Question
You are given two carts, A and B. They look
identical, and you are told that they are made
of the same material. You place A at rest on
an air track and give B a constant velocity directed to the right so that it collides elastically
with A. After the collision, both carts move
to the right, the velocity of B being smaller
than what it was before the collision.
What do you conclude?
1. Cart A is hollow
2. The two carts are identical
3. need more information
4. Cart B is hollow
identical, and you are told that they are made
of the same material. You place A at rest on
an air track and give B a constant velocity directed to the right so that it collides elastically
with A. After the collision, both carts move
to the right, the velocity of B being smaller
than what it was before the collision.
What do you conclude?
1. Cart A is hollow
2. The two carts are identical
3. need more information
4. Cart B is hollow
Answers
GPT-4o mini
In this scenario, since the collision is elastic and both carts are made of the same material, we can analyze the situation in terms of momentum and kinetic energy conservation.
Since cart B has a constant initial velocity and collides elastically with cart A (which is initially at rest), we know that:
1. The total momentum before the collision equals the total momentum after the collision.
2. The kinetic energy before the collision equals the kinetic energy after the collision.
After the collision, it is noted that cart B’s velocity is smaller than it was before the collision, and both carts are moving to the right.
Given that cart B loses some of its velocity but still keeps moving forward suggests that it transfers some of its momentum and kinetic energy to cart A. The fact that cart A starts to move means it has gained some velocity; for this to happen:
- If cart A was less massive than cart B, cart B would not significantly lose speed while imparting velocity to cart A.
- If both carts are identical in mass, the expected outcome in an elastic collision could lead to cart B having a final velocity that is equal to that of cart A, which contradicts our observation that cart B is moving slower than its initial velocity.
Thus, the only feasible conclusion without any further specific information about the physical structure of the carts (i.e., whether they are hollow or solid) is that they cannot have identical masses, leading us to conclude that one cart must be hollow. Since cart B lost speed, it suggests that cart B must be the lighter, likely hollow cart; while cart A, gaining velocity, could be the denser one.
So the best conclusion to draw from the information provided is:
**4. Cart B is hollow.**
Since cart B has a constant initial velocity and collides elastically with cart A (which is initially at rest), we know that:
1. The total momentum before the collision equals the total momentum after the collision.
2. The kinetic energy before the collision equals the kinetic energy after the collision.
After the collision, it is noted that cart B’s velocity is smaller than it was before the collision, and both carts are moving to the right.
Given that cart B loses some of its velocity but still keeps moving forward suggests that it transfers some of its momentum and kinetic energy to cart A. The fact that cart A starts to move means it has gained some velocity; for this to happen:
- If cart A was less massive than cart B, cart B would not significantly lose speed while imparting velocity to cart A.
- If both carts are identical in mass, the expected outcome in an elastic collision could lead to cart B having a final velocity that is equal to that of cart A, which contradicts our observation that cart B is moving slower than its initial velocity.
Thus, the only feasible conclusion without any further specific information about the physical structure of the carts (i.e., whether they are hollow or solid) is that they cannot have identical masses, leading us to conclude that one cart must be hollow. Since cart B lost speed, it suggests that cart B must be the lighter, likely hollow cart; while cart A, gaining velocity, could be the denser one.
So the best conclusion to draw from the information provided is:
**4. Cart B is hollow.**