Cannon Question: Loose Cannon Velocity

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The discussion focuses on a physics problem involving a cannon and the conservation of momentum and energy. When the cannon is bolted to the Earth, it fires a shell with a specific velocity, and the kinetic energy imparted to the system is considered. Once unbolted, the cannon can recoil freely, affecting the velocity of the fired shell. The key point is that the same kinetic energy is imparted to the system in both scenarios, which allows for the calculation of the shell's velocity when the cannon is loose. Understanding these conservation laws is crucial for solving the problem accurately.
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Homework Statement


A cannon of mass 5.80 x 10^3 kg is rigidly bolted to the Earth so it can recoil only by a negligible amount. The cannon fires an 85.0-kg shell horizontally with an initial velocity of +551 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 by this loose cannon? (Hint: In both cases assume that the burning gunpowder imparts the same kinetic energy to the system.)


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The Attempt at a Solution

 
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Two conservation laws apply here. One of them is already implicitly mentioned in the hint. The other one has to do with the masses and velocities.
 

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