A cannon of mass 6.35 103 kg is rigidly bolted to the earth so it can recoil onl
ID: 1449653 • Letter: A
Question
A cannon of mass 6.35 103 kg is rigidly bolted to the earth so it can recoil only by a negligible amount. The cannon fires an 82.5-kg shell horizontally with an initial velocity of +565 m/s. Suppose the cannon is then unbolted from the earth, and no external force hinders its recoil. What would be the velocity of an identical shell fired by this loose cannon? (Hint: In both cases assume that the burning gunpowder imparts the same kinetic energy to the system. Enter your answer to the nearest whole number. Indicate the direction with the sign of your answer.)
Explanation / Answer
cannon is unbolted , momentum conservation
m1vf1+m2vf2 = 0
m1 = mass of cannon
m2 = mass of shell
in both case the burning gun powder imparts the same kinetic energy
KE = m2v2^2/2 = 1.3168 x 10^7 J
The kinetic energy imparted to the system when the cannon is unbolted has the same value
KE = m1*v1f^2/2 + m2*v2f^2/2
above momentum conservation equation solve for vf1
KE = m2^2*vf2^2/2m1 + m2*vf2^2/2
vf2 = sqrt(2KE/m2*[(m2/m1)+1])
vf2 = +561 m/s
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