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

[thomero]

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.

 

[pongo38]

Do you know how the force varies with time? Is there a function that expresses this?

 

[thomero]

No. Its just a research question that just ask what happens when the applied force is not constant.

 

[haruspex]

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.

 

[HalfLostAndSearching]

When the applied force is not constant, the work done will also not be constant. This is because work is defined as the product of force and distance, and if the force is changing, then the amount of work done will also change. In other words, the work done will depend on the magnitude and direction of the force at each point along the distance. This can be seen in real-life situations, such as pushing a shopping cart up a hill. As the incline of the hill changes, the force required to push the cart will also change, resulting in varying amounts of work being done. Therefore, it is important to consider the variation of force when calculating work.