Elastic and Inelastic Collisions

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AP Physics 1 › Elastic and Inelastic Collisions

Questions 1 - 10
1

Two carts collide on a horizontal track. They bounce apart, and measurements show the system’s total kinetic energy decreases. Which statement must be true about the collision?

The collision is inelastic, but momentum of the system is still conserved.

Momentum is not conserved because kinetic energy decreased.

The collision is elastic because the carts did not stick together.

Both momentum and kinetic energy are conserved since the track is horizontal.

Explanation

This question examines the distinction between elastic and inelastic collisions based on energy changes. Momentum conservation holds in isolated systems for all collisions, regardless of energy loss. In elastic collisions, kinetic energy is fully conserved alongside momentum. In inelastic collisions, momentum is conserved, but kinetic energy decreases, often due to deformation or sound. A common distractor is choice A, which assumes bouncing means elastic, but KE decrease confirms inelasticity. To solve collision problems, calculate or compare kinetic energy before and after to classify the type while always applying momentum conservation.

2

Cart $A$ collides with cart $B$ on a frictionless track. The collision is described as elastic. Immediately after, the carts separate and the total kinetic energy of the two-cart system is unchanged.

Which statement is correct for the two-cart system?

Momentum is conserved only if the carts have equal mass.

Both momentum and kinetic energy are conserved.

Only kinetic energy is conserved in an elastic collision.

Momentum is not conserved because the carts exert forces on each other.

Explanation

This question evaluates the definition and implications of elastic collisions in AP Physics 1. Conservation of momentum applies to all isolated collisions, elastic or inelastic, due to balanced internal forces. Elastic collisions uniquely conserve kinetic energy as well, with total KE unchanged post-collision. Inelastic collisions do not conserve KE, even if objects separate. Choice D mistakenly states that only kinetic energy is conserved in elastic collisions, overlooking that momentum is also always conserved. A transferable strategy is to verify elasticity by confirming unchanged total KE and apply both conservation laws simultaneously for elastic problems.

3

A moving cart collides with a stationary cart on a frictionless track. After the collision, the two carts move together with a smaller speed than the original cart had. The collision is stated to be perfectly inelastic.

Which conclusion is correct?

Total kinetic energy is conserved, and total momentum decreases.

Total momentum is conserved, and total kinetic energy decreases.

Both total momentum and total kinetic energy are conserved.

Total momentum becomes zero because the carts stick together.

Explanation

This question examines conservation principles in perfectly inelastic collisions in AP Physics 1. Momentum conservation holds in both elastic and inelastic collisions for isolated systems, ensuring the total momentum remains constant. Elastic collisions preserve kinetic energy, with no loss to other forms. Inelastic collisions, particularly perfectly inelastic ones where objects stick, result in kinetic energy decrease while momentum is conserved. Choice D erroneously states that momentum becomes zero when carts stick, but momentum is conserved and depends on initial conditions, not zero unless initially zero. A transferable strategy is to calculate post-collision velocity using momentum conservation and compare kinetic energies to confirm loss in inelastic cases.

4

A rubber ball rolls right and collides head-on with a cart initially at rest on a low-friction track. The ball bounces back to the left after the collision. External forces are negligible.

What can be concluded about kinetic energy conservation?

Kinetic energy must decrease because the cart was initially at rest.

Kinetic energy cannot be conserved because momentum is always lost in collisions.

Kinetic energy may or may not be conserved; more information is needed.

Kinetic energy must be conserved because the ball reverses direction.

Explanation

This question assesses uncertainty in kinetic energy conservation for collisions in AP Physics 1. Momentum is always conserved in isolated collisions, but kinetic energy conservation distinguishes elastic from inelastic types. In elastic collisions, both quantities are conserved, often with objects rebounding. In inelastic collisions, kinetic energy decreases, though rebounding can still occur depending on masses and velocities. Choice A wrongly claims kinetic energy must be conserved due to direction reversal, but reversal can happen in inelastic cases without KE conservation. A transferable strategy is to gather data on masses and velocities to calculate both momentum and KE before and after, determining the collision type empirically.

5

Two identical pucks collide on nearly frictionless ice. Before the collision, puck 1 moves right and puck 2 is at rest. After the collision, puck 1 stops and puck 2 moves right with the same speed puck 1 initially had. Assume external forces are negligible.

What type of collision is most consistent with these observations?

Perfectly inelastic, because one object stops after impact.

Inelastic, because momentum is not conserved in collisions.

Elastic, because kinetic energy is conserved in addition to momentum.

Inelastic, because kinetic energy is always conserved in collisions.

Explanation

This question evaluates the distinction between elastic and inelastic collisions in AP Physics 1. In isolated systems, momentum is conserved in both elastic and inelastic collisions due to Newton's third law and no external forces. Elastic collisions conserve both momentum and kinetic energy, often resulting in objects bouncing apart with unchanged total KE. Inelastic collisions conserve momentum but not kinetic energy, with objects possibly sticking or separating but with energy loss. For instance, choice B wrongly labels it perfectly inelastic because one object stops, but perfectly inelastic requires sticking together, not separation. A transferable strategy is to check if initial and final kinetic energies match to confirm elasticity, especially for equal-mass head-on collisions where velocities exchange.

6

Two carts on a frictionless track collide and stick. Before the collision, cart $A$ moves right and cart $B$ moves right more slowly. Afterward, they move together to the right. External forces are negligible.

Which statement best describes the system during the collision?

Momentum is conserved, but kinetic energy is not conserved.

Kinetic energy is conserved because both carts move in the same direction.

Momentum is not conserved because both carts were moving before impact.

Both momentum and kinetic energy are not conserved because they stick.

Explanation

This question probes the application of conservation laws to inelastic collisions in AP Physics 1. In any collision without external forces, momentum is conserved for the system, reflecting the internal nature of interaction forces. Elastic collisions additionally conserve kinetic energy, keeping the total unchanged. Inelastic collisions conserve momentum but not kinetic energy, especially when objects stick together after colliding. Choice A incorrectly asserts that momentum is not conserved because both were moving, but conservation applies regardless of initial motions in isolated systems. A transferable strategy is to treat the system as isolated and use vector momentum for direction-dependent collisions, while checking for KE conservation separately.

7

A moving cart collides with a stationary cart on a nearly frictionless track. After the collision, the carts move together as a single unit. What can be concluded about kinetic energy in the collision?

It becomes zero because the carts stick together.

It must decrease because the collision is perfectly inelastic.

It must be conserved because momentum is conserved.

It must increase because the carts combine masses.

Explanation

This question probes the behavior of kinetic energy in elastic versus inelastic collisions. Momentum is conserved in all isolated collisions without external forces. Elastic collisions maintain both momentum and total kinetic energy. Inelastic collisions, especially perfectly inelastic ones where objects merge, conserve momentum but result in kinetic energy loss. Choice A is a distractor, incorrectly linking KE conservation directly to momentum without considering collision type. A transferable strategy is to recognize sticking as a sign of perfectly inelastic collisions and expect KE reduction accordingly.

8

A steel ball rolls right and collides with an identical ball at rest on a level, low-friction surface. The balls bounce apart and do not stick. Which statement best describes the collision?

Momentum is conserved, and kinetic energy is conserved (elastic collision).

Momentum is conserved only if the balls stick together.

Momentum is not conserved because the balls separate after contact.

Kinetic energy is conserved in all collisions, so it must be conserved here.

Explanation

This question evaluates knowledge of elastic and inelastic collisions involving identical objects. Momentum is always conserved in isolated collisions with no external forces, such as on a low-friction surface. Elastic collisions conserve both momentum and kinetic energy, often resulting in objects bouncing apart with the same relative speeds. Inelastic collisions conserve momentum but not kinetic energy, and while objects can bounce apart, steel balls bouncing suggests an elastic nature here. A frequent distractor is choice B, which wrongly claims momentum is not conserved because the balls separate, ignoring that conservation applies regardless of separation. A useful strategy for collision problems is to assume momentum conservation first, then verify kinetic energy equality to classify as elastic or inelastic.

9

Cart $A$ collides with cart $B$ on a frictionless track. They stick together and continue moving right with nonzero speed. Which statement about the system’s momentum after the collision is correct?

The final momentum is greater than the initial momentum because mass increased.

The final momentum must be zero because the carts stick together.

Momentum is not conserved in perfectly inelastic collisions.

The final momentum equals the initial total momentum (conserved).

Explanation

This question evaluates momentum conservation in inelastic collisions. Total momentum remains conserved in isolated collisions, equaling initial momentum post-collision. In elastic collisions, KE is also conserved, but this is irrelevant here. Inelastic collisions with sticking conserve momentum but not KE, yet final momentum matches initial. Choice A distracts by suggesting final momentum is zero due to sticking, confusing it with equal opposite initial momenta. Always calculate total initial momentum and set it equal to final for conserved systems in collision problems.

10

On a frictionless track, cart $A$ moves right and collides head-on with cart $B$ at rest. After the collision, the carts stick together and move right as one. Which statement about the collision is correct?

Which quantity is conserved during the collision?

Momentum is not conserved because cart $B$ was initially at rest.

Neither momentum nor kinetic energy is conserved because the carts stick together.

Only momentum is conserved; kinetic energy is not conserved.

Only kinetic energy is conserved because the carts stick together.

Explanation

This question assesses the understanding of conservation laws in elastic and inelastic collisions in AP Physics 1. In all isolated collisions where external forces are negligible, linear momentum is always conserved because the system is closed. In elastic collisions, both momentum and kinetic energy are conserved, with the total kinetic energy remaining the same before and after. In inelastic collisions, such as when objects stick together, momentum is conserved, but kinetic energy is not, as some is lost to other forms like heat or sound. For example, choice A incorrectly claims that only kinetic energy is conserved because the carts stick together, ignoring that kinetic energy decreases in inelastic collisions. A transferable strategy is to identify if objects stick together to classify the collision as inelastic and apply conservation of momentum while noting kinetic energy loss.

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