Question

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 58 m/s and the cheese has a mass of 134 g, what is the coefficient of friction between the cheese and ice?

Answer 1

mass of pellet (m₁) =1.1 g
mass of the system (pellet+cheese) (m₂) = 134+1.1 = 135.1g
now using conservation of momentum
m₁v₁=m₂v₂
where v₁ is velocity of the pellet and v₂ is the initial velocity of the (pellet+cheese ) system
1.1*58=135.1*v₂
v₂= 0.472 m/s

now, initial velocity of (pellet+cheese)system = v₂ =0.472 m/s
and final velocity is zero
by using
v₂² - 0 = 2as
where a is the retardation and s =25cm

(0.472)^2 = 2*a*0.25
a= 0.445 m/s2

now, friction force = applied force
m₂*a=meu*m₂*g
where meu is the coefiicient of friction
meu= a/g=0.445 / 9.81 = 0.045.