# Loss of potential energy

Tags:
1. May 22, 2015

### toforfiltum

1. The problem statement, all variables and given/known data

2. Relevant equations
GPE=mgh

3. The attempt at a solution
I don't understand why the answer is B. My approach is assigning h a random value, say 10m. When the depths of water in both vessels are equal, the height is 5m. Therefore, since the mass of water in both vessels are still m, shouldn't the loss in GPE be half? I don't know why I'm wrong.

2. May 22, 2015

### TSny

For an extended object, the gravitational potential energy is determined by the location of the center of gravity of the object. Consider the height of the center of gravity before and after.

3. May 22, 2015

### toforfiltum

I still don't get one quarter. I will only get that answer if I don't consider the gain in GPE in vessel Y.

4. May 22, 2015

### TSny

What is the initial height of the center of gravity? The final height?

5. May 22, 2015

### toforfiltum

1/2h and 1/4h?

6. May 22, 2015

### TSny

Yes. So, what are the initial and final values of gravitational PE?

7. May 22, 2015

### toforfiltum

1/2mgh - 1/4mgh?

8. May 22, 2015

### TSny

OK, that would be the loss of gravitational PE.

9. May 22, 2015

### toforfiltum

But how about the gain in GPE in vessel Y?

10. May 22, 2015

### TSny

That is already taken care of. If you consider only vessel X, then the change in PE would be

PEf - PEi = (m/2)g(h/4) - mg(h/2) = (1/8)mgh - (1/2)mgh = -(3/8)mgh.

Vessel Y gains PE in the amount (m/2)g(h/4) = (1/8)mgh.

Overall, there is a change of -(3/8)mgh + (1/8)mgh = -(1/4)mgh.

But you don't need to consider each vessel individually. Just consider the entire volume of water and work with the center of gravity of the entire volume.

11. May 22, 2015

### toforfiltum

Oh, thanks. I didn't know that I should use centre of gravity to solve this question. And what do you mean by an extended object?

12. May 22, 2015

### TSny

Extended just means that the mass is spread out over some region rather than being concentrated at a point.

13. May 22, 2015

### toforfiltum

Ok, thanks again