How is work calculated with a variable force?

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To calculate work done by a variable force, the integral of the force function over the distance must be used. For the given problem, the force varies as (1.4*10^4 N/m)x for 0 < x < 0.21 m, and is constant at 2940 N for x > 0.21 m. The total work done from x = 0 to x = 0.30 m involves integrating the variable force from 0 to 0.21 m and adding the work done by the constant force from 0.21 m to 0.30 m. Similarly, for the range from x = 0.10 m to x = 0.40 m, the integration must account for both the variable and constant force sections. Understanding how to apply the integral to find work is crucial for solving these types of problems.
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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?
 
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matt@USA said:

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.
 
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