(A) Bored, a boy shoots his pellet gun at a piece of cheese that sits, keeping c

Question

(A) 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 67 m/s and the cheese has a mass of 107 g, what is the coefficient of friction between the cheese and ice?________



(b) A heavy wooden block rests on a flat table and a high-speed bullet is fired horizontally into the block, the bullet stopping in it. How far will the block slide before coming to a stop? The mass of the bullet is 11.8 g, the mass of the block is 8.9 kg, the bullet's impact speed is 860 m/s, and the coefficient of kinetic friction between the block and the table is 0.220. (Assume that the bullet does not cause the block to spin.)__________cm

Explanation / Answer

here,

mass of the gun , m = 0.0013 g

distance to stop , d = 0.25 m

the muzzle velocity of gun , vo = 67 m/s

mass of chesse , M = 0.107 kg

let the coefficient of friction be u

let the velocity of chesse after the collsion be v

using conservation of momentum

m * v0 = ( m + M) * v

0.0013 * 67 = ( 0.0013 + 0.107 ) * v

v = 0.8042 m/s

let the deaccleration be a

using third equation of motion

v^2 - u^2 = 2 * a*s

- 0.8042^2 = 2 * 0.25 * a

a = 1.29 m/s^2

a= u*g

1.29 /9.8 = u

u = 0.13

the coeffiecint of friction between the block and the ice is 0.13

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