Calculating Work Done by a Variable Force

[ecthelion4]

Homework Statement

A force F=bx^3 acts in the x-direction. How much work is done by this force in moving an object from x=0.0m to x=2.2m? The value of bis 3.7 N/m^3

Homework Equations

Work=Force*Distance

The Attempt at a Solution

Ok since the above equation is true, then the problem would solution would be obtained by simply multiplying our force which is (3.7N/m^3) by the given distance which would be 2.2m. The thing is that once you do that, the problem is over and there is still a variable there bothering us which is x^3. What am I supposed to do with that variable?

 

[hage567]

(3.7N/m^3)

This is not the force, this is a constant. The force is b*x^3. Since it contains the x^3 term, the force is variable and you can't use W=Fd. Do you know integration?

 

[ecthelion4]

yes, but how would i use it in this case?edit: ok i figured it out, it should be the definite integral from 0-2m of F right?

 

[hage567]

yes, but how would i use it in this case?


edit: ok i figured it out, it should be the definite integral from 0-2m of F right?

Yes, but the upper limit is 2.2m, right?

 

[ecthelion4]

that was exactly it. The answer was 21.6 which rounded up to 22J . Thanks you were a great help!