# Work=Force*Stretch: Why is this?

I am- and have always been a bit puzzled as to why Work=Force*Stretch. I guess it makes sense that both stretch and force is involved, but why such a simple equation? Why Isn't it for example;

W=0,25F*S^2

or..

W=(F^S)/2

or some other equation?

How did we figure out that Work=Force*Stretch???

## Answers and Replies

i believe you want to know why work is force*displacement(stretch as you called it), right?.......

Here's the deal, you cannot have another equation of work with powers greater than one or less than it for force or the displacement.....why?.........because work isnt something that you see in nature, as it is with distance,

Work is a concept invented by physicists to understand whether a system is efficient enough.....it has been defined that way, F*S, no other way is possible......the equations you mentioned .........they could mean something ........but certainly not work........just like you being happy means having a smile and stuff ...........Why isn't being happy associated with having a frown..........same logic here.......cause it is defined as having a smile........

sophiecentaur
Gold Member
2020 Award
I am- and have always been a bit puzzled as to why Work=Force*Stretch. I guess it makes sense that both stretch and force is involved, but why such a simple equation? Why Isn't it for example;

W=0,25F*S^2

or..

W=(F^S)/2

or some other equation?

How did we figure out that Work=Force*Stretch???

Actually, it very often isn't as simple as force times stretch because the force tends to change as you stretch things. It is, however, force times distance moved (in the direction of the force) as long as the force doesn't change.

Why is it such a simple formula? Well, consider a (zero weight) lever and assume there is no friction. The work you do in moving the long bit must be equal to the work done on the heavy weight on the short bit. If there is no extra energy put in or lost then this must be true. It always turns out that the force times the distance moved is the same value whatever the lengths on each side of the lever. This quantity that is always equal to force times distance is the work done.
Also, consider the energy involved in lifting a block. Lifting it twice as far would, reasonably, take twice as much energy. Lifting two blocks would also take twice as much energy.
Need I go on? Don't look a gift horse in the mouth. You would really be moaning if it were a more difficult formula to remember.

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