A cannon of mass 6.10 10 3 kg is rigidly bolted to the earth so it can recoil on

Question

A cannon of mass 6.10 103 kg is rigidly bolted to the earth so it can recoil only by a negligible amount. The cannon fires an 86.5-kg shell horizontally with an initial velocity of +580 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

conserve the momentum

after unbolted

MsVs = McVc

86.5 Vs = 6.10 10^3 Vc ---------- 1

now,

kinetic energy of the system remains constant before unloted and after unbolted

so,

0.5 Ms (Vs1)^ = O.5 Ms (Vs)^2 + 0.5 Mc (Vc)^2

0.5 * 86.5 (580)^2 = 0.5 * 86.5 (Vs)^2 + 0.5 * 6.10 10^3 (Vc)^2 ----------------2

putting the value of Vc from eqn 1 into eqn 2

Vs = 575.93 m/s { in the same direction as before unbolted or opposite to the direction of cannon}

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