Agent Arlene devised the following method of measuring the muzzle velocity of a
ID: 2297989 • 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 4.145-kg wooden block resting on a smooth surface, and attached to a spring of spring constant k = 165.0N/m . The bullet, whose mass is7.870 g, remains embedded in the wooden block. She measures the maximum distance that the block compresses the spring to be 9.460cm .
What is the speed v of the bullet?
Express your answer to four significant figures and include the appropriate units.
Explanation / Answer
total m =4145+7.87=4152.87gm=4.15287Kg
w=sqrt(k/m)=sqrt(165/4.15287)=6.3 /sec
vel=aw=0.0946*6.3=0.59m/sec
conserving momentum
7.87/1000*v=0.59*4.1528
v=311.32 m/sec