Bored, a boy shoots his pellet gun at a piece of cheese that sits, keeping cool

Question

Bored, a boy shoots his pellet gun at a piece of cheese that sits, keeping cool for dinner guest, on a massive block of ice. On one particular shot, his 1.2g pellet gets stuck in the cheese, causing it to slide 25cm before coming to a stop. If the muzzle velocity of the gun is 55m/s and the cheese has a mass of 117g, what is the coeficient of fricition between the cheese and ice? Bored, a boy shoots his pellet gun at a piece of cheese that sits, keeping cool for dinner guest, on a massive block of ice. On one particular shot, his 1.2g pellet gets stuck in the cheese, causing it to slide 25cm before coming to a stop. If the muzzle velocity of the gun is 55m/s and the cheese has a mass of 117g, what is the coeficient of fricition between the cheese and ice?

Explanation / Answer

Let u is the speed of pellet and cheese after pellet entrs the cheese.
Apply momentum conservation,

m1*u1 + m2*u2 = (m1+m2)*u

1.2*55 + 0 = (1.2+117)*u

==> u = 1.2*55/(1.2+117)

= 0.558 m/s

now use equation, v^2 - u^2 = 2*a*d

0^2 - 0.558^2 = 2*a*0.25

==> a = -0.558^2/(2*0.25)

= -0.623 m/s^2

Now use the equation, a = -mue_k*g

==> mue_k = -a/g

= 0.623/9.8

= 0.064 <<<<<<<<--------------Answer

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