# Change in Potential Energy

1. Feb 27, 2014

### Medgirl314

1. The problem statement, all variables and given/known data
A 20 kg child slides down a slide at a playground. The slide is 5 meters long, and is inclined at an angle of 37 degrees above the horizontal. What is the child's change in potential?

2. Relevant equations
PE=mgy

With m=mass, g=gravity, and y=distance.

3. The attempt at a solution

I have solved potential energy problems before this,but I don't know how to account for the angle. If there was no angle, the formula would be PE=20*9.8*5, and I think that would be the change in energy since when the child reaches the bottom y=0, canceling out the entire equation. Could someone please tell me where the angle comes in? I don't want it done for me, I just need one post with a helpful explanation, and then I should be good. :)

Thanks so much!

2. Feb 27, 2014

### Staff: Mentor

There are two ways of doing this that give the same answer.

Method 1: You use the equation you presented, but instead of the 5, you use the vertical distance that the child descended.

Method 2. You use the equation you presented, but instead of the 9.8, you use the tangential component of g along the slide.

Chet

3. Feb 27, 2014

### Medgirl314

Thank you! I knew trig would come in somewhere, I just couldn't figure out how to bring it in. So using Method 1, would the vertical distance be 3.94 meters?

4. Feb 27, 2014

### Staff: Mentor

No. Try again. Draw a diagram this time.

Chet

5. Feb 27, 2014

### Medgirl314

I drew one, but I did the trig wrong, I think. Would 5tan38 work?

Thanks again!

6. Feb 27, 2014

### Staff: Mentor

No. The hypotenuse is the slide. try again.

7. Feb 28, 2014

Find h.
You won't need me here(Adjacent side)

#### Attached Files:

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8. Feb 28, 2014

### Medgirl314

Hm, I'm not sure why I can't wrap my mind around this. It would have to be sine, but why? Wouldn't that be the two unknown sides?

Thanks!

9. Feb 28, 2014

### Staff: Mentor

What's the definition of sine for a right triangle?

10. Feb 28, 2014

### Staff: Mentor

11. Feb 28, 2014

### Medgirl314

Sine=opposite/hypotenuse

Oh! Obviously, 5 is the hypotenuse. I let adjacent's letter choice confuse me. So 5sin 37=3.0 m. Correct?

12. Feb 28, 2014

### Medgirl314

Thanks, I know the functions fairly well, but I tend to overcomplicate them. Oops.

13. Feb 28, 2014

### Staff: Mentor

Correct.

14. Feb 28, 2014

### Medgirl314

PE=mgy
PE=20*9.8*3.0=588 Joules

Correct?

Thanks again!

15. Feb 28, 2014

### Staff: Mentor

Good. That's the magnitude of the change, but what's the sign of the change?

16. Mar 28, 2014

### Medgirl314

I forgot about this thread. Oops. The sign, as in negative or positive? It depends on what direction we decided is the positive direction, right? So if we decided that down was the positive direction, then h would be negative, so the answer would be negative? But can you have negative energy? Would I just say 588 Joules down?

Thanks!

17. Mar 28, 2014

### Staff: Mentor

Right.

It's got nothing to do with direction (energy is not a vector). It has to do with whether the potential energy increases (a positive change) or decreases (a negative change).

Since the child slides down the incline, is her change in PE positive or negative?

18. Apr 5, 2014

### Medgirl314

Her change in PE would be negative, so the KE would be positive.

19. Apr 6, 2014

### Staff: Mentor

Right. Since the change in PE is negative (the PE decreases), the change in KE will be positive (the KE increases). (The KE itself is always positive--unless it's zero.)

20. Apr 6, 2014

Thank you!