# Finding maximum height

1. May 11, 2006

### whoknows123

A ball (solid sphere of mass=0.1 kg, outer radius=0.1 m) is cocked back 0.7 m on a spring (k= 50 N/m), and on a tilted surface.

How much energy is stored in the spring initially?
(I found that to be 12.25 J)

Find the maximum height the pinball rolls to (above its initial location.)
How do I find the maximum height given only those information.

2. May 11, 2006

### Tide

What have you tried so far?

HINT: Energy is conserved.

3. May 11, 2006

### whoknows123

E= (1/2)mv^2 + (1/2)kx^2

4. May 11, 2006

### whoknows123

but i don't have velocity

5. May 11, 2006

### whoknows123

12.25 J = (1/2)(.1kg)v^2 + (1/2)(50 N/M)x^2 but i have no idea what velocity is

6. May 11, 2006

### Lee

Exactly, but through some anaylsis of energy conservation and the above formula I'm sure you could find one.

7. May 11, 2006

### Tide

But you do have a velocity. You know the velocity is zero just as the spring begins to accelerate the mass. And, if the object is confined to travel along the incline during acceleration then energy conservation gives you the velocity (both components!) just as the object leaves the incline.

8. May 11, 2006

### Lee

Well what you've put above is not strictly true, when the spring is released your energy is conserved so all your potential is turned into kinetic energy....

9. May 11, 2006

### whoknows123

anyway of helping me find velocity with those give information?

10. May 11, 2006

### whoknows123

velocity intial is zero, but what about velocity final?

11. May 11, 2006

### whoknows123

A = velocity of obj times squareroot(m/k)?

12. May 11, 2006

### Lee

you were very close to the right answer with 12.5J. That is E, now when the object is being released from the sling it then has no potential energy, but has alot of kinetic, so....

13. May 11, 2006

### Pengwuino

Think about the situation, when it reaches the top of that incline, what's its velocity?

14. May 11, 2006

### whoknows123

PE=KE? but KE=(1/2)mv^2 (there's no distance for me to find)

15. May 11, 2006

### whoknows123

velocity would be zero wouldn't it?

16. May 11, 2006

### whoknows123

nvm i take that back, i was thinking of something else

17. May 11, 2006

### whoknows123

E = (1/2)kx^2?

18. May 11, 2006

### Lee

Yes, that is the enregy from the sling that you worked out initially, but what does that also equal from your conservation of energy.

19. May 11, 2006

### Pengwuino

You can simplify this by figuring out 2 things

Initial: Potential + Kinetic

You know that the velocity is 0 so its all potential.

Since you know energy is conserved, you have:

Final: Potential + Kinetic

Again the velocity would be 0 again.

Thus, there must exist a potential at the final position. What do you think it is?

20. May 11, 2006

### whoknows123

thanks guys, i think i got it