| A large cannon is mounted on a cart with frictionless wheels that is initially at rest on a horizontal surface. The cannon fires a large cannonball to the right with a speed \[{{v}_{cannonball}},\] which is then caught by a trap firmly attached to the cart. What is the filial speed v of the cannon-cart cannonball system? |
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A) \[v>{{v}_{cannonball}},\] to the left
B) \[v>{{v}_{cannonball}},\] to the right
C) 0
D) \[v<{{v}_{cannonball}},\] to the left
Correct Answer: C
Solution :
| The overall momentum of the system at the beginning of the problem is 0, and with no external forces applied, this will continue to be the total momentum of the system. During the ball?s motion to the right, the cart will have a motion to the left. However, once the cannonball is caught by the trap, they have the same velocity, which has to be zero if linear momentum is to be conserved |
| \[{{m}_{cart}}{{v}_{cart}}+{{m}_{cannonball}}{{v}_{cannonball}}\]\[={{m}_{cart}}{{\text{v}}_{cart}}+{{m}_{cart}}{{v}_{cart}}\] |
| \[({{m}_{cart}}+{{m}_{cannonball}}){{v}_{initial}}\]\[=({{m}_{cart}}+{{m}_{cannonball}}){{v}_{final}}\] |
| \[({{m}_{cart}}+{{m}_{cannonball}})(0m/s)\]\[=({{m}_{cart}}+{{m}_{cannonball}}){{v}_{final}}\] |
| \[{{v}_{final}}=0\,m/s\] |
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