How is work calculated with a variable force?

[matt@USA]

Homework Statement

A block is acted on by a force that varies as (1.4*10^4N/m)x for 0<x<.21m , and then remains constant at 2940N for larger x. How much work does the force do on the block in moving it from x= 0 to x= 0.30m? How much work does the force do on the block in moving it from x= 0.10m to x= 0.40m?

Homework Equations

The Attempt at a Solution

I am not understanding the question or something. Can someone help me with the equation?

 

[rock.freak667]

Homework Equations

Well how would you find the work done with a variable force? (hint: it has an integral in it)

Essentially, the question is telling you that for 0<x<.21 m the force is F = 1.4(10⁴)x and for x>0.21 m, F=2940.

When you get the formula you will need to see what the force will be for the range of x=0 to x=0.4 m. Not that you can split the range as so:


x = 1 to x=4 is the same as x=1 to x=2 + x=2 to x=4.