A cannon of mass 5.60 103 kg is rigidly bolted to the earth so it can recoil onl

Question

A cannon of mass 5.60 103 kg is rigidly bolted to the earth so it can recoil only by a negligible amount. The cannon fires an 81.5-kg shell horizontally with an initial velocity of +600 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

Momentum is conserved in both case.

When the canon is unbolted, let its recoil speed is Vc.

KE = 1/2 * m *v^2 = 1/2* 81.5*600^2 = 14670000 J.....

.. KE after unbolting = 1/2*Mc*Vc^2 + 1/2*m*v^2 = 1/2*m^2*V^2 /Mc + 1/2*m*v^2

so solving it we get v= 595.68 m/s = 596 m/s

V = 596 m/s

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