As shown in the figure below, a bullet is fired at and passes through a piece of

Question

As shown in the figure below, a bullet is fired at and passes through a piece of target paper suspended by a massless string. The bullet has a mass m, a speed v before the collision with the target, and a speed (0.526)v after passing through the target. The collision is inelastic and during the collision, the amount of kinetic energy lost by the bullet and paper is equal to [(0.383)Kb BC] , that is, 0.383 of the kinetic energy of the bullet before the collision. Determine the mass M of the target and the speed V of the target the instant after the collision in terms of the mass m of the bullet and speed v of the bullet before the collision. (Express your answers to at least 3 decimals.)

Explanation / Answer

using the law of consrvation of linear momentum.

momentum before= momentum after

m v = M V + m (0.526)
m (v - .526 v) = .474 m v = M V
v / V = 2.11 M / m    -----------------------(a)

now using the conservation of energy
1/2 m v2 = 1/2 m(0.526v)2+ 1/2 M V2 + 0.383 m v2 / 2
.0.340 m v^2 = M V^2
v^2 / V^2 = 2.94M / m -------------------------(b)

dividing equation a by equation b , we get

v / V = 1.39   

V=0.72 v

now from equation (a), we have

v / V = 2.11 M / m

1.39= 2.11 M/m

M=0.658 m

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