Cart A, of mass 3.00 kg, approaches and collides with cart B, which has a mass of 7.00 kg and is initially at rest.
When the springs have reached their maximum compression,
a. cart A has come to rest relative to the ground.
b. both carts have the same velocity.
c. both carts have the same momentum.
d. all the initial kinetic energy of cart A has been converted to elastic potential energy.
To determine which statement is true, we need to analyze the conservation of momentum and energy during the collision.
a. Cart A has come to rest relative to the ground:
For this statement to be true, all of the initial kinetic energy of Cart A must be converted to other forms of energy, such as elastic potential energy. This means that the collision must be perfectly elastic, with no energy losses.
b. Both carts have the same velocity:
In an elastic collision, kinetic energy is conserved. Since Cart B is initially at rest, for both carts to have the same velocity, all the kinetic energy of Cart A must be transferred to Cart B during the collision.
c. Both carts have the same momentum:
The principle of conservation of momentum states that the total momentum of an isolated system remains constant if no external forces act on it. If the collision between the carts is elastic, then momentum is conserved during the collision.
d. All the initial kinetic energy of Cart A has been converted to elastic potential energy:
This statement aligns with option (a). If all the initial kinetic energy of Cart A is converted to elastic potential energy, it means that the collision is perfectly elastic, and there are no energy losses.
To determine the correct statement, let's analyze the collision between the two carts. Since the problem provides no additional information about the specific nature of the collision, we can assume the collision is perfectly elastic.
In a perfectly elastic collision, both momentum and kinetic energy are conserved. Therefore, the correct statement is:
c. Both carts have the same momentum.
During the collision, some of the initial kinetic energy of Cart A will indeed be converted into elastic potential energy, but not all of it. Since the collision is elastic, there will be no energy losses, meaning Cart A will still have some kinetic energy after the collision while Cart B starts to move with the same velocity. However, none of the other statements (a, b, and d) are entirely true in the scenario provided.