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.s16) after passing through the target. The collision is inelastic and during the collision, the amount of energy lost is equal to a fraction ((0.493)KEb acl 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.) (a) Before collision (b) After collision

Explanation / Answer

Applying momentum conservation,

m v + (M x 0) = (m x 0.516 v) + M V

M V = 0.484 m v ..... (i)

Applying work - energy,

m v^2 / 2 = m (0.516v)^2 / 2 + M V^2 /2 + (0.493)( m v^2 / 2)

m v^2 = 0.266 m v^2 + M V^2 + 0.493 m v^2

M V^2 = 0.241 m v^2 .... (ii)

(ii) /(i)

V = 0.241 v / 0.484

V = 0.497 v ......Ans

M = 0.973 m .....Ans

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