Archimedes’ Principle and Cannonballs

a boat is travelling in a pond a man fires a cannon ball from the boat in to the pond will the level of water in the pond raise or fall or stay the same
- Anonymous

The water level in the lake will go down a little bit. Archimedes’ principle says that an object which is floating displaces an amount of water which weighs the same as the object. In the first case, the boat with the cannonball pushes aside water that has the same weight as the boat+cannonball. In the second case, the boat displaces only enough water to keep it afloat, and the cannonball is resting on the bottom, not floating. The cannonball then displaces only as much water as its volume.

If the cannonball is heavier than water, then the amount of water the cannonball displaces when it sits on the bottom is less than that when it is responsible for when it is in the floating boat, and the total level in the lake will go down.

You can try it yourself with a plastic or styrofoam cup (the boat), some marbles, and a pot of water.

Tom

(published on 10/22/2007)

I hope this does not sound silly. The cannonball was originally sitting in the boat and contributed whatever weight it has on land to the amount of water that the boat displaced in order for it to float, right? However, when the cannonball is loaded and fired, it now departs from the boat which means the boat has less weight to displace. Is this correct or what am I missing?
- Jim Conlon (age 78)
southampton, ny USA

You interpret it quite correctly and for this reason the boat's level will elevate slightly so that the volume within the water decreases. The amount of the decreased underwater volume will be equal to the weight of the ball + gunpowder. However, the motion will be quite interesting: you obviously will have to fire the ball with a certain angle above the horizon (unless you want to destroy your own boat). The horizontal component will cause your boat to start travelling in the opposite way to . But the vertical component of the momentum should also be conserved, which means your boat needs to gain some speed downwards. It therefore will oscillate a bit up and down till the friction forces settle the elevation at this new equilibrium level.

Tunc

(published on 03/06/2015)