Solving Question: Speed of Ball with Rigid Cannon

[srhly]

I had a two-part question but I've figured out the first part. A cannon with mass of 1960 kg fires a 24.5 kg ball horizontally. The cannonball has a speed of 120 m/s after it has left the barrel. For the first part I found that if the cannon was free to roll horizontally, its speed immediately after it was fired was 1.4907 m/s. The part I'm stuck on says imagine the same charge is used so total energy of cannon plus cannonball system is the same. Disregarding friction how much faster would the ball travel if the cannon were mounted rigidly and all other parameters remained the same? Answer in units of m/s.

 

[Joel]

What if you thought of momentum instead of energy? It is also conserved.

 

[ZapperZ]

I had a two-part question but I've figured out the first part. A cannon with mass of 1960 kg fires a 24.5 kg ball horizontally. The cannonball has a speed of 120 m/s after it has left the barrel. For the first part I found that if the cannon was free to roll horizontally, its speed immediately after it was fired was 1.4907 m/s. The part I'm stuck on says imagine the same charge is used so total energy of cannon plus cannonball system is the same. Disregarding friction how much faster would the ball travel if the cannon were mounted rigidly and all other parameters remained the same? Answer in units of m/s.

It usually is adviceable to write down the exact question verbatim. Sometime, what you interpret as being asked is different than what it is actually asking. If I have understood your question here correctly, this is what it is asking for:

1. Since you already found the first part, you know the KE of the cannonball and the cannon separately.

2. If the cannon is fixed, then ALL the KE is now transferred to the cannonball. So the cannonball now will have the KE of what it had before PLUS the KE from the non-moving cannon. So this is its new KE for the cannonball. From here, find the new speed.

Zz.

 

[xanthym]

I had a two-part question but I've figured out the first part. A cannon with mass of 1960 kg fires a 24.5 kg ball horizontally. The cannonball has a speed of 120 m/s after it has left the barrel. For the first part I found that if the cannon was free to roll horizontally, its speed immediately after it was fired was 1.4907 m/s. The part I'm stuck on says imagine the same charge is used so total energy of cannon plus cannonball system is the same. Disregarding friction how much faster would the ball travel if the cannon were mounted rigidly and all other parameters remained the same? Answer in units of m/s.

For item #1, did you calculate the cannon's recoil speed correctly?? The recoil speed should be (1.5 m/sec). Although the difference is small, it may indicate a problem somewhere. (Perhaps in copying the problem??) When using (1.5 m/sec) for item #1, the item #2 cannonball speed (with the cannon fixed) should be approx (120.75 m/sec).


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