulum with the period of Student Y's pendulum?

D. The period of Student X's pendulum is half the period of Student Y's pendulum.

In experiment 1, a block of mass M is attached to the end of vertical spring of spring constant k0 with its free end at vertical position L0, as shown in Figure 1. The mass of the spring is considered to be negligible. When the block is attached to the spring and is at rest at the block-spring's equilibrium position, the spring is stretched so that its end is at a new position L1, as shown in Figure 2. The block is then pulled down to a new vertical position L2 and then released from rest so that the block-spring system oscillates. Assume that the reference line for zero gravitational potential energy of the system is at the lowest point in the system's vertical displacement from equilibrium. The experiment is assumed to be performed near Earth's surface. The students conduct experiment 2 in which the same block is connected to the same spring on a horizontal surface. The spring is stretched a distance L2 beyond its natural length and released from rest, allowing the block-spring system to oscillate. Frictional forces are considered to be negligible. Which of the following claims is correct about how the period of oscillation for the block-spring system in experiment 2 compares with the period of oscillation for the system in experiment 1, and what evidence supports the claim?

D. The periods of oscillation for experiment 2 and experiment 1 are the same, because the block and the spring used in both experiments are identical.

A group of students must conduct an experiment to determine how the location of an applied force on a classroom door affects the rotational motion of the door. The rotational inertia of the door about its hinges is known. The initial angular velocity of the door is zero. The students must determine how to test the relationship between a torque exerted on the door and the change in the angular velocity of the door. All frictional forces are considered to be negligible. How should the experiment be conducted to test the relationship between the torque exerted on the door and the change in the door's angular velocity in a way that minimizes experimental uncertainty?

D. The students should perform several trials, applying the same force at different horizontal distances from the hinges.

The force diagram above shows a box accelerating to the right on a horizontal surface of negligible friction. The tension T is exerted at an angle of 30°above the horizontal. If μ is the coefficient of kinetic friction between the box and the surface, which of the following is a correct mathematical equation derived by applying Newton's second law to the box?

D. a=Tcos(θ)−μ(Mg−Tsin(θ))Ma=Tcos(θ)−μ(Mg−Tsin(θ))M

A point on a rotating object has an initial angular velocity ω0 and rotates with an angular acceleration α0 for a time interval from t=0 to time t=t0. The point then rotates at a constant angular speed until time t=t1. What is the angular displacement of the point from t=0 to t=t1? Express your answer in terms of ω0, α0, t0, t1, and/or any fundamental constants as appropriate.

D. ω0t0+12α0t20+(ω0+α0t0)t1

How does an air mattress protect a stunt person landing on the ground after a stunt?

E. It lengthens the stopping time of the stunt person and reduces the force applied during the landing.

A sphere of mass m1, which is attached to a spring, is displaced downward from its equilibrium position as shown above left 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 above 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?

E. m1g / l