Question

Two carts on an air track have the same mass and speed and are traveling toward each other. If they collide and stick together, find the total momentum and total kinetic energy of the system.

Answer 1

Answer:

$p = 0$, $K_{A} = m\cdot v^{2}$ (before collision), $K_{B} = 0$ (after collision).

Explanation:

The total momentum is obtained using the Principle of Momentum Conservation:

$m\cdot v_{A} - m \cdot v_{A} = 2\cdot v_{B}$

It is trivial to find that final speed and total momentum of the system are zero:

$p = 0$

The total kinetic energy of the system becomes zero due to the inellastic collision and the same masses and speeds. Total kinetic energies before and after collision are, respectively:

$K_{A} = m\cdot v^{2}$

$K_{B} = 0$