Conservation of Linear Momentum (College Board AP® Physics 1: Algebra-Based): Exam Questions

2 hours30 questions
1a
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1 mark

State the principle of conservation of momentum for an isolated system.

1b
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4 marks
Two blocks, A and B, of mass m on a horizontal surface. Block A moves right at 2 m/s; Block B moves left at 4 m/s.

Figure 1

Two identical blocks, each of mass m, slide toward each other along a horizontal surface with negligible friction. Block A moves to the right at 2 space straight m divided by straight s and Block B moves to the left at 4 space straight m divided by straight s, as shown in Figure 1. After the collision, Block A moves to the left at 3 space straight m divided by straight s.

i) Calculate the speed of Block B after the collision.

ii) Indicate the direction of motion of Block B after the collision.

1c
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2 marks

i) Identify the system by drawing a circle around the objects in Figure 1 for which the total momentum is constant.

ii) Calculate the velocity of the center of mass of the two-block system before the collision.

1d
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2 marks

Indicate whether the velocity of the center of mass of the two-block system increases, decreases, or remains constant after the collision. Justify your answer.

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2a
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2 marks

Describe the difference between an elastic collision and an inelastic collision.

2b
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2 marks
Two identical balls on a horizontal surface. Before the collision, the ball on the left moves to the right with velocity v, and the ball on the right is stationary. After the collision, the ball on the left is stationary, and the ball on the right moves to the right with velocity v.

Figure 1

A ball of mass m is sliding toward a stationary identical ball with speed v. After the collision, the first ball comes to rest and the second ball slides away with speed v, as shown in Figure 1.

Indicate whether the collision is elastic or inelastic. Justify your answer.

2c
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4 marks
Two balls on a horizontal surface, the ball on the left has mass 2m and the ball on the right has mass m. Before the collision, the 2m ball moves to the right with velocity v, and the m ball is stationary. After the collision, the balls move to the right together with an unknown velocity.

Figure 2

A ball of mass 2 m is sliding toward a stationary ball of mass m with speed v. After the collision, the balls stick together and continue to move in the same direction, as shown in Figure 2.

i) Determine the speed of the balls after the collision in terms of v.

ii) Indicate whether the collision is elastic or inelastic. Justify your answer.

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3a
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1 mark

Two ice skaters are initially at rest. Skater A has a mass of 50 space kg, and Skater B has a mass of 75 space kg. They push off each other and move in opposite directions.

State the name of this type of interaction.

3b
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3 marks

The impulse received by Skater A is space J subscript A and the impulse received by Skater B is space J subscript B.

Is the magnitude of space J subscript A greater than, less than, or equal to the magnitude of space J subscript B? Justify your answer.

3c
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3 marks

After the push, the velocity of Skater A is 3 space straight m divided by straight s.

Using conservation of momentum, determine the velocity of Skater B after the push.

3d
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3 marks

The push happens at time t subscript 0. On the axes provided, sketch and label a graph of the velocity of the skaters as a function of time.

Graph with labelled axes; vertical axis is "Velocity (m/s)" and horizontal axis is "Time (s)" with points 0, t0, and 2t0 marked.

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4a
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2 marks
Before the collision, a 3 kg object moves to the right with velocity v0 toward a stationary 2 kg object. After the collision, the 3 kg object moves with speed 2 m/s at an angle 30° above the horizontal, the 2 kg object moves with speed v at an angle 30° below the horizontal.

Figure 1

A 3 space kg puck is moving with speed v subscript 0 before colliding with a stationary 2 space kg puck. Figure 1 shows the velocities of the pucks after the collision.

The arrow in Figure 2 represents the total momentum of the pucks immediately before the collision.

An 8 by 8 grid with dashed lines with a dot at the center and an arrow of 2 units in length pointing right.

Figure 2

On the dot in Figure 3, draw an arrow to represent the total momentum of the pucks immediately after the collision.

A grid of small squares with dashed lines, featuring a single black dot at the centre intersection of the grid.

Figure 3

4b
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4 marks

i) Calculate the final speed v of the 2 space kg puck by considering the total momentum of the system in the y-direction.

ii) Calculate the initial speed v subscript 0 of the 3 space kg puck by considering the total momentum of the system in the x-direction.

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5a
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2 marks
Two carts on a track: Cart 1 moves right with velocity v0 towards stationary Cart 2, which has a spring attached to it.

Figure 1

A group of students have two carts, Cart 1 and Cart 2, each of known mass m subscript 1 and m subscript 2, respectively. The carts are placed on a straight horizontal track. Cart 1 is given an initial speed v subscript 0 toward the right. Cart 2 is initially at rest and has a spring attached to it, as shown in Figure 1. Cart 1 collides with Cart 2.

The group of students want to determine if the collision between the carts is elastic or inelastic at different speeds. Describe an experimental procedure to collect data that would allow the students to test their idea. Include any steps necessary to reduce experimental uncertainty.

5b
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2 marks

Describe how the collected data should be analyzed to determine if the collision between the carts is elastic or inelastic at different speeds.

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1a
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3 marks
Two blocks on a line: Block 1 (mass M1) moves right with velocity v0 towards Block 2 (mass M2), both positioned on a horizontal surface.

Figure 1

Block 1 of mass M subscript 1 slides to the right along a horizontal surface with speed v subscript 0 toward Block 2 of mass M subscript 2, which is initially at rest, as shown in Figure 1. When Block 1 collides with Block 2, the blocks stick together. Friction between the blocks and the surface is negligible.

If Block 2 is much less massive than Block 1 open parentheses M subscript 2 space much less-than space M subscript 1 close parentheses, estimate the approximate speed of the two-block system after the collision in terms of v subscript 0. Justify your estimate using qualitative reasoning beyond referencing equations.

1b
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3 marks

Starting with conservation of momentum, derive an equation for v subscript f, the speed of the two–block system after the collision, in terms of M subscript 1, M subscript 2, and v subscript 0. Begin your derivation by writing a fundamental physics principle or an equation from the reference book.

1c
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2 marks

If Block 2 is much less massive than Block 1, does the equation you derived in part b) agree with your qualitative reasoning from part a)? Justify why or why not.

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2a
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3 marks
Two blocks on a horizontal surface; Block A (6 kg) moving left to right towards Block B (2 kg) at time t = 0, with motion lines indicating speed.

Figure 1

At time t space equals space 0, Block A slides along a horizontal surface toward Block B, which is initially at rest, as shown in Figure 1. The masses of blocks A and B are 6 space kg and 2 space kg, respectively. The blocks collide elastically at t space equals space 1.0 space straight s and, as a result, the magnitude of the change in kinetic energy of Block B is 9 space straight J. All frictional forces are negligible.

i) Determine the speed of Block B immediately after the collision.

ii) Determine the speed of Block A immediately after the collision.

2b
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2 marks

The arrow in Figure 2 represents the velocity of the center of mass of the two-block system immediately after the collision.

An 8 by 8 grid with dashed lines with a dot at the center and an arrow of 1.5 units in length pointing right.

Figure 2

The dots in Figure 3 represent Block A and B respectively.

Two grids, labeled Block A (left) and Block B (right), each with a black dot at the center.

Figure 3

On the dots in Figure 3, draw arrows to represent the velocities of Block A and Block B immediately after the collision.

  • If the velocity is zero, write “zero” next to the dot.

  • The velocity, if it is not zero, must be represented by an arrow starting on, and pointing away from, the dot.

  • The length of the arrows, if not zero, should reflect the magnitude of the velocity relative to the arrow in Figure 2.

2c
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4 marks
Graph showing position vs time with lines for Block A, Block B, and Centre of Mass. Block A starts at 0, Block B at 2. Time spans 0 to 2 seconds.

Figure 4

The graph shown in Figure 4 represents the positions x of Block A, Block B, and the center of mass of the two-block system as functions of t between t space equals space 0 and t space equals space 1.0 space straight s.

On the graph in Figure 4, draw and label three lines to represent the positions of Block A, Block B, and the center of mass of the two-block system as functions of t between t space equals space 1.0 space straight s and t space equals space 2.0 space straight s. Each line should be distinctly labeled.

2d
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3 marks

A student considers if in the original scenario, instead of colliding elastically, the blocks collided and stuck together. They make the following claim about the graph drawn in part c):

“The slope of the line drawn for the center of mass of the two-block system would be less”.

Justify whether or not the student’s claim is correct.

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3a
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4 marks
Diagram of a spring-mass system with a block labelled M, connected to a wall by a spring. Marked points show equilibrium and extremes at -A1 and A1.

Figure 1

Block 1 of mass M is oscillating with amplitude A subscript 1 at the end of a spring with spring constant k. The other end of the spring is attached to a wall, as shown in Figure 1. Friction between the block and the floor is negligible.

A block of mass 2M is dropped on to the block of mass M as it passes through equilibrium. New amplitudes A2 and -A2 are marked.

Figure 2

Block 2 of mass 2 M is dropped from rest and sticks to Block 1 as it passes through its equilibrium position, as shown in Figure 2. The two-block system oscillates with amplitude A subscript 2.

i) Derive an expression for the velocity v of Block 1 at the equilibrium position before Block 2 is dropped, in terms of k, M, and A subscript 1. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

ii) Starting with conservation of momentum, derive an expression for the velocity of the two-block system immediately after Block 2 sticks to Block 1 in terms of v.

3b
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2 marks

Indicate whether amplitude A subscript 2 is greater than, less than, or equal to amplitude A subscript 1.

⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ A subscript 2 space greater than space A subscript 1‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ A subscript 2 space equals space A subscript 1 ‎ ‎ ‎‎ ‎ ‎ ‎ ‎ ‎ ‎ ⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ A subscript 2 space less than space A subscript 1

Justify your answer using the principle of conservation of momentum.

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4a
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2 marks

Block 1 of mass m subscript 1 and Block 2 of mass m subscript 2 are sliding along a horizontal frictionless surface when they collide at time t subscript c. Before the collision, the blocks slide toward each other. After the collision, the blocks slide together.

Indicate whether the kinetic energy of the two-block system after the collision is greater than, equal to, or less than the kinetic energy before the collision. Justify your answer using qualitative reasoning beyond referencing equations.

4b
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3 marks
Graph showing velocity as a function of time for two blocks. Before tc, Block 1 has velocity 4v and Block 2 has velocity -v. After tc, Blocks 1 and 2 have velocity v.

Figure 1

The graph in Figure 1 shows the velocities of the blocks as a function of time.

Using the graph in Figure 1, derive an expression for the ratio of the mass of Block 2 to the mass of Block 1, m subscript 2 over m subscript 1. Begin your derivation by writing a fundamental physics principle or an equation from the reference book.

4c
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3 marks

Does the graph in Figure 1 agree with your qualitative reasoning from part a)? Use the expression derived in part b) to justify your answer.

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5
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3 marks
Diagram showing a launching device propelling a projectile to the right at a speed of vx towards a block hanging by a string from the ceiling.

Figure 1

A block of mass M subscript b is suspended from the ceiling using a string with negligible mass. A projectile of mass M subscript p is fired horizontally from a launching device with speed v subscript x into the block, as shown in Figure 1. While the projectile is in the launching device, the impulse given to it is space J subscript p. When the projectile strikes the block, the impulse given to the block isspace J subscript b. After the collision, the projectile becomes embedded in the block.

If the projectile is much less massive than the block open parentheses M subscript p space much less-than space M subscript b close parentheses, estimate the approximate magnitude of the impulse given to the block in terms of space J subscript p. Justify your estimate using physical principles.

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1a
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3 marks
Two experiments: A rubber ball hits a block on a table in Experiment A; a clay ball hits a block on a table in Experiment B.

Figure 1

A student conducts an experiment using a clay ball of mass m and a rubber ball of the same mass. Each ball is thrown horizontally with speed v subscript 0 toward two identical blocks of mass M that are at rest at the edge of identical tables, as shown in Figure 1. After each collision, the blocks fall to the floor. Friction between the blocks and the table is negligible.

In Experiment A, the clay ball sticks to Block A. In Experiment B, the rubber ball bounces off of Block B at a speed of v subscript r. After the collisions, Block A lands a horizontal distance d subscript A, and Block B lands a horizontal distance d subscript B from the table's edge.

Indicate whether d subscript A is greater than, less than, or equal to d subscript B.

⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ d subscript A space greater than space d subscript B‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ d subscript A space equals space d subscript B ‎ ‎ ‎‎ ‎ ‎ ‎ ‎ ‎ ‎ ⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ d subscript A space less than space d subscript B

Justify your answer using qualitative reasoning beyond referencing equations.

1b
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3 marks

Starting with conservation of momentum, derive an equation for the ratio of the speed of Block A after the collision to the speed of Block B after the collision, v subscript A over v subscript B. Express your answer in terms of m, M, v subscript 0 and v subscript r. Begin your derivation by writing a fundamental physics principle or an equation from the reference book.

1c
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2 marks

If the balls are much less massive than the blocks open parentheses m space much less-than space M close parentheses, does the equation you derived in part b) agree with your qualitative reasoning from part a)? Justify why or why not.

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2a
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3 marks
Diagram showing two scenarios: t = 0 and t > tc. At t=0, mass m1  compresses the spring by a distance delta x. At t>tc, the spring is at its uncompressed length at x = 0 and mass m1 is moving to the right where it collides with a smaller mass m2. m1 and m2 move together to the right at velocity v.

Figure 1

Block 1 of mass m subscript 1 is held at rest while an ideal spring of spring constant k is compressed by increment x. Block 2 has mass m subscript 2 where m subscript 2 space less than space m subscript 1. At time t space equals space 0, Block 1 is released. At time t space equals space t subscript C , the spring is no longer compressed and Block 1 immediately collides with and sticks to Block 2. The two-block system moves with constant speed v, as shown in Figure 1. Friction between the blocks and the surface is negligible.

Derive an expression for the velocity of the two-block system after the collision in terms of m subscript 1, m subscript 2, k and increment x. Begin your derivation by writing a fundamental physics principle or an equation from the reference book.

2b
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2 marks

In another scenario with the same equipment, Block 1 is used to compress the spring by the same amount as before, and Block 2 is placed in the same initial position. When the spring is released, Block 1 remains attached to the spring as it collides with Block 2.

Indicate whether the velocity of Block 2 immediately after the collision would be greater than, less than, or equal to the velocity of the two-block system in the original scenario. Briefly justify your answer.

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3a
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4 marks
A ball launched at angle φ with initial velocity v0 towards a pendulum. The pendulum hangs from length L and swings up by angle θ after the collision with the ball.

Figure 1

A clay ball of mass m is launched at an angle ϕ above the horizontal with initial speed v subscript 0. At the moment it reaches the highest point in its trajectory and is moving horizontally, it collides with and sticks to a wooden block of mass M, as shown in Figure 1. The block is suspended from a light string of length L. The block and the clay then swing up to a maximum height h subscript 0 above the block’s initial position and make an angle theta with the vertical.

i) Starting with conservation of momentum, derive an expression for the velocity of the block-clay system immediately after the collision. Express your answer in terms of m, M, v subscript 0 and ϕ. Begin your derivation by writing a fundamental physics principle or an equation from the reference book.

ii) Starting with conservation of energy, derive an expression for the speed of the clay ball immediately before it strikes the block. Express your answer in terms of m, M, L, theta and physical constants, as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference book.

3b
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3 marks

The momentum diagrams in Figure 3 represent the velocity of the clay ball and the block before the collision, and the velocity of the clay-block system after the collision relative to their mass. Draw shaded rectangles to complete the momentum diagrams in Figure 3 before and after the clay ball strikes the block.

  • Positive values of velocity are above the zero line (“0”), and negative values of velocity are below the zero line.

  • Shaded regions should start at the lines representing zero velocity and mass.

  • Represent any velocity that is equal to zero with a distinct line on the zero line.

  • The relative height and width of each shaded region should reflect the magnitude of the velocity and mass respectively, consistent with the scale shown.

Three graphs showing momentum against mass. Left: Initial momentum of clay. Centre: Initial momentum of block. Right: Final momentum of clay-block system.

Figure 3

3c
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2 marks

In a second experiment, a steel ball is used instead of a clay ball. The steel ball is launched at the same speed and angle, but instead collides elastically with the block. The block swings up to a maximum height h subscript 0 superscript apostrophe.

Indicate whether h subscript 0 superscript apostrophe is greater than, less than, or equal to h subscript 0 .

⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ h subscript 0 superscript apostrophe space greater than space h subscript 0‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ h subscript 0 superscript apostrophe space equals space h subscript 0 ‎ ‎ ‎‎ ‎ ‎ ‎ ‎ ‎ ‎ ⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ h subscript 0 superscript apostrophe space less than space h subscript 0

Justify your answer.

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4a
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3 marks
Plunger moves from position A to position F with a block at A and E; textured section between C and D.

Figure 1

Blocks 1 and 2, each of mass m, are placed on a horizontal surface at points A and E, respectively, as shown in Figure 1. The surface is frictionless except for the region between points C and D.

In the time interval t space equals space t subscript A to t space equals space t subscript B, a mechanical plunger pushes Block 1 with a constant horizontal force of magnitude F subscript p. At point B, Block 1 loses contact with the plunger and continues moving to the right with speed v subscript B. In the time interval t space equals space t subscript C to t space equals space t subscript D, Block 1 moves over the rough surface where the coefficient of kinetic friction between the block and the surface is mu. At point D, Block 1 is moving to the right with speed v subscript D. At point E, Block 1 collides with and sticks to Block 2, after which the two-block system continues moving across the surface, eventually passing point F at time t subscript F.

Two blocks on a line; left image shows block 1 at D moving with velocity vD and block 2 at E with zero velocity; right image shows blocks together at E.

Figure 2

Figure 2 shows the location of the center of mass of the two-block system just before and during the collision.

The dots in Figure 3 represent the blocks while they are in contact during the collision, and the center of mass of the two-block system.

Three grids labelled Block 1, Block 2, and Two-block system, each with a central black dot on a 6x6 grid.

Figure 3

On each of the dots in Figure 3, draw arrows to indicate the direction of the net force, if any, exerted on each block, and the two-block system.

  • If the net force is zero for either block or the two-block system, write “zero” next to the dot.

  • The net force must be represented by a distinct arrow starting on, and pointing away from, the appropriate dot.

  • The length of the arrows, if not zero, should reflect the magnitude of the net force relative to the other arrows.

4b
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4 marks

On the axes provided below, sketch and label a graph of the velocity of the center of mass of the two-block system as a function of time, from time t subscript A until the blocks pass point F at time t subscript F. The times at which Block 1 reaches points A through F are indicated on the time axis.

Graph with time on the x-axis and velocity of center of mass on the y-axis, showing six points from tA to tF along the time axis.

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5a
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2 marks
Two carts with mass M. Cart 2 contains a plunger-spring system. Before recoil: carts at rest next to each other, spring compressed within Cart 2. After recoil: carts move apart, spring extended.

Figure 1

A group of students have two carts, Cart 1 and Cart 2, each of identical, unknown mass M. The carts are initially at rest and placed next to each other on a horizontal track. Cart 2 contains a compressed spring which can be released by pressing a switch on top of the cart. When the switch is pressed, the spring expands and pushes a plunger outward, causing the two carts to recoil, as shown in Figure 1. Blocks of different known masses can be attached to each cart.

The group of students is asked to determine whether the total momentum of the system is conserved. The students have access to equipment that can be found in a typical school physics laboratory.

Describe an experimental procedure the students could use to collect the data needed to determine whether the total momentum of the system is conserved. Provide enough detail so that the experiment could be replicated, including any steps necessary to reduce experimental uncertainty.

5b
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2 marks

Describe how the data collected in part a) could be graphed and how that graph would be analyzed to determine whether the total momentum of the system is conserved.

5c
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4 marks
Two carts, 1 and 2, of mass M on a track. Cart 2, with a spring and a block on top, is against a wall to the left. Cart 1 is to the right of Cart 2, with 4 blocks on top.

Figure 2

In a later experiment, Cart 2 is placed next to a wall. When the switch is pressed, the spring expands and the plunger pushes on the wall, causing Cart 2 to move towards Cart 1, as shown in Figure 2. Cart 1 is initially at rest. After the collision, the two carts stick together and move along the track with speed v. Blocks of identical, known mass can be attached to Cart 1 and Cart 2, as long as the total mass of the system remains constant. The spring constant k of the spring in Cart 2 is unknown. When the spring is contained within the cart, it is compressed by a fixed distance x from its equilibrium position.

The students are asked to determine the value of the spring constant of the spring. The students measure the combined mass M subscript 1 comma B end subscript of Cart 1 and the blocks, the combined mass M subscript 2 comma B end subscript of Cart 2 and the blocks, and the final speed of the two-cart-block system.

The students measure the fixed value x space equals space 0.062 space straight m. The students repeat the experiment using different numbers of blocks on each cart and collect the data shown in the following table.

Combined mass of Cart 1 and blocks,

M subscript 1 comma B end subscript space open parentheses kg close parentheses

Combined mass of Cart 2 and blocks,

M subscript 2 comma B end subscript space open parentheses kg close parentheses

Final speed of the two-cart-block system,

v space open parentheses straight m divided by straight s close parentheses

‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎

1.750

0.500

0.410

1.500

0.750

0.505

1.250

1.000

0.585

1.000

1.250

0.650

0.750

1.500

0.720

0.500

1.750

0.775

i) Indicate two quantities that could be graphed to yield a straight line that could be used to determine the spring constant k of the spring. Use the blank columns in the table to list any calculated quantities you will graph other than the data provided.

Vertical Axis: ⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ Horizontal Axis: ⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽

ii) Plot the data points for the quantities indicated in part c)i) on the graph provided. Clearly scale and label all axes, including units, as appropriate.

Square grid paper with evenly spaced lines.

iii) Draw a best-fit line to the data graphed in part c)ii).

5d
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2 marks

Using the line drawn in part c)iii) and the measured value x space equals space 0.062 space straight m as needed, calculate the spring constant k of the spring.

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