As shown in the figure below, a bullet is fired at and passes through a paper ta

Question

As shown in the figure below, a bullet is fired at and passes through a paper target suspended by a massless string. The bullet has a mass m, a speed v before the collision with the target, and a speed

(0.506)v

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

[(0.253)KEb BC]

of the kinetic energy of the bullet before the collision. Determine the mass M of the target and the speed Vof 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=

M=

http://www.webassign.net/webassignalgphys1/8-p-035.gif

Explanation / Answer

bullet’s KEf = (0.506)² * [KEb BC]

KEf = 0.256 * [KEb BC]

Lost energy = 0.253 * [KEb BC], so the target has
KEt = (1 - 0.256 - 0.253) * [KEb BC]

KEt = 0.491 * [KEb BC]

[KEb BC] = ½mv²
KEt = 0.2455mv² = ½MV2

momentum is conserved
mv + 0 = 0.506mv + MV

MV = 0.494mv
M = 0.494mv / V

Plug that into the KEt equation:
0.2455mv² = ½(0.494mv / V)V²

0.2455v = 0.247 V

V = 0.99392713 v

V = 0.994 v

M = 0.494mv / V

M = 0.494mv / 0.99392713 v

M = 0.497m

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