Elastic and Inelastic Collisions - AP Physics 1

1. 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?
   Answer: Kinetic energy may or may not be conserved; more information is needed. 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.
2. A moving cart collides with an identical cart at rest on a nearly frictionless track. Afterward, the two carts move together as one object. Which conclusion about energy and momentum is most accurate?
   Answer: Momentum is conserved, but kinetic energy is not conserved. This question tests understanding of elastic and inelastic collisions. When two objects collide and stick together, this is a perfectly inelastic collision - the most inelastic type possible. In all collisions of isolated systems, momentum is conserved because the forces between objects are internal and cancel out according to Newton's third law. However, kinetic energy is not conserved in inelastic collisions; some energy is transformed into heat, sound, and permanent deformation as the objects merge. Choice C incorrectly assumes identical masses guarantee energy conservation, while choice D wrongly claims sticking implies zero final momentum. Remember that objects sticking together is the hallmark of a perfectly inelastic collision where maximum kinetic energy is lost while momentum remains conserved.
3. Two carts collide on a frictionless track. After the collision, they move apart, and the total kinetic energy of the system is measured to be smaller than before. External forces are negligible. Which classification is consistent with the measurement?
   Answer: Inelastic, because kinetic energy is not conserved. This question tests classification based on energy measurements in collisions for AP Physics 1. Momentum is conserved in both elastic and inelastic collisions when the system is isolated. Elastic collisions conserve kinetic energy, resulting in no net loss. Inelastic collisions feature kinetic energy loss, even if objects move apart after impact. Choice D incorrectly suggests that kinetic energy decreases in elastic collisions, but by definition, it remains constant in elastic ones. A transferable strategy is to measure pre- and post-collision KE; if it decreases but objects separate, classify as inelastic and use momentum for velocity calculations.
4. A clay blob slides right and hits a cart at rest; the clay sticks and the combined object moves right more slowly. Which statement is correct?​
   Answer: Momentum is conserved, but kinetic energy decreases during the collision. This question tests understanding of elastic and inelastic collisions. When objects stick together (like clay adhering to a cart), this is a perfectly inelastic collision where kinetic energy is not conserved. However, momentum is always conserved in collisions without external forces, regardless of whether objects stick or bounce. The combined object moving more slowly than the initial clay confirms kinetic energy was lost to deformation and adhesion. Choice A incorrectly claims momentum is not conserved when objects stick, but sticking doesn't violate momentum conservation. Remember that perfectly inelastic collisions (sticking) have maximum kinetic energy loss while still conserving momentum.
5. A cart collides with a second cart at rest on a low-friction track. The carts separate after impact, and measurements show total kinetic energy after is less than before. What type of collision occurred?
   Answer: Inelastic (but not perfectly inelastic), because kinetic energy decreased while the carts did not stick. This question tests understanding of elastic and inelastic collisions. Collisions are classified by whether kinetic energy is conserved: elastic collisions conserve both momentum and kinetic energy, while inelastic collisions conserve only momentum. When kinetic energy decreases but objects don't stick together, this is an inelastic collision that isn't perfectly inelastic - some energy is lost to heat, sound, and temporary deformation, but the objects retain separate identities. A perfectly inelastic collision specifically requires objects to stick together, resulting in maximum kinetic energy loss. Choice A incorrectly assumes not sticking means elastic, while choice D wrongly claims momentum conservation implies elasticity. To classify collisions, check both whether objects stick (perfectly inelastic) and whether kinetic energy is conserved (elastic) or lost (inelastic).
6. A $0.50\,\text{kg}$ cart moving right collides with a $1.0\,\text{kg}$ cart initially at rest on a low-friction track. The carts bounce apart and do not stick. Which additional information is needed to decide whether kinetic energy is conserved?
   Answer: The carts' velocities after the collision. This question tests understanding of elastic and inelastic collisions. To determine whether a collision is elastic (kinetic energy conserved) or inelastic (kinetic energy not conserved), we need to compare the total kinetic energy before and after the collision. We already know the masses and initial velocities, so we can calculate the initial kinetic energy. However, to calculate the final kinetic energy, we need the final velocities of both carts after they bounce apart. Choice A incorrectly assumes rebounding guarantees elasticity, while choices C and D ask for information we already have or that's always true. The key strategy is to calculate kinetic energy using KE = ½mv² for each object before and after collision - if the totals match, it's elastic.
7. Two carts collide in one dimension on a nearly frictionless track; high-speed video shows they bounce apart and return to their original speeds (opposite directions). Which claim is correct?​
   Answer: The collision is elastic; both momentum and kinetic energy are conserved. This question tests understanding of elastic and inelastic collisions. When objects return to their original speeds after bouncing apart (just in opposite directions), both momentum and kinetic energy are conserved, indicating an elastic collision. In elastic collisions, objects exchange momentum and energy without permanent deformation or energy loss. The fact that they bounce back to original speeds is a classic signature of elastic behavior. Choice A incorrectly labels this as perfectly inelastic, which would require the carts to stick together. To identify elastic collisions, look for objects that bounce apart while maintaining the same total kinetic energy as before the collision.
8. Two carts on a frictionless track collide and stick together. The combined cart continues moving in the same direction as cart $A$ was initially moving. External forces are negligible. Which statement best distinguishes this collision from an elastic collision?
   Answer: In this collision, kinetic energy is not conserved, unlike an elastic collision. This question distinguishes inelastic from elastic collisions in AP Physics 1. Momentum is conserved in all types of isolated collisions, but kinetic energy conservation is specific to elastic ones. In elastic collisions, both momentum and KE are preserved, often with separation. Inelastic collisions, especially those where objects stick, do not conserve KE, though momentum remains constant. Choice A wrongly states that momentum is not conserved in this inelastic case, but momentum conservation is universal in isolated systems. A transferable strategy is to compare collision types by checking KE conservation; if lost, it's inelastic, and apply momentum to find final velocities regardless.
9. A $0.40\,\text{kg}$ cart moving right at $3.0\,\text{m/s}$ collides with a $0.40\,\text{kg}$ cart initially at rest on a level track. After the collision, the carts stick together and move as one. Which statement about this collision is correct?
   Answer: Momentum is conserved, but kinetic energy is not conserved because the carts stick together. This question tests understanding of elastic and inelastic collisions. In all collisions between objects in an isolated system, momentum is conserved due to Newton's third law - the internal forces between objects are equal and opposite, so the total momentum remains constant. However, kinetic energy is only conserved in elastic collisions where objects bounce apart without permanent deformation. In this collision, the carts stick together, which is the defining characteristic of a perfectly inelastic collision where kinetic energy is lost to deformation, sound, and heat. Choice A incorrectly claims both are conserved, ignoring that sticking indicates energy loss. When objects stick together after collision, remember that momentum is still conserved but kinetic energy is always lost.
10. Two identical carts collide; after impact they move together at half the initial speed of the moving cart. Which classification is consistent with this outcome?
    Answer: Perfectly inelastic, because the carts stick and kinetic energy is not conserved. This question tests understanding of elastic and inelastic collisions. When two objects stick together after collision, this is the definition of a perfectly inelastic collision, where kinetic energy is not conserved. Using momentum conservation: if identical carts collide and stick, with one initially at rest, the final speed equals half the initial speed of the moving cart, which matches the given outcome. This kinetic energy loss (from mv²/2 to m(v/2)²/2 = mv²/4 for each cart) confirms the collision is perfectly inelastic. Choice D incorrectly claims momentum isn't conserved when carts stick—momentum is always conserved in collisions with negligible external forces. The strategy: when objects stick together, it's always perfectly inelastic with kinetic energy loss but momentum conservation.
11. Two identical carts collide in one dimension on a nearly frictionless track. They stick together after the collision. Which claim about conservation laws is correct for the two-cart system?
    Answer: Momentum is conserved, but kinetic energy is not conserved. This question tests understanding of elastic and inelastic collisions. When objects stick together after collision, this is the defining characteristic of a perfectly inelastic collision. In all collisions of isolated systems, momentum is conserved because the forces between colliding objects are internal and cancel according to Newton's third law - the total momentum before equals the total momentum after. However, kinetic energy is not conserved in inelastic collisions; energy transforms into heat, sound, and permanent deformation as the objects merge. Choice B incorrectly claims deformation prevents momentum conservation, while choice D misunderstands that internal forces don't violate momentum conservation. Remember that sticking together always indicates a perfectly inelastic collision where momentum is conserved but kinetic energy is lost.
12. 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?
    Answer: It must decrease because the collision is perfectly inelastic. 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.
13. Two identical pucks collide on frictionless ice and rebound; afterward, the total kinetic energy is the same as before. Which type of collision occurred?​
    Answer: Elastic, so both momentum and kinetic energy are conserved. This question tests understanding of elastic and inelastic collisions. In elastic collisions, both momentum and kinetic energy are conserved for the system. The problem states that total kinetic energy remains unchanged after the collision, which is the defining characteristic of an elastic collision. In inelastic collisions, kinetic energy is converted to other forms like heat or deformation, so total kinetic energy decreases. Choice B incorrectly claims kinetic energy is always lost in collisions, but elastic collisions preserve kinetic energy. To identify collision types, check if kinetic energy is conserved (elastic) or lost (inelastic), while momentum is conserved in both cases.
14. A glider moving right collides with another glider at rest on an air track. They bounce apart, and the total kinetic energy is the same before and after. What type of collision occurred?
    Answer: Elastic This question tests identifying collision types from energy conservation. Momentum is conserved in all isolated collisions on frictionless tracks like air tracks. Elastic collisions are defined by conservation of both momentum and kinetic energy, with KE unchanged. Inelastic collisions conserve momentum but not KE, which decreases. Choice A is a distractor, assuming sticking for perfectly inelastic, but bouncing with equal KE indicates elastic. To classify collisions, compare pre- and post-collision KE after confirming momentum conservation.
15. Cart $A$ moving right collides with cart $B$ moving left; they latch and move together afterward. Which statement best describes conservation laws during the collision?​
    Answer: Momentum is conserved, but kinetic energy is not conserved. This question tests understanding of elastic and inelastic collisions. When objects latch together after collision, this is a perfectly inelastic collision where kinetic energy is not conserved due to the energy required for latching and deformation. However, momentum is always conserved in collisions without external forces, even when objects move in opposite directions initially. The vector nature of momentum means oppositely directed momenta partially cancel, but total momentum is still conserved. Choice C incorrectly claims momentum is not conserved due to opposite initial directions, but momentum conservation applies regardless of initial directions. Remember that latching or sticking indicates perfectly inelastic collisions with kinetic energy loss but momentum conservation.
16. 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?
    Answer: Momentum is conserved, but kinetic energy is not conserved. 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.
17. A rubber ball cart collides head-on with another cart on a low-friction track; afterward, the system's kinetic energy is unchanged. Which is correct?​
    Answer: Elastic collision: momentum and kinetic energy are conserved for the two-cart system. This question tests understanding of elastic and inelastic collisions. When the system's total kinetic energy remains unchanged after a collision, this defines an elastic collision. In elastic collisions, both momentum and kinetic energy are conserved for the isolated system. The rubber ball cart likely has elastic properties that allow it to bounce without permanent deformation or energy loss. Choice C incorrectly calls this perfectly inelastic while claiming kinetic energy is conserved, but perfectly inelastic collisions always lose kinetic energy. To identify collision types, check kinetic energy: unchanged means elastic, decreased means inelastic, and maximum loss with sticking means perfectly inelastic.
18. Two identical carts collide head-on on a frictionless track and rebound. If the collision is elastic, which statement is correct for the two-cart system?
    Answer: Both momentum and kinetic energy are conserved. This question assesses conservation principles in elastic collisions with rebounding objects. In isolated systems, momentum is always conserved for any collision type. Elastic collisions uniquely conserve both momentum and kinetic energy, allowing rebound with no energy loss. Inelastic collisions conserve momentum but lose kinetic energy, even if rebound occurs. A typical distractor is choice B, which claims only momentum is conserved and KE always lost, but elastic cases preserve KE. For analyzing rebounds, verify if KE is conserved to confirm elasticity while applying momentum conservation universally.
19. Two carts collide and stick on a horizontal air track; the track provides negligible external horizontal impulse. What must remain constant for the system?
    Answer: Total momentum, even though kinetic energy decreases. This question tests understanding of elastic and inelastic collisions. On a horizontal air track with negligible external horizontal forces, momentum is always conserved for the system, regardless of collision type. When carts stick together, this is a perfectly inelastic collision where kinetic energy is not conserved—it decreases as some converts to other forms. The conservation of momentum doesn't depend on whether objects stick or their masses; it depends only on external forces being negligible. Choice C incorrectly claims momentum isn't conserved because carts stick—sticking affects kinetic energy conservation, not momentum conservation. Remember: momentum conservation depends on external forces, while sticking determines if the collision is perfectly inelastic with kinetic energy loss.
20. A glider moving right collides with a second glider; after collision they separate and the measured total kinetic energy is smaller. Which statement is correct?
    Answer: The collision is inelastic; momentum of the two-glider system is still conserved. This question tests understanding of elastic and inelastic collisions. When total kinetic energy decreases after a collision, this defines an inelastic collision—some kinetic energy has converted to other forms like heat or sound. However, momentum is still conserved for the two-glider system because external forces are negligible. The fact that gliders separate doesn't make it elastic; what matters is that kinetic energy decreased. Choice C incorrectly claims momentum isn't conserved because kinetic energy decreased—these are independent conservation laws, and momentum is conserved regardless of energy changes when external forces are negligible. The key principle: inelastic means kinetic energy decreases, but momentum is still conserved in isolated systems.

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