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

(0.536)v

after passing through the target. The collision is inelastic and during the collision, the amount of energy lost is equal to a fraction

[(0.363)KEb BC]

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

conserving the momentum

initial momentum of th e bullet = mv

final momentum of bullet = m x .536 v

change in momentum = 0.464mv

now this much momentum is transfered to the target

initial momentum of target = 0

fnal = MV

change = .464mv

MV = .464mv...................................1

KE of bullet BC = .5mv^2

enegy lost = .363

final enegy = .637 x .5mv^2 = .3185mv^2

final KE 0f bullet = .5 x m x .536^2v^2 = 0.144mv^2

so energy of the target = 0.175 mv^2

or

.5 x MV^2 = 0.175mv^2

MV^2 = 0.349mv^2.............................2

MV = .464mv...................................1

dividing 2 by 1

V = 0.752v

squaring 1 and dividing by 2

M = .61689 m

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