1. Dec 22, 2012

### songoku

1. The problem statement, all variables and given/known data
A cup of water has weight X. A stone has weight Y in the air is immersed fully in the cup and it displaces water of weight Z. What will be the new reading on the balance after the stone is immersed inside the cup?

2. Relevant equations

3. The attempt at a solution
My guess that the new reading will be X + Y - Z, where X is the weight of the cup and Y - Z is additional weight by the stone (weight of stone in water). Am I correct?

Thanks

2. Dec 22, 2012

### Bandersnatch

So, if you were to use a stone that displaces all the water(Z=X), you'd make the water weightless?

3. Dec 22, 2012

### songoku

errr....didn't cross my mind before

So, second guess, X + Z. The weight of water will be added by the weight displaced by the stone. Correct?

Thanks

4. Dec 22, 2012

### Staff: Mentor

I think you'd better define what the balance is weighing. What's on the balance?

Does the displaced water remain in the cup, or does it overflow and become lost?

5. Dec 23, 2012

### songoku

The displaced water remains in the cup.

I think the balance weighs the normal force acting on it. My guess still X + Z

Thanks

6. Dec 23, 2012

### soothsayer

I think the answer would be different based on whether the rock had just become fully emerged and was still sinking toward the bottom, or whether the rock had already come to rest at the bottom of the cup, would it not?

7. Dec 23, 2012

### Staff: Mentor

So the balance is weighing the cup and all its contents, while the stone was weighed separately (yielding weight Y in air). That is: the cup is on the pan of the balance; the cup has water in it; the stone is added to the cup.
That would depend upon whether the stone is allowed to sink to the bottom of the cup, or is being held in a fixed position under the water by some external force.

If you assume that the stone is allowed to sink freely and come to rest at the bottom of the cup (so there are no external forces acting), then what the balance reads should only depend upon the total mass and the total volume of air displaced by the "object" that is the cup+water+stone.

Does the total amount of air displaced by all the objects change when the stone is immersed?