Mechanical Energy and Friction Quiz

A student must determine the effect of friction on the mechanical energy of a small block as it slides up a ramp. The block is launched with an initial speed v0 from point A along a horizontal surface of negligible friction. It then slides up a ramp, where friction is not negligible, that is inclined at angle θ with respect to the horizontal, as shown in the figure. The student measures the maximum vertical height h attained by the block while on the ramp, labeled as point B in the figure. At point B, the block comes to rest. The student performs three trials with the ramp at different angles, launching the block at the same initial speed v0 for each trial. The results from the trials are displayed in the table. How should the student use the data collected and the known quantities from the experiment to determine the initial total mechanical energy of the block-ramp-Earth system for all trials in the experiment?

A student must determine the effect of friction on the mechanical energy of a small block as it slides up a ramp. The block is launched with an initial speed v0 from point A along a horizontal surface of negligible friction. It then slides up a ramp, where friction is not negligible, that is inclined at angle θ with respect to the horizontal, as shown in the figure. The student measures the maximum vertical height h attained by the block while on the ramp, labeled as point B in the figure. At point B, the block comes to rest. The student performs three trials with the ramp at different angles, launching the block at the same initial speed v0 for each trial. The results from the trials are displayed in the table. Consider the trial with the 45° ramp. Suppose the block is launched up the ramp such that it comes to rest at point B and then travels down the ramp. Which of the following best describes the block’s kinetic energy KA when it again reaches point A at the bottom of the ramp in comparison to the initial kinetic energy K0 before it travels up the ramp?

A student must determine the effect of friction on the mechanical energy of a small block as it slides up a ramp. The block is launched with an initial speed v0 from point A along a horizontal surface of negligible friction. It then slides up a ramp, where friction is not negligible, that is inclined at angle θ with respect to the horizontal, as shown in the figure. The student measures the maximum vertical height h attained by the block while on the ramp, labeled as point B in the figure. At point B, the block comes to rest. The student performs three trials with the ramp at different angles, launching the block at the same initial speed v0 for each trial. The results from the trials are displayed in the table. Consider the trial in which the ramp is at a 20° angle with the horizontal. The surface of the ramp has been replaced with a surface in which frictional forces are considered to be negligible. If the mass of the block is doubled and the initial launch speed is doubled, how could the student predict the new vertical of the block at point B?

A block of mass M on an inclined surface is attached to a spring of negligible mass, as shown. The other end of the spring is attached to a wall, and there is negligible friction between the block and the incline. The block is pulled to a position such that the spring is stretched from its equilibrium position. The block is then released from rest. Which of the following systems can be classified as a closed system?

The total mechanical energy of a system as a function of time is shown in the graph. Which of the following statements is true regarding the system?

A planet orbits a star along an elliptical path from point X to point Y, as shown in the figure. In which of the following systems does the total mechanical energy of the system remain constant?

A 5 kg object near Earth's surface is released from rest such that it falls a distance of 10 m. After the object falls 10 m, it has a speed of 12 m/s. Which of the following correctly identifies whether the object-Earth system is open or closed and describes the net external force?

A toy car has an initial acceleration of 2m/s2 across a horizontal surface after it is released from rest. After the car travels for a time t=5 seconds, the speed of the car is 25m/s. Is the system consisting of only the car an open system or a closed system, and why?

A student performs an experiment in which a ball travels in a perfect circle. The ball is attached to a string and travels in the horizontal, circular path, as shown in Figure 1. At time t0, the ball has a speed ν0. During the time interval of 0s to 2s, the force of tension in the string is recorded and graphed, as shown in Figure 2. Is the system consisting of the ball, string, and student an open system or closed system, and why?

A block on a rough, horizontal surface is attached to a horizontal spring of negligible mass. The other end of the spring is attached to a wall. The spring is compressed such that the block is located at position X. When the block-spring system is released, the block travels to the right through position Y and continues to travel to the right through position Z. Free body diagrams for the block at positions X, Y, and Z are shown in the figure. At which position does the block have the greatest kinetic energy?

A 5 kg block moves with a constant speed of 10 ms to the right on a smooth surface where frictional forces are considered to be negligible. It passes through a 2.0 m rough section of the surface where friction is not negligible, and the coefficient of kinetic friction between the block and the rough section μk is 0.2. What is the change in the kinetic energy of the block as it passes through the rough section?

A rock of mass M is thrown from the edge of a cliff of height h with an initial velocity v0 at an angle θ with the horizontal, as shown in the figure. Point P is the highest point in the rock’s trajectory, and point Q is level with the initial position of the rock. All frictional forces are considered to be negligible. Which of the following could correctly describe the total energy of the rock-Earth system at points P and Q?

A ball of mass M is attached to a string of negligible mass that has a length R. The ball moves clockwise in a vertical circle, as shown above. Which of the following is true about the ball-string-Earth system as the ball moves from point 1 to point 2?

A small block of mass M=0.10 kg is released from rest at point 1 at a height H=1.8 m above the bottom of a track, as shown in the diagram. It slides down the track and around the inside of a loop of radius R=0.6 m. The speed of the block is 2.5 m/s at point 3. Which of the following claims about the situation is correct?

Objects X and Y are connected by a string of negligible mass and suspended vertically over a pulley of negligible mass, creating an Atwood’s machine, as shown in the figure. The objects are initially at rest, and the mass of object Y is greater than the mass of object X. As object Y falls, how does the kinetic energy of the center of mass of the two-object system change? Justify your selection. All frictional forces are considered to be negligible.

A small object of mass M is shot horizontally from a spring launcher that is attached to a table. All frictional forces are considered to be negligible. The ball strikes the ground a distance D from the base of the table, as shown in the figure. A second object of mass M2 is launched from the same launcher such that the spring is compressed the same distance as in the original scenario. The distance from the base of the table that the object lands is

One end of a vertical spring is attached to the ground with the other end above the ground such that the spring is at its equilibrium position. The spring has negligible mass and a spring constant k0 , as shown in Figure 1. When an object of mass m0 is released from rest above the spring, the object falls and then makes contact with the top of the spring with a speed v0 , as shown in Figure 2. The spring then compresses such that the object reaches a position x0 below the spring’s equilibrium position, as shown in Figure 3, where the object comes to rest. The object is then directed upward by the spring until it is no longer in contact with the spring. The object then continues upward. The object-spring-Earth system has zero gravitational potential energy at the instant shown in Figure 2. All frictional forces are considered to be negligible. When the object is located at the position shown in Figure 3, which of the following equations correctly indicates the total mechanical energy of the object-spring-Earth system?

After the object reaches the position in Figure 3, the spring pushes the object upward until the object is no longer in contact with the spring. A graph of the force exerted by the spring on the object as a function of the position of the object is shown. How much work does the spring do on the object as it pushes the object upward until the object is no longer in contact with the spring?

One end of a vertical spring is attached to the ground with the other end above the ground such that the spring is at its equilibrium position. The spring has negligible mass and a spring constant k0 , as shown in Figure 1. When an object of mass m0 is released from rest above the spring, the object falls and then makes contact with the top of the spring with a speed v0 , as shown in Figure 2. The spring then compresses such that the object reaches a position x0 below the spring’s equilibrium position, as shown in Figure 3, where the object comes to rest. The object is then directed upward by the spring until it is no longer in contact with the spring. The object then continues upward. The object-spring-Earth system has zero gravitational potential energy at the instant shown in Figure 2. All frictional forces are considered to be negligible. Which of the following describes the total mechanical energy of the object-Earth system during the time in which the object is in the air and the time in which the object is in contact with the spring? Assume all frictional forces are considered to be negligible.

A roller coaster track at a park includes a loop of radius R. A cart of mass M is located at the peak of the track, which has a height of 4R. The cart is subsequently released from rest such that it can slide down the track and go around the loop, as shown in the figure above. All frictional forces are considered to be negligible. Which of the following expressions for the cart’s initial and final kinetic energy KE and the cart-Earth system’s initial and final gravitational potential energy Ug could be used to determine the speed vf of the cart when it reaches the top of the loop?

A block of mass 3kg on a horizontal surface travels at 6m/s toward the free end of a horizontal spring of negligible mass and spring constant k=200N/m , as shown in the figure. 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 comes into contact with the free end of the spring such that the block remains fixed to the spring as the spring is compressed. A graph of the kinetic energy of the block as a function of the distance the spring is compressed is shown that was collected from experimental data. Which of the following data tables could best represent the spring potential energy of the block-spring system as a function of the distance that the spring is compressed?

A block of mass 3kg on a horizontal surface travels at 6m/s toward the free end of a horizontal spring of negligible mass and spring constant k=200N/m , as shown in the figure. 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 comes into contact with the free end of the spring such that the block remains fixed to the spring as the spring is compressed. A graph of the kinetic energy of the block as a function of the distance the spring is compressed is shown that was collected from experimental data. Which of the following data tables could best represent the spring potential energy of the block-spring system as a function of the distance that the spring is compressed?

A student must determine the work done on an object when an external force is exerted on it after it travels a specific distance. An external force F is exerted on an object at position x = 0 by a string as the object moves a distance D across a horizontal surface for a time tf . The force changes such that it decreases as the object moves. Which procedure could be used to determine the work done on the object by the external force?

An experiment is conducted such that an applied force is exerted on an object as it travels across a horizontal surface with a constant speed. A graph of the applied force exerted on the object as a function of the object’s distance traveled is shown. Which of the following claims is correct regarding the work done on the object by the applied force from one data point to the next data point?

A block of mass M is placed on a semicircular track and released from rest at point P, which is at vertical height H1 above the track’s lowest point. The surfaces of the track and block are considered to be rough such that a coefficient of friction exists between the track and the block. The block slides to a vertical height H2 on the other side of the track. How does H2 compare to H1?

A block of mass M slides with speed v0 at the bottom of a ramp of negligible friction that has a height H, as shown. How do the total mechanical energy of the block alone and the total mechanical energy of the block-Earth system change when the block slides up the ramp to point P?

A planet orbits a star along an elliptical path, as shown in the figure. Consider the system consisting of the planet and the star. How do the magnitude of the force exerted on the planet by the star and the total mechanical energy of the system change as the planet moves from point X to point Y?

A cart of mass M travels from point A at height h1 above the ground to point B on a track that is at a height h2, as shown in the figure. The speed of the cart at point A is nearly zero, and the frictional forces between the wheels, cart, and track are considered to be negligible. Which of the following graphs could represent the potential energy of the cart-Earth system at point A and point B? Select two answers.

A block is initially sliding along a surface of negligible friction with a speed v0. A constant force F0 is then exerted on the block. Which of the following figures represents the situations in which the kinetic energy of the block will initially decrease? Select two answers.

A block of mass M is held at rest on an inclined ramp that can be considered frictionless. The ramp makes an angle θ with the horizontal, as shown in Figure 1. When released, the block slides down the incline and comes into contact with an uncompressed spring with spring constant k0 . The block slides an additional distance x0 before it compresses the spring a maximum distance, as shown in Figure 2. A student wants to use the law of conservation of energy to analyze the energies associated with the block-ramp-spring-Earth system. Which of the following equations should the student use to analyze the specific forms of energy in the system from the instant the block is released to the instant that the spring is at its maximum compression? Select two answers.

A student must perform an experiment to determine the work done by a spring as it launches a block across a horizontal surface. The spring is initially compressed and the block is initially held at rest. After the spring is uncompressed, the block is no longer in contact with the spring. The spring constant is unknown, and the student may not use the mass or weight of the block in the experiment for any calculation. Which of the following measuring tools, when used together, can be used to determine the work done by the spring on the block? Select two answers.

Two objects of the same mass travel in opposite directions along a horizontal surface. Object X has a speed of 5ms and object Y has a speed of 5ms, as shown in the figure. After a period of time, object X collides with object Y. In scenario 1, the objects stick together after the collision. In scenario 2, the objects do not stick together after the collision. Which of the following claims is true regarding how the outcome of scenario 1 is different from the outcome of scenario 2?

Object X collides into object Y and exerts a force on object Y while both objects are in contact. A graph of the force that object X exerts on object Y is shown. How could the graph be used to determine the change in momentum of object Y during the collision?

Two objects of the same mass travel in opposite directions along a horizontal surface. Object X has a speed of 5ms and object Y has a speed of 5ms, as shown in the figure. After a period of time, object X collides with object Y. In scenario 1, the objects stick together after the collision. In scenario 2, the objects do not stick together after the collision. Consider scenario 1. Is the object X–object Y system open or closed? Predict whether both the momentum and the kinetic energy of the system will be the same or different after the collision.

Block X and block Y are tied together by a rope. The system containing block X and block Y is released from rest on a ramp, as shown in the figure. Block Y has a smaller mass than block X. Which of the following claims is correct regarding the momentum of the system containing only block X and the system that contains block X and block Y?

An experiment is conducted in which a cart travels across a horizontal surface and collides with a wall. Data collected from the experiment are used to create the graph of the cart’s velocity as a function of time. All frictional forces are considered to be negligible. Which data from the graph should the student use to determine the direction of the net force exerted on the cart and the direction of the change in momentum of the cart from the time intervals of A to B?

During an experiment, a toy car accelerates forward for a total time of 5s. Which of the following procedures could a student use to determine the average net force exerted on the car during the 5s that the car accelerates?

A cart is attached to a hanging block by a string that passes over a pulley, as shown in the figure. The pulley has negligible friction in its axle and negligible mass. A student must determine the change in momentum of the cart as it is pulled across the horizontal surface from the moment the cart is released from rest to the moment immediately before the cart collides with the pulley. Which of the following lists the measuring devices that are needed to determine the change in momentum of the cart?

A student conducts an experiment in which a cart is pulled by a variable applied force during a 2 s time interval. In trial 1, the student exerts the force on a cart of mass M. In trial 2, the student exerts the force on a cart of mass 3M. In trial 3, the student exerts the force on a cart of 5M. In which trial will the cart experience the greatest change in momentum from 0 s to 2 s?

A toy car of mass 2kg travels along a horizontal surface with negligible friction at a speed of 1.0ms. The car then collides with a vertical wall. The wall applies a force of magnitude 20N for 0.2s on the toy car. Which of the following predicts the motion of the toy car immediately after the collision?

A block of mass of 10kg travels in the positive direction along a surface with negligible friction. The block has an initial momentum 18kg⋅ms. The block collides with an object of an unknown mass that is at rest. The force exerted on the block as a function of time is shown on the graph. Which of the following best predicts the speed and direction of the block immediately after the collision?

Block X travels towards Block Y that is initially at rest, as shown in the figure, and eventually collides with Block Y. Which of the following diagrams represents the final velocities for Block X and Block Y after the collision if the collision is elastic?

Astronaut X of mass 50kg floats next to Astronaut Y of mass 100kg while in space, as shown in the figure. The positive direction is shown. Astronaut X applies a force against Astronaut Y such that the kinetic energy of each astronaut as a function of time is shown in the graph. What is the change in momentum of the two-astronaut system and the change in momentum of each astronaut from immediately before the force was applied to immediately after the force was applied?

A force is applied to a 2kg object, and measurements of the force as a function of time are shown. The force is the only force exerted on the object and is applied in the direction of the object’s velocity. Which of the following could represent the initial velocity, v0, and the final velocity, vf, of the object?

A 9000kg rock slides on a horizontal surface with negligible friction at 3m/s toward a 3000kg rock that is at rest, as shown in Figure 1. A collision occurs such that the two rocks remain stuck together and travel with a common final speed vf , as shown in Figure 2. What is the speed vf of the two-object system after the collision?

A student performs several experiments in which two carts collide as they travel along a horizontal surface. Cart X and Cart Y both have a mass of 1kg. Data collected from the three experiments are shown in the table. During which experiment does the center of mass of the system of two carts have the greatest change in its momentum?

A mass M1 slides along a horizontal surface and collides with and sticks to a mass M2 that is initially at rest at the bottom of a ramp, as shown in Figure 1. Frictional forces between the masses, the surface, and the ramp are considered to be negligible. After the collision, masses M1 and M2 slide together up the curved ramp as a total mass of M12 , as shown in Figure 2. The two masses eventually come to rest at their highest position along the ramp. Which of the following claims is correct regarding the momentum of the system of mass M1 and the system of mass M1 and M2 in terms of their momenta?

A block travels across a horizontal surface in which frictional forces are not considered to be negligible, as shown in the figure. Which of the following quantities should a student measure to verify that the direction of the frictional force exerted on the block from the surface is in the same direction as the change in momentum of the block? Select two answers. Justify your selections.

Block X of mass M slides across a horizontal surface where friction is negligible. Block X collides with block Y of mass 2M that is initially at rest, as shown in Figure 1. After the collision, both blocks slide together with a speed vs , as shown in Figure 2. What is the kinetic energy of the two-block system before the collision?

Block X of mass M slides across a horizontal surface where friction is negligible. Block X collides with block Y of mass 2M that is initially at rest, as shown in Figure 1. After the collision, both blocks slide together with a speed vs , as shown in Figure 2. What is the kinetic energy of the two-block system before the collision?

Block X of mass M slides across a horizontal surface where friction is negligible. Block X collides with block Y of mass 2M that is initially at rest, as shown in Figure 1. After the collision, both blocks slide together with a speed vs , as shown in Figure 2. What is the speed of the center of mass of the two-block system immediately before the collision?

Block X of mass M slides across a horizontal surface where friction is negligible. Block X collides with block Y of mass 2M that is initially at rest, as shown in Figure 1. After the collision, both blocks slide together with a speed vs , as shown in Figure 2. How could a student verify that the collision under consideration is an inelastic collision for the two-block system?

Block X of mass M travels with a speed v0. Block Y of mass 2M travels with a speed 2v0. Both blocks travel toward each other and collide. After the blocks collide, they separate so that the kinetic energy of the system remains conserved. Which of the following equations for the conservation of momentum could a student use to help determine the speed vf of each block after the collision?

Block X and block Y travel toward each other along a horizontal surface with block X traveling in the positive direction. Block X has a mass of 4kg and a speed of 2ms. Block Y has a mass of 1kg and a speed of 1 ms. A completely inelastic collision occurs in which momentum is conserved. What is the approximate speed of block X after the collision?

Block X and block Y travel toward each other along a horizontal surface with block X traveling in the positive direction. Block X has a mass of 2kg and a speed of 3m/s. Block Y has a mass of 1kg and a speed of 3m/s. After the collision, block X travels in the horizontal direction with a speed of 1m/s in the negative direction. What is the speed of block Y if the collision is elastic?

Cart X travels in the positive direction along a horizontal surface, and cart Y travels in the positive direction. The carts collide, and a student collects data about the carts’ velocities as a function of time before, during, and after a collision, as shown. The masses of both objects are known. Which of the following best indicates how the student should use the graph to determine whether the collision is elastic or inelastic and provides a correct justification?

In an experiment, two objects, Object X and Object Y, travel toward each other and collide. Data are collected about each object before, during, and after the collision to create a graph that shows the momenta of Object X and Object Y as a function of time. How should a student use the data found on the graph to verify the conservation of momentum?

A student must conduct an experiment to verify the conservation of momentum. Cart X and Cart Y travel toward each other and eventually collide, as shown in the figure. The student has access to the two carts, one mass balance, and two motion detectors. If the mass of each cart is known, how should the student arrange one or both motion detectors so that the student can collect enough information about the motion of the carts, in order to verify the conservation of momentum of the system?

A student conducts three experiments in which two carts, cart 1 and cart 2, travel toward each other and collide. A graph of each cart’s momentum as a function of time is shown above. In which experiment, if any, does the graph indicate the presence of a net external force exerted on the two-cart system?

A student conducts an experiment to verify whether momentum is conserved for a situation in which a collision occurs. The two objects, Object X and Object Y, travel toward each other, as shown in Figure 1. After the collision, the two objects travel as shown in Figure 2. Data collected from three trials of this experiment are shown in the table. Which of the following statements is correct based on the data?

A student must conduct an experiment in which an elastic collision occurs. In the experiment, Block X of mass 2kg travels with a velocity vX in the positive direction toward Block Y of mass 2kg that is at rest, as shown in Figure 1. After the collision, Block Y travels in the positive direction with velocity vY while Block X remains nearly at rest. Data collected of the initial and final velocities of both blocks for three trials of the experiment are shown in the table. Did the student conduct an experiment in which an elastic collision occurred? Is the system of Block X and Block Y open or closed?

Cart X with a mass of 1kg is released from rest at the top of an inclined ramp, and the cart rolls down the ramp with negligible friction. At the bottom of the ramp, cart X collides with cart Y, which is initially at rest. The collision is completely inelastic, and both cart X and cart Y have equal masses. Before and after the collision, data are collected about the distance d each cart travels as a function of time t. The table shows data about cart X before the collision as it travels down the ramp. Which of the following sets of data could represent the collision for cart X and cart Y?

Block X of mass 2kg travels across a horizontal surface toward block Y of unknown mass that is initially at rest. Block X then collides elastically with block Y. A graph of the position as a function of time for block X is shown. Block X and block Y are made of the same material. Which of the following predictions is correct about the motion of block Y immediately after the collision?

A constant force FA is applied to an object of mass M, initially at rest. The object moves in the horizontal x-direction, and the force is applied in the same direction. After the force has been applied, the object has a speed of vf. Which mathematical routines can be used to determine the time in which the force is applied to the object of mass M? Select two answers.

An object travels in the positive direction with a momentum of 5 kg⋅ms . An applied force is exerted on the object, and a graph of the magnitude of the applied force as a function of time is shown. All frictional forces are considered to be negligible. Which of the following could represent the approximate momentum of the object after the force has been applied? Select two answers.

A variable applied force is exerted on a 2kg block as it travels across a horizontal surface for a time of 2s, as shown in the graph. Before the force is applied to the block, it travels with a speed of 1 ms. The force is exerted on the block in the same direction as the block’s displacement while the force is exerted. After the force is applied to the block, the block travels with a speed of 5  ms. Which of the following statements are correct regarding the motion of the block? Select two answers.

A student must perform an experiment in which two objects travel toward each other and collide so that the data collected can be used to show that the collision is elastic within the acceptable range of experimental uncertainty. Which of the following measuring tools, when used together, can the student use to verify that the collision is elastic? Select two answers.