Forensic scientists can determine the speed at which a rifle fires a bullet by s

Question

Forensic scientists can determine the speed at which a rifle fires a bullet by shooting into a heavy block hanging by a wire. As the bullet embeds itself in the block, the block and embedded bullet swing up; the impact speed is determined from the maximum angle of the swing. (a) Which would make the block swing higher, a 0.204 Ruger bullet of mass 2.14 g and muzzle speed 1290 m/s or a 7-mm Remington Magnum bullet of mass 9.71 g and muzzle speed 948 m/s? Assume the bullets enter the block right after leaving the muzzle of the rifle. The Remington bullet will make the block swing higher The Ruger bullet will make the block swing higher (b) Using your answer in part (a), determine the mass of the block so that when hit by the bullet it will swing through a 60° angle. The block hangs from wire of length 1.19 m and negligible mass. kg (c) What is the speed of a 9-g bullet that causes the block to swing upward through a 29° angle? m/s

Explanation / Answer

(a) momentum of ruger = 2.14 x 1290 = 2760.6 g m/s

of remington = 9.71 x 948 = 9205.1 g m/s

Ans: The Remington bullet will make the block swing higher.

(b) Applying energy conservation to find speed after the collision,
v = sqrt[ 2 g L ( 1 - cos60)]

v = 3.42 m/s

Applying momentum conservation,

9205.1 x 10^-3 kg m/s = ( M + 0.00971) x 3.42

M = 2.68 kg ...Ans

(c) v = sqrt(2 g L (1 - cos29) ) = 1.71 m/s

0.009 v0 = (2.68 + 0.009)(1.71)

v0 = 511 m/s

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