Agent Arlene devised the following method of measuring the muzzle velocity of a
ID: 1701346 • Letter: A
Question
Agent Arlene devised the following method of measuring the muzzle velocity of a rifle. She fires a bullet into a 4.500-kg wooden block resting on a smooth surface, and attached to a spring of spring constant k = 139.0 N/m. The bullet, whose mass is 7.700 kg, remains embedded in the wooden block. She measures the maximum distance that the block compresses the spring to be 9.460 cm. I need to find the velocity of the bullet when it strikes the block???
Agent Arlene devised the following method of measuring the muzzle velocity of a rifle. She fires a bullet into a 4.500-kg wooden block resting on a smooth surface, and attached to a spring of spring constant k = 139.0 N/m. The bullet, whose mass is 7.700 kg, remains embedded in the wooden block. She measures the maximum distance that the block compresses the spring to be 9.460 cm. I need to find the velocity of the bullet when it strikes the block???Explanation / Answer
This problem requires you to use both conservation of momentum and conservation of energy. You know from conservation of momentum that:
mv0=(m+M)vf
So in order to find v0, you must first find vf. When the bullet first strikes, the energy is entirely kinetic with zero potential energy (since we define the point where the spring is not compressed to be U=0). After moving the given distance, the potential energy is equal to 0.5kx2. So, by conservation of energy:
0.5(m+M)vf2=0.5kx2. Solving for vf gives vf=x(k/(m+M))
You can then plug this final velocity into the original conservation of momentum equation and solve for the initial velocity of the bullet, v0.
You then obtain that v0=(x(m+M)/m)(k/(m+M)). I'll leave you to plug in the actual numbers.