A cannon of mass 5.06 x 10 3 kg is rigidly bolted to the earth so it can recoil

Question

A cannon of mass 5.06 x 103 kg is rigidly bolted to the earth so it can recoil only by a negligible amount. The cannon fires a 71.3 kg shell horizontally with an initial velocity of 594 m/s. Suppose the cannon is then unbolted from the earth, and no external force hinders its recoil. What would be the velocity of a shell fired from this loose cannon? (Hint: In both cases assume that the burning gunpowder imparts the same kinetic energy to the system.)

Explanation / Answer

When the cannon is loose, the cannon and the shell attain the same momentum p on firing. K.e. = p^2/2m of each. Therefore, kinetic energy of both = p^2/2m1 + p^2/2m2 This is equal to initial kinetic energy of shell when cannon was bolted. => p^2/2(1/5060 + 1/71.3) = 0.5*71.3*594^2 => p = 42056.9 => velocity = p/m = 42056.9/71.3 = 589.85 m/s

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