When is work actually done?

Question

Wikipedia says:

For example, when a ball is held above the ground and then dropped, the work done on the ball as it falls is equal to the weight of the ball (a force) multiplied by the distance to the ground (a displacement). When the force F  is constant and the angle between the force and the displacement s  is θ, then the work done is given by W = Fs cos θ.

From what I have learned work is only done when a force displaced something against another force. (For example if you lift something you lift it opposite to gravity). But Wikipedia doesn’t agree. What is it that I have not understood correctly?

Answer 1

From what I have learned work is only done when a force displaced something against another force

This is incorrect. Work is done whenever a force causes (or influences) displacement. That's all. It has got nothing to do with whether or not it fights against other forces. If you push a spaceship in outer space with no other forces present, then you are doing work (which the spaceship absorbs as kinetic energy). Mathematically: $$W=\int \vec F\cdot \mathrm d\vec s$$

Answer 2

$\text{Work}=\text{Force}\times\text{Distance}$, or in more formal terms $W=Fd$. Work is done when something moves from one point to another. Another way of expressing work to express this idea is $W=\Delta{E}$ where $E$ is the total energy in the system. (I hope that answers your question, because work is not opposing a force but rather when an object moves position).

Answer 3

From what I have learned work is only done when a force displaced something against another force. (For example if you lift something you lift it opposite to gravity)

From what you are showing, Wikipedia is simply using the example of someone doing work to lift an object against gravity, and gravity doing work on the freely falling object converting the potential energy into kinetic energy according to the work- energy theorem. I don't see it saying that all work is done "against another force" (maybe you left something out?)

If you have a mass at rest on a frictionless horizontal surface and you apply a constant horizontal force $F$ through a distance $d$ in the direction of the force, the work done will equal $Fd$ and there is no opposing force (assume no air drag). This work was not done "against another force". In addition, if the mass started at rest by the time it has gone a distance $d$ it will acquire kinetic energy according to the work-energy theorem which states that the net work done on an object equals its change in kinetic energy, or

$$\frac{mV^2}{2}=Fd cos θ$$

Hope this helps.

Answer 4

Work done by a force is defined as:-$$W=\int \vec{F}.d\vec{s}$$

I don't think any other definition of work exists.

work is only done when a force displaced something against another force.

A force will do non-zero work if its dot product with displacement is a real number.As you are also including an opposing force,then we talk about the work done by the net force and the work done by net force is equal to the algebraic sum of work done by individual forces.