Help with Archimedes' Principle

[lmbiango]

Homework Statement

A solid aluminum sphere has a radius of 1.84 m and a temperature of 77.5 °C. The sphere is then completely immersed in a pool of water whose temperature is 26.7 °C. The sphere cools, while the water temperature remains nearly at 26.7 °C, because the pool is very large. The sphere is weighed in the water immediately after being submerged (before it begins to cool) and then again after cooling to 26.7 °C. Use Archimedes' principle to find the magnitude of the difference between the weights.

Homework Equations

Volume of the sphere: (4/3) pi (R)^3
V=26.094

and change in volume: coefficient of volume expansion for aluminum (69 x 10^-6) * (Initial Volume: 26.094) * (Change in Temp: -50.8)
= - .0915

This is the other equation I have:
difference in weight = -(density)(gravity)(volume)
But the answer I get isn't right...

The Attempt at a Solution

I think everything I am doing is right up until the part about finding the difference in weights. I don't know what equation to use, or how to use it I guess. Any help would be appreciated.

 

[mgb_phys]

Remember the difference in volume leads to a different upthrust because of the different amount of water displaced - the mass of the Al sphere doesn't change.

 

[lmbiango]

Remember the difference in volume leads to a different upthrust because of the different amount of water displaced - the mass of the Al sphere doesn't change.

So, are you saying that the difference between the weights would be zero? I thought that would make sense, but I tried that also (although I thought it seemed too easy) and the homework tool said it wasn't right... all I know is the units are Newtons ...

 

[mgb_phys]

No the weight would be different because the shrunk ball would displace less water and so receive less upthrust and so weigh more.
But the difference in volume corresponds to a different amount of water - not a different amount of Al so it is the density of water not Al that you need.