Understanding Elastic Collisions: Masses of Objects

When the separation between the carts is a minimum, What can be said about the masses of the carts?

1) The mass of Cart A is greater than the mass of Cart B.

2) The mass of Cart A is less than the mass of Cart B.

3) The masses of Cart A and Cart B are equal.

4) The masses of the carts cannot be determined.

Final answer:

If the separation between the carts is a minimum, it means the collision is elastic and the carts will bounce off each other. In an elastic collision, the relative velocity of the colliding objects before and after the collision remains the same. Therefore, if the separation is a minimum, it implies that the masses of Cart A and Cart B are equal.

When two carts with spring bumpers collide, their masses can be determined based on the minimum separation between them. If the separation is a minimum, it means that the collision is elastic and the carts will bounce off each other. In this type of collision, the momentum and kinetic energy are conserved. Since Cart A is initially moving to the right and Cart B is initially stationary, the final velocities of the carts after the collision will be such that the momentum and kinetic energy are conserved.

In an elastic collision, the relative velocity of the colliding objects before and after the collision remains the same. Therefore, if the separation between the carts is a minimum, it means that their velocities after the collision will be equal and opposite. The momentum of Cart A is given by its mass (mA) times its final velocity (vA), and the momentum of Cart B is given by its mass (mB) times its final velocity (vB). Since the carts stick together after the collision, their final velocities will be equal but opposite in direction. This means that the magnitude of vA will be equal to the magnitude of vB, but their signs will be opposite.

From the conservation of momentum, we have:

mA * vA + mB * vB = 0

Since both carts have equal magnitude of final velocities, we can write:

mA * v + mB * (-v) = 0

Simplifying this equation, we get:

mA * v - mB * v = 0

(mA - mB) * v = 0

Since v cannot be zero, the only way for the equation to hold is if mA - mB = 0, which implies that the masses of Cart A and Cart B are equal. Therefore, option 3) The masses of Cart A and Cart B are equal.