Question

A 7 kg cart is moving down a track at a speed of 9 m/s and hits a 11 kg cart sitting still. The two have an inelastic collision. What is the resulting speed after the collision?

Answer 1

Answer: 3.5 m/s

Explanation:

This problem can be solved by the Conservation of Momentum principle which establishes the initial momentum $p_{i}$ must be equal to the final momentum $p_{f}$, and taking into account this is an inelastic collision:

Before the collision:

$p_{i}=mV_{o}+MU_{o}$ (1)

After the collision:

$p_{f}=(m+M)V_{f}$ (2)

Where:

$m=7 kg$ is the mass of the first cart

$V_{o}=9 m/s$ is the velocity of the first cart

$M=11 kg$ is the mass of the second cart

$U_{o}=0 m/s$ is the velocity of the second cart

$V_{f}$ is the final velocity of both carts

$p_{i}=p_{f}$ (3)

$mV_{o}+MU_{o}=(m+M)V_{f}$ (4)

Since $U_{o}=0 m/s$:

$mV_{o}=(m+M)V_{f}$ (5)

$V_{f}=\frac{mV_{o}}{m+M}$ (6)

$V_{f}=\frac{(7 kg)(9 m/s)}{7 kg + 11 kg}$ (7)

Finally:

$V_{f}=3.5 m/s$