A) The expanding gases that leave the muzzle of a rifle also contribute to the r

Question

A) The expanding gases that leave the muzzle of a rifle also contribute to the recoil. A .30 caliber bullet has mass 7.20×103 kg and a speed of 601 m/s relative to the muzzle when fired from a rifle that has mass 3.00 kg . The loosely held rifle recoils at a speed of 2.15 m/s relative to the earth. Find the momentum of the propellant gases in a coordinate system attached to the earth as they leave the muzzle of the rifle.

B) A bullet of mass 6.00 g is fired horizontally into a wooden block of mass 1.14 kg resting on a horizontal surface. The coefficient of kinetic friction between block and surface is 0.220. The bullet remains embedded in the block, which is observed to slide a distance 0.300 m along the surface before stopping. What was the initial speed of the bullet?

Explanation / Answer

A)

mass of bullet , m = 0.0072 kg

speed of bullet , v = 601 m/s

speed of rifle , V = 2.15 m/s

mass of rifle , M = 3 kg

let the momentum of the propellant gasses be P

using the conservation of momentum

P + m * v = M * V

P + 0.0072 * 601 = 3 * 2.15

P = 2.12 kg.m/s

the momentum of the propellant gases in a coordinate system attached to the earth as they leave the muzzle of the rifle is 2.12 kg.m/s

B)

mass of bullet , m = 0.006 kg

mass of block , M = 1.14 kg

let the initial speed of the bullet be u

using conservation of momentum

m * u = ( m +M ) * v

v = 0.00524 * u ....(1)

s = 0.3 m

uk = 0.22

a = uk * g = 0.22 * 9.8 = 2.156 m/s^2

using third equation of motion

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

(0.00524 * u )^2 - 0 = 2 * 2.156 * 0.3

u = 217.05 m/s

the initial speed of the bullet is 217.05 m/s

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