Agent Arlene devised the following method of measuring the muzzle velocity of a
ID: 1464976 • Letter: A
Question
Agent Arlene devised the following method of measuring the muzzle velocity of a rifle (the figure below). She fires a bullet into a 4.107-kg wooden block resting on a smooth surface, and attached to a spring of spring constant k = 162.9 N/m . The bullet, whose mass is 7.870 g, remains embedded in the wooden block. She measures the maximum distance that the block compresses the spring to be9.460 cm .
What is the speed v of the bullet?
Express your answer to four significant figures and include the appropriate units.
Explanation / Answer
By the conservation of momentum
Initial momentum = final mometnum
mv = (M+m)V
V = mv/(M+m)
BY the conservation of energy,
the kinetic energy of the block and bullet system = spring energy
1/2 (M+m) V^2 = 1/2 kx^2
(M+m) (mv / M+m) ^2 = kx^2
m^2v^2 / (M+m) = kx^2
(7.87*10^-3*v)^2 / (4.107 + 7.87*10^-3) = 162.9 * 0.0946^2
v = 311.21 m/s
so the speed of the bullet is 311.21 m/s