# Homework Help: Potential energy vs x graph

1. Oct 10, 2009

### sonutulsiani

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

You are given the plot of a potential energy function U(x) versus x.

http://bcs.whfreeman.com/WebPub/Physics/tiplerphysics6e_bridge/question_bank_images/7-8.png?3200

1. For each point indicated, state whether the x component of the force associated with this function is positive (+), negative(−), or zero (0)), by matching the points with the corresponding sign.
1. Zero
2. Negative
3. Positive

A = ?
B = ?
C = ?
D = ?
E = ?
F = ?

2. At which point does the force have the greatest magnitude?

3. Which point is a stable equilibrium point?

2. Relevant equations

3. The attempt at a solution

2. Oct 11, 2009

### Gear300

For conservative fields, which is usually what we take potential energy for, F = -dU/dx

3. Oct 11, 2009

### sonutulsiani

I didn't understand what you said.

4. Oct 11, 2009

### Gear300

The force is negative the rate of change of potential energy with respect to displacement. So you can evaluate it as negative the derivative of U with respect to x.

5. Oct 11, 2009

### sonutulsiani

You mean we have to convert this graph into it's derivative? And then what?

6. Oct 11, 2009

### Gear300

Well...you don't really have to convert it to its derivative...you can just imagine the tangents at the different points. Since force is negative the derivative, if the tangent has a negative slope, then the force is positive, and so on. The case of stable equilibrium is essentially when you have a restoring force - meaning that if you move to the left (- displacement), then the force is to the right (+ direction) and vice versa.

7. Oct 11, 2009

### sonutulsiani

So

A=2
B=1
C=3
D=1
E=2
F=1

2nd question, force having greatest magnitude is point C ?

3rd question, is it point F ??

8. Oct 11, 2009

### ideasrule

All of those answers are correct except the last one. Why F? For a stable equilibrium, you need to find a point where decreasing x causes a positive force, so U has to have a negative slope on the let. Increasing x must cause a negative force, so U has to have positive slope on the right. There's only one point where this is true.

9. Oct 11, 2009

### sonutulsiani

Is it C then? Because it has a positive slope on the right and negative on the left.

10. Oct 11, 2009

### sonutulsiani

C or E

11. Oct 11, 2009

### sonutulsiani

It is E! Isn't it?

12. Oct 11, 2009

### ideasrule

Actually, the slope is negative on both the left and the right. For E, the slope is positive on both left and right.

Another way to think about this: if you need to add potential energy to move away from a certain x value, that x value is a stable equilibrium point.

13. Oct 11, 2009

### sonutulsiani

It's D

14. Oct 11, 2009

### sonutulsiani

is it???

15. Oct 11, 2009

### Gear300

Yup.

16. Oct 11, 2009

### sonutulsiani

Ohh! Okk thank you so much!! Thanks a lot! :)