Mercury, a metal that is liquid at room temperature, has a density 13.5 times the density of water. How many pennies could your boat hold if we were floating it in mercury instead of water?

Question

Mercury, a metal that is liquid at room temperature, has a density 13.5 times the density of water.  How many pennies could your boat hold if we were floating it in mercury instead of water?

anonymous · Answer

just same basic info:
mass of a PENNY: 2.5 grams
Denisty of water: 1.0 g/cm3

anonymous · Answer

anyone

dape · Answer

Well, the boat still displaces 75 ml of volume. So in this case it should be able to hold 13.5 times more weight, or 13.5*30=405 pennies. Lets do it from the start to be sure that it comes out the same.

According to Archimedes' principle, the buoyant force on the boat is equal to the displaced weight of the fluid. The weight of the displaced mercury is $$(75\,ml)\times(13.5\,\frac{g}{ml})=1012.5\,g$$
The weight of a penny is 2.5 g, so the number of pennies that the boat can hold is
$$\frac{1012.5}{2.5}=405.$$

anonymous · Answer

what if it doesn't displace at a volume of 75 ml?

dape · Answer

If the boat itself still weighs the same, it will displace 13.5 times less volume of mercury since it's that much denser. So it would be the same number of pennies as in water in that case.

dape · Answer

$$\frac{1}{13.5}\times13.5=1$$

anonymous · Answer

so it would still hold 405 pennies?

dape · Answer

If the boat displaces the same amount of volume, it holds 405 pennies in mercury and 30 in water. If the boat weighs the same, it holds 30 pennies in both cases.

dape · Answer

I think they mean the first case, that the boat displaces a 75 ml volume in both cases. But it could be the second one.