What Happens When Force is Not Constant in W = f x D?

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When the applied force is not constant, the equation W = f x D, which calculates work, becomes invalid. This equation only applies when both force and distance are constant and measured in the same direction. To analyze variable forces, a more general approach involving calculus and vectors is necessary. By considering small increments of distance and summing the contributions of force over the total distance, one can calculate work done under varying forces. Understanding these concepts is essential for accurately determining work in dynamic systems.
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Homework Statement


W = f x D
W = work
f = force
D = distance

What happens when the applied force is not constant?


I have no idea. Can anyone please answer?
Thank you.
 
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Do you know how the force varies with time? Is there a function that expresses this?
 
No. Its just a research question that just ask what happens when the applied force is not constant.
 
W = F*D is only valid for a constant force and distance measured in the direction in which the force acts. There is a more general equation relating a variable force to distance and work. Properly, it involves calculus and vectors. Not sure what level you're at.
Ignoring the vector aspect, consider the force advancing a small distance ds, so that the force can be taken as not varying enough to matter. Then add up all these contributions over the total distance moved.
 

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