Question

1. Bored, a boy shoots his pellet gun at a piece of cheese that sits, keeping cool for dinner guests, on a massive block of ice. On one particular shot, his 1.1 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 67 m/s and the cheese has a mass of 139 g, what is the coefficient of friction between the cheese and ice?

2. Bored, a boy shoots his pellet gun at a piece of cheese that sits, keeping cool for dinner guests, on a massive block of ice. On one particular shot, his 1.3 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 55 m/s and the cheese has a mass of 131 g, what is the coefficient of friction between the cheese and ice?

Both of these are the same with different numbers. Thanks in advance!

Answer 1

1)from conservation of momwntum

mv1 + 0 = (m1 + m2) Vf

Vf = [m1/(m1 + m2)] v1

KE = 1/2 M vf^2

KE = 1/2 (m1 + m2) x m1^2/(m1 + m2)^2 v1^2

KE = 1/2 [m1^2/(m1 + m2)] v1^2

Work done by the frictional force is:

W = u (m1 + m2) g d

from conservation of energy

W = KE

u (m1 + m2) g d = 1/2 [m1^2/(m1 + m2)] v1^2

u = 0.5 [m1^2 v1^2/ (m1 + m2)^2 g d ]

u = 0.5 x 0.0011^2 x 67^2/(0.1401) x 9.8 x 0.25 = 0.0079

Hence, u = 0.0079