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

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(0.493)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

conservation of momentum

m v = m*0.546v + M V

M = 0.454*mv/V

KE loss = KE final - KE initial

-0.493* 1/2 mv^2 = ( 1/2 M V^2 +0.5* m*(0.546 v)^2 ) - 1/2 m v^2

plug in M

-0.493 m v^2 = 0.454 m v V + 0.546^2 m v^2 - m v^2

m cancels

-0.493 v^2 - 0.546^2 v^2 + v^2 = 0.454 v V

V = [( -0.493 - 0.564^2 +1)/0.454] v=0.416 v

so M = 0.454 m v/(0.416 v) = 0.454/0.416 m=1.091 m

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