Question

A 2 kg wooden box is initially at rest. A 0.1 kg clay ball is thrown with a velocity of 15m/s against the side of box and sticks. The box slides toward a spring. How far does the spring, with k = 200 N/m, compress in order to stop the box?

Answer 1

Mass of Wooden Box, mw= 2 Kg
Mass of Clay, mc = 0.1Kg
Initial Velocity of Clay = Vi
Initial Velocity of Wooden Box = 0

Final Velocity of Clay + Wooden Box = Vf

Uisng Momentum Conservation,
mw*0 + mc* vi = (mc + mw)* vf
0 + 0.1*15 = (2+0.1)* vf
vf = 1.5/2.1 m/s
vf = 0.714 m/s
Kinetic Energy = 0.5 * (mc + mw)* vf^2

Kinetic Energy is Transferred to Spring Energy.

Final Potential Energy of String = 0.5*kx^2

0.5*kx^2 = 0.5 * (mc + mw)* vf^2
x = sqrt((2+0.1)*0.714^2 / 200)
x = 0.0732 m
Compression = 7.32cm