We define the Kinetic energy of an object as KE = KE = 1 / 2 mv2. We define the

Question

We define the Kinetic energy of an object as KE = KE = 1 / 2 mv2. We define the Potential energy due to gravity as PE = mgh, where h is the HEIGHT of the object with respect to the ground. Obtain the Kinetic energy of the cannonball just when it left the cannon. Obtain the Potential energy of the cannonball just when it left the cannon. ADD the value of (g) and (h) together. Obtain the kinetic energy of the cannonball when it reaches the maximum height. Obtain the Potential energy of the cannonball when it reaches the maximum height. ADD the value of (j) and (k) together. Obtain the kinetic energy of the cannonball JUST before it hits the ground. Obtain the kinetic energy of the cannonball JUST before it hits the ground. ADD the value of (m) and (n) together. Look at your answers to (i), (1), and (o). EXPLAIN what's going on, in terms of the total energy of the system.

Explanation / Answer

An easy way to do this is to rewrite the equation for kinetic energy in terms of momentum. Here, p = momentum, K = kinetic energy, m = mass, v = velocity p = mv K = (1/2)mv^2 Check to see that K = p^2/2m Now, since momentum is conserved in the cannon-cannonball system (the only forces are internal to this system), the momentum of the cannon and cannonball must be equal in magnitude (if opposite in direction). So, p^2 will be the same for both. The cannon has a higher mass than the cannon ball, so it will have a lower kinetic energy, since p^2/2m will be smaller.

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