Force and Potential Energy Graphs: Mastering Physics HW 11.39

[Rimi]

Homework Statement

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.

Homework Equations

F=-dU/dx

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?

 

[Dick]

Homework Statement

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.

Homework Equations

F=-dU/dx

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?

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

 

[Rimi]

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

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

 

[haruspex]

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.

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.

 

[Rimi]

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.

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! ^.^