Question

Did the calculated change in momentum of the cart equal the measured impulse applied to it by the wall during the nearly elastic collision? Explain.

Answer 1

The calculated change in momentum of the cart does not always equal the measured impulse applied to it by the wall during a nearly elastic collision. This is because the impulse is used to both change the cart's velocity and its direction.

Step-by-step explanation:

In a nearly elastic collision between a cart and a wall, the calculated change in momentum of the cart does not always equal the measured impulse applied to it by the wall.

This is because during an elastic collision, the kinetic energy is conserved, so some of the impulse is used to change the cart's velocity, while the rest is used to change its direction.

Therefore, while the calculated change in momentum provides information about the magnitude of the impulse, it does not account for the change in direction.

Answer 2

In a nearly elastic collision, the calculated change in momentum of the cart equals the measured impulse applied by the wall, consistent with the impulse-momentum theorem.

Step-by-step explanation:

The calculated change in momentum of the cart should equal the measured impulse applied to it by the wall during a nearly elastic collision. This is supported by the impulse-momentum theorem which states that the impulse on an object is equal to the change in its momentum. To calculate the change in momentum for a ball or cart, you take the difference between the initial and final momentum (mass times velocity) of the cart, which should then equal the impulse (force times time). When an object like a cart collides with a rigid wall and recoils, this change in momentum occurs over the duration of the collision and is due to the force applied by the wall. According to Newton's third law, the wall experiences the same magnitude of force but in the opposite direction. If the collision is nearly elastic, and assuming no other external forces like friction are acting on the system, the measured impulse on the wall and the change in momentum of the cart should equal in magnitude but have opposite signs.