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

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

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.)

V = ? v M = ? m 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 (0.546)v after passing through the target. The collision is inelastic and during the collision, the amount of energy lost is equal to a fraction [(0.293)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

energy lost =mv^2/2 - m ( 0.546v)^2 /2 - MV^2/2

that is equal to 0.293 K.E. bBc = 0.293mv^2 /2

mv^2/2 - m ( 0.546v)^2 /2 - MV^2/2 = 0.293mv^2 /2  

MV^2 =0.161mv^2    ---- i

and momentum conservation,

mv +0 = MV + m x 0.546v

MV = 0.454mv    ------ ii

i / ii

V = 0.161mv^2 / 0.454mv = 0.355v m/s

b) M = 0.454mv / 0.355v = 1.28m

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