Block X of mass $$M$$ travels in the positive direction with speed $$v_X$$ toward block Y of mass $$M$$ that is at rest. After the collision, block Y travels with speed $$v_Y$$ in the positive direction while block X remains at rest. The surface is smooth. How can a student determine whether the collision is elastic or inelastic? $$\Sigma\overrightarrow{p_0}=\Sigma\overrightarrow{p_f}$$

The masses of both blocks are known, and the initial and final velocities are both blocks are known. Therefore, the student must compare the initial kinetic energy of the two-block system before the collision and after the collision using $$\Delta K=\frac{1}{2}m\Delta v^2$$

Observe that the blocks do not stick together, which means the collision is elastic.

The masses of both blocks are known, and the initial and final velocities are both blocks are known. Therefore, the student must compare the initial momentum of the two-block system before the collision and after the collision using $$\Sigma\overrightarrow{p_0}=\Sigma\overrightarrow{p_f}$$ .

The masses of both blocks are known, and the initial and final velocities are both blocks are known. The student should use $$\overrightarrow{\Delta p}=m\overrightarrow{\Delta v}$$ for either block X or block Y to determine how much the block’s momentum has changed.

Two identical objects, X and Y, move toward each other at different speeds on a horizontal surface with negligible friction and collide elastically, then move away from each other. The kinetic energy of object X versus time is shown in the graph. Which statement about the speed $$v_Y$$ of object Y is true?

$$v_Y$$ after the collision is greater than it was before the collision.

$$v_Y$$ after the collision is equal to what it was before the collision.

$$v_Y$$ after the collision is less than it was before the collision.

$$v_Y$$ after the collision cannot be compared to what it was before the collision without knowing the mass of the objects.

In Scenario 1, a block is placed at the bottom of a semicircular track. An identical block, released from rest from a height $$H$$ above the bottom, slides down and collides elastically with the block at the bottom. The bottom block then slides up the track and reaches a maximum height $$h_{\max}$$ . Friction is negligible. In Scenario 2, the process is repeated except the blocks stick together when they collide. Which correctly indicates the maximum height that the bottom block reaches in Scenario 2?

Less than $$\tfrac12 h_{\max}$$

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

Kinetic energy is conserved only in elastic collisions.

Momentum is conserved only in elastic collisions.

Momentum is conserved only in inelastic collisions.

Kinetic energy is conserved only in inelastic collisions.

Both require the same conditions in order to be conserved.

A dart and a rubber sphere are suspended from the same point by light strings. When the dart is released from the position shown, it swings downward until its tip strikes the sphere. The dart can have different tips attached: Tip A will stick into the rubber sphere upon impact, Tip B will bounce inelastically off the sphere, and Tip C will bounce elastically off the sphere. For which tip, if any, will the sphere swing to the greatest maximum angle θ?

None of the tips; the angle will be the same for each.

A 500 g cart moves to the right with a kinetic energy of 0.14 J on a horizontal surface. The cart collides with a 250 g block that is initially at rest. The cart and block collide elastically and the block moves to the right with a kinetic energy of 0.12 J. Frictional forces are negligible. Which of the following correctly indicates how the internal energy of the block–cart system changes, if at all, during the collision, and provides a valid justification?

It does not change, because no mechanical energy is lost during the collision.

It does not change, because momentum is constant in the collision.

It increases, because momentum is transferred from the cart to the block during the collision.

It increases, because some mechanical energy is transferred from the block to the cart during the collision.

Two identical carts move along the same line immediately before they collide. Before the collision, the left cart has speed 2v and the right cart has speed v (both to the right). After the collision, the left cart has speed v. Frictional forces are negligible. Which statement about the kinetic energy of the two-cart system is true?

None of the kinetic energy is lost during the collision.

More than zero, but less than half, of the kinetic energy is lost during the collision.

More than half, but not all, of the kinetic energy is lost during the collision.

All of the kinetic energy is lost during the collision.

The graph shows the velocities of two carts as functions of time as the carts move toward each other, collide, and then move away from each other on a horizontal track. Which statement correctly indicates whether the momentum and total kinetic energy of the two-cart system are the same before and after the collision?

Both momentum and total kinetic energy are the same before and after the collision.

Only momentum is the same before and after the collision.

Only total kinetic energy is the same before and after the collision.

It cannot be determined without knowing the relative masses of the carts.

A student analyzes an experiment in which a block of mass $$2M$$ traveling with speed $$v_0$$ collides with a block of mass $$M$$ initially at rest. After the collision, the blocks stick together (completely inelastic). Which applications of momentum conservation correctly represent the system’s initial and final momentum? Select two answers.

$$2Mv_0 = 3Mv_f$$ , because the blocks stick together after the collision.

$$2Mv_0 = 2Mv_f + Mv_f$$ , because the blocks stick together after the collision.

$$3Mv_0 = 3Mv_f$$ , because the blocks stick together after the collision.

$$2Mv_0 = Mv_0 + 3Mv_f$$ , because the blocks do not stick together after the collision.

A ball is dropped and bounces off the floor. Its speed is the same immediately before and immediately after the collision. How does the height to which the ball bounces compare to the height from which it was dropped?

It cannot be determined without knowing the value of the height from which the ball was dropped.

It cannot be determined without knowing the value of the ball’s speed as it hits the floor.

Block 1 of mass $$m_1$$ and block 2 of mass $$m_2$$ are sliding along the same line on a horizontal frictionless surface when they collide at time $$t_C$$ . The graph shows the velocities of the blocks as a function of time. How does the kinetic energy of the two-block system after the collision compare with its kinetic energy before the collision, and why?

It is less, because the blocks have the same velocity after the collision, so some of their kinetic energy was transformed into internal energy.

It is less, because the blocks have velocities in opposite directions before the collision, so some of their kinetic energy cancels.

It is the same, because the collision was instantaneous, so the effect of external forces during the collision is negligible.

It is the same, because the blocks have the same velocity after the collision, and there is no friction acting on them.

Block 1 of mass $$m_1$$ and block 2 of mass $$m_2$$ are sliding along the same line on a horizontal frictionless surface when they collide at time $$t_C$$ . The graph shows the velocities of the blocks as a function of time. Which block has the greater mass, and what information indicates this?

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.

Block 1, because it had a greater speed before the collision.

Block 1, because the velocity after the collision is in the same direction as its velocity before the collision.

Block 2, because it had a smaller speed before the collision.

A block of mass 1 kg slides on a frictionless, horizontal surface with a velocity of 3.0 m/s to the right and collides with a block of mass 2 kg that is at rest. As a result of the collision, the 1 kg block comes to rest. Which of the following correctly states whether the collision is elastic or inelastic and provides a valid justification?

Inelastic, because some of the initial kinetic energy is converted into nonmechanical energy.

Elastic, because the total momentum before the collision equals the total momentum after.

Elastic, because some of the initial kinetic energy is converted to other forms of energy but the total energy is conserved.

Inelastic, because the total momentum before the collision does not equal the total momentum after.

Object X of mass $$m_0$$ travels to the right with a velocity $$v_0$$ . Object Y of mass $$2m_0$$ moves to the left at $$2v_0$$ . The objects collide and then stick together. What is the change in kinetic energy of the two-object system from immediately before the collision to immediately after the collision?

The kinetic energy decreases by $$3m_0 v_0^2$$ .

The kinetic energy increases by $$6m_0 v_0^2$$ .

The kinetic energy increases by $$3m_0 v_0^2$$ .

The kinetic energy decreases by $$6m_0 v_0^2$$ .

A ball of clay is thrown at and sticks to a target mounted on the back of a cart that is at rest. After the collision, the cart and clay move together. Which of the following correctly describes the kinetic energy of the clay-cart system following the collision?

The kinetic energy is less than that of the clay just before the collision.

The kinetic energy is greater than that of the clay just before the collision.

The kinetic energy is equal to that of the clay just before the collision.

The kinetic energy cannot be determined without knowing if the cart has greater or less mass than the clay.

A puck of mass $$2m$$ slides with speed $$v$$ toward a stationary puck of mass m, as shown. Friction between the pucks and the surface is negligible. The pucks collide and stick together. Which of the following correctly describes the change in the kinetic energy of the two-puck system during the collision?

It decreases by $$\frac{1}{3}mv^2$$

It increases by $$\frac{1}{3}mv^2$$

A sphere of mass 3 kg attached to a thin string is released from the position shown so that at its lowest point the sphere strikes a block of mass 1 kg that is initially at rest. Using measurements of the objects speeds taken by two motion detectors immediately before and after the collision, a student calculates that the total kinetic energy of the sphereblock system after the collision is significantly less than it was before the collision. Which of the following most plausibly explains this result?

The sphere or the block was deformed during the collision and dissipated part of the sphere-block system's mechanical energy.

The student made a mistake in obtaining data, because in a collision the kinetic energy must be conserved.

In calculating kinetic energy after the collision, the student did not account for the energy lost when the block slid on the table.

In calculating kinetic energy, the student did not consider the potential energy of the sphere-Earth system as the sphere was released.

A student conducts an experiment to verify that a collision is elastic. Two objects, object X and object Y, travel toward each other. The mass and the initial speed of both objects are known. Which of the following equations should the student consider using to verify that the collision is elastic, and why? Equation I: $$\Delta \vec p = \vec F \Delta t$$ . Equation II: $$\sum \vec p_0 = \sum \vec p_f$$ . Equation III: $$\Delta K = K_f - K_0$$ .

Equation II and equation III, because the conservation of momentum must be verified for the system of object X and object Y, and the difference in the kinetic energy of the system before and after the collision should be determined.

Equation I only, because the change in momentum of object X will be equal to the negative change of momentum for object Y.

Equation II only, because the conservation of momentum must be verified for the system of object X and object Y.

Equation I and equation III, because the change in momentum of object X will be equal to the negative change of momentum for object Y, and the difference in the kinetic energy of the system before and after the collision should be determined.

Unit 5 - Elastic and Inelastic Collisions

Authored by Richard Miller

Physics

12th Grade

Unit 5 - Elastic and Inelastic Collisions

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

A 1.0 kg lump of clay is sliding to the right on a frictionless surface with speed 2 m/s. It collides head-on and sticks to a 0.5 kg metal sphere that is sliding to the left with speed 4 m/s. What is the kinetic energy of the combined objects after the collision?

6 J

4 J

2 J

0 J

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

A 2 kg object traveling at 5 m/s on a frictionless horizontal surface collides head-on and sticks to a 3 kg object initially at rest. Which choice correctly identifies the change in total kinetic energy and the resulting speed of the objects after the collision?

Kinetic energy:

increases

Speed:

2 m/s

Kinetic energy:

increases

Speed:

3.2 m/s

Kinetic energy:

decreases

Speed:

2 m/s

Kinetic energy:

decreases

Speed:

3.2 m/s

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

A cart of mass m moves with negligible friction along a track with known speed v1 to the right. It collides with and sticks to a cart of mass 4m moving with known speed v2 to the right. Which principle(s) must be applied to determine the final speed of the carts, and why?

Only conservation of momentum, because the momentum lost by one cart is gained by the other and there is only one unknown quantity

Both conservation of mechanical energy and conservation of momentum, because both principles apply in any collision

Both conservation of mechanical energy and conservation of momentum, because neither cart changes direction

Either conservation of momentum or conservation of mechanical energy, because only one equation is required to solve for the one unknown variable

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Object X travels across a horizontal surface and collides with object Y. The velocity as a function of time for object X and object Y before, during, and after the collision is shown in the graph. Both objects have a mass of 2 kg. Which of the following correctly describes the momentum of the system and the kinetic energy of the system?

Momentum:

conserved

Kinetic energy:

conserved

Momentum:

conserved

Kinetic energy:

not conserved

Momentum:

not conserved

Kinetic energy:

conserved

Momentum:

not conserved

Kinetic energy:

not conserved

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

A railroad car of mass m is moving with speed u when it collides with and connects to a second railroad car of mass 3m, initially at rest, as shown. How do the speed and kinetic energy of the connected cars compare to those of the single car of mass m before the collision?

Speed:

less

Kinetic energy:

less

Speed:

less

Kinetic energy:

the same

Speed:

the same

Kinetic energy:

less

Speed:

the same

Kinetic energy:

the same

Speed:

greater

Kinetic energy:

the same

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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