# Ball attached to String (Potential Energy)

1. May 14, 2011

### goluigi2196

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

A 2.40 kg ball is attached to a ceiling by a 2.00 m long string. The height of the room is 3 m. What is the gravitational potential energy of the ball relative to:

a) the ceiling?

b) the floor?

c) a point at the same elevation as the ball?

Variables
P for potential energy
m for mass in kg
g for gravity
h for height

2. Relevant equations
P=mgh

3. The attempt at a solution
For b), I found the answer which was 23.52.

For a), though, I got 70.56 because P=(2.4)(9.8)(3)=70.56. The 3 is from the fact that the ceiling is 3m off the ground and a) is asking about the ceiling. It says that I'm wrong

For c), I don't have any idea of what they're talking about. Is it the same thing as b)?

2. May 14, 2011

### zhermes

Energy is always relative. Potential energy is defined as the potential energy of one point, vs. the potential energy at another point. The equation, more precisely, should be written $$U = mg \Delta h$$ for some different in height $$\Delta h \equiv h - h_0$$.

Usually the 'reference' point ($$h_0$$) is taken to be "zero height" ($$h_0 = 0$$), and that is often either sea-level, or ground-level, or floor-level, etc.

While the ceiling is 3m off the ground ($$h_0 = 3$$), it is only 1m away from the ball (the ball is what you're finding the potential energy of). h = 3m - 2m = 1m

If they're asking for the potential of the ball with respect to something at the same height, what is the difference in height $$\Delta h$$?

3. May 14, 2011

### goluigi2196

ok, so I did 2.4(9.8)(1)=23.52 for a). i still get it wrong....

and for c), do i just do 2.4(9.8)(2) because it's the inverse?

4. May 14, 2011

### zhermes

Sorry, forgot to highlight a key point. In this case, the ball is lower than the reference point. I.e. $$\Delta h = h - h_0 = 2m - 3m$$

Its not the inverse problem. Its asking what is the potential difference between something at h = 2m, and a reference point at $$h_0$$ = 2m

5. May 14, 2011

### Vespa71

How far is it between ball and ceiling? Ball and floor?

6. May 14, 2011

### goluigi2196

so will a) be negative because 2-3=-1? therefore, will the answer be -23.52?

and will c) be zero because 2-2=0 and 2.4(9.8)(0)=0?

7. May 14, 2011

### goluigi2196

@vespa71

the problem said the ceiling to the floor was 3m

8. May 14, 2011

### Vespa71

a) will be negative becaus there's a 2!! meter negative drop from the ball to the ceiling. c) is zero as there's no drop. Well done.

9. May 14, 2011

### Vespa71

I recommend to make a simple drawing to visualize the problem. Best of luck

10. May 14, 2011

### goluigi2196

well ok, i did 2.4(9.8)(-1). that gives me -23.52. it still tells me i'm wrong

11. May 14, 2011

### goluigi2196

oh and thanks for c). i got it right.

12. May 14, 2011

### Vespa71

If you have a -2m drop from ball to ceiling, and a 1m drop from ball to floor, and a 0m drop from ball to somthing on the same level, I think it will solve.