Impulse Momentum

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 (0.456)v

 after passing through the target.

The collision is inelastic and during the collision, the amount of energy lost is equal to a fraction [(0.463)KE_b 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.)

Answer 1

Hi Jose S.,

In order, determine

(1) the kinetic energy of the bullet after the collision as a fraction of its initial kinetic energy, you are given v(initial) and v(final) as v and 0.456v respectively.

(2) Now, of the initial kinetic energy of the bullet, some goes into the final kinetic energy of the bullet. You are also given the energy loss in the collision. So how much energy is retained (not lost) in the collision?

(3) Since you know the final kinetic energy of the bullet, any energy determined in (2) in excess of that determined in (1) must be held by the target. How much is that? Express first as f(m, v) and then as f(M, V) [these two quantities are equal, since they refer to the same thing!]

(4) Total momentum is conserved in the collision, as it is in any process. Write an equation to express this.

(5) Use the relationship in (4) and the equality in (3) to solve for the desired answer.

-- Cheers, -- Mr. d.