Physics 18 Spring 2011 Homework 7 - Solutions Wednesday March ...

2. Bored, a boy shoots his pellet gun at a piece of cheese that sits on a massive block of
ice. On one particular shot, his 1.2 g pellet gets stuck in the cheese, causing it to slide
25 cm before coming to a stop. If the muzzle velocity of the gun is known to be 65
m/s and the cheese has a mass of 120 g, what is the coefficient of friction between the
cheese and the ice?
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Solution
Let’s start by looking at the momentum. Since the cheese isn’t moving, initially, the
initial momentum is just that of the pellet, pi = ppellet. If the mass of the pellet is m,
and it has an initial velocity v, then pi = mv. After the collision, the pellet is stuck in
the cheese. If the cheese has a mass M, and if the system has a final velocity V , then
the final momentum is pf = (m + M) V . Solving for the final velocity gives
m
V =
v.
m + M
So, the combined system has an initial kinetic energy of KE = 1
2 (m + M) V 2 =
m 2
2(m+M) v2 . After the cheese/pellet system has come to rest, its kinetic energy is zero.
The energy lost has to go into the work done by friction, which is W = µkFNd =
µk (m + M) gd, where d is the distance the system slides. So, setting this equal to the
kinetic energy and solving for the coefficient we find
Plugging in numbers gives
µk =
µk =
m 2 v 2
2 (m + M) 2 gd =
m 2 v 2
2 (m + M) 2 gd .
0.0012 2 × 65 2
2 (0.1212) 2 × 9.8 × 0.25
2
= 0.085