# Force and Potential Energy Graphs: Mastering Physics HW 11.39

1. Apr 13, 2013

### Rimi

1. The problem statement, all variables and given/known data
The figure below shows the force exerted on a particle that moves along the x-axis. Draw a graph of the particle's potential energy as a function of position from x=0 to x=1.1 . Let U be zero at x=0.

2. Relevant equations
F=-dU/dx

3. The attempt at a solution
I decided to divide the force graph into three separate graphs:

From x=0 to x=.5: F(x)= 4x
From x=.5 to x=1: F(x)= -4x + 4
From x=1 to x=1.1: F(x)= 0

I then integrated each equation, and multiplied them by -1, getting U(x)= -2x^2, U(x)= 2x^2 - 2 and U(x)= 0, respectively.

When I try to graph these equations, only the first one and the last one, U(x)= -2x^2 - 2 and U(x)= 0, seem to give me the correct answer. Can someone help me figure out where I went wrong?

#### Attached Files:

• ###### 11.P39a.jpg
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2. Apr 13, 2013

### Dick

Your U(x) should be continuous. If you define U(0) to be 0 then U(1) isn't 0. Adjust your constants.

3. Apr 14, 2013

### Rimi

Does that mean that U(x) would have to be an absolute value function?

4. Apr 14, 2013

### haruspex

In each integral, you get an unknown constant. To figure out what the constant is for that integral, you have to plug in known values for U and x at the start of that range.
I don't see how you got 2-2x2 by integrating -4x+4.

5. Apr 14, 2013

### Rimi

It should read 2x^2 - 4x. My mistake.

And I forgot all about solving for the constant first...whoops! I figured it out, though. Thanks! ^.^