Forensic scientists can measure the muzzle velocity of a gun by firing a bullet
ID: 2096705 • Letter: F
Question
Forensic scientists can measure the muzzle velocity of a gun by firing a bullet horizontally into a large hanging block that absorbs the bullet and swings upward. The measured maximum angle of swing can be used to calculate the speed of the bullet. In one such test a rifle, a 4.20 g bullet into a 2.50 kg block.
Explanation / Answer
Energy is conserved: KE (block-bullet system after the collision) = PE (at the max angle) mv^2/2 = mgh ===> v = sqrt(2gh) Here h is the change in height of the block with the bullet in it. h = L[1 - cos(theta)] = 0.13 m. Now we can calculate the speed of the block after the collision: v = sqrt(2gh) = sqrt[(2)(9.8)(0.13)] = 1.59 m/s Momentum is conserved: mv = (M + m)V (0.0042)v = (0.0042 + 2.5)(1.59) ===> v = 950 m/s