Finding Work from Force Equation

[mintsnapple]

Homework Statement

Homework Equations

W = F*d

The Attempt at a Solution

a. W = Ce^(ax)*2a^-1
b. W = Ce^(ax)*2a^-1
c. w = Ce^(ax)*(-4a^-1)

I feel like this problem is more than just this simple...

 

[SammyS]

Homework Statement

Homework Equations

W = F*d

The Attempt at a Solution

a. W = Ce^(ax)*2a^-1
b. W = Ce^(ax)*2a^-1
c. w = Ce^(ax)*(-4a^-1)

I feel like this problem is more than just this simple...

Those results don't look right.

What do you get for the indefinite integral $\displaystyle \int C e^{\alpha x}\ dx \ \ ?$

 

[haruspex]

Those results don't look right.

... in particular, there should not be any x in the answers.

 

[mintsnapple]

Ah, I just re-read the question and saw my mistake.

How would I approach this problem with a changing force though? Do I just plug in the end position, and multiply that force by displacement?

 

[SammyS]

Ah, I just re-read the question and saw my mistake.

How would I approach this problem with a changing force though? Do I just plug in the end position, and multiply that force by displacement?

dW = F dx .

You need to integrate to integrate the force with respect to x .

 

[mintsnapple]

dW = F dx .

You need to integrate to integrate the force with respect to x .

Ahh, I see. So integrate the force with respect to x, and use the positions as my limits.

 

[haruspex]

Ahh, I see. So integrate the force with respect to x, and use the positions as my limits.

Yes.