# How was the concept of work-energy developed? [duplicate]

I doubt that the concept of work-energy was actually discovered this way. However in the algebra based physics book I am reading, work done by a constant net force is defined as $W = fcos \theta s$ The other side of the equation is worked out to be $\Delta 1/2(mv^2)$ or $mg\Delta h$. This is the work energy thereom given. The right sides are given names KE and GPE.

To me this is just deriving equations using substitutions and transposing. Without being given explanations of what KE and GPE are, how would a person know their meanings? W=$fcos \theta s=1/2(mv^2)$ They are just equivalent expressions.

How would one go from that to knowing $1/2(mv^2)$ KE is energy possessed due to its motion? That this can do negative work if acting on another object? Or likewise the mgh is PE and is independent of the path taken between two points making a line perpendicular to the earths surface?

Please don't use any mathematics beyond a 1st year undergraduate course to explain as I wont understand it.

• Hi Liein. I think the duplicate I suggested covers what you're asking. Some of the answers to it are really good! Mar 23, 2016 at 15:26

The concept of work can be interpreted as the "measure"of the amount of energy used in doing /performing a task . To do work, human or other agency's effort (force) is essential.

Having capacity of performing tasks /effort however does not mean that work is being done. The effort must accomplish something useful -a displacement/change of state/change in state of motion must be coupled to the effort.e.g.

A lady asks the delivery boy to put the carton of weight W on the I st floor which is at h meter height.

So the boy used a force(at least of W kgm-wt) to raise the carton h meters high(displacement)- his effort has produced a new state of the carton. He was working against the direction of earth's pull.

If either the net force or the displacement is zero, the work performed will be zero.

For physical work another requirement is that the displacement must be in the direction of the force. If they are not in the same direction, only the component of the displacement , in the direction of the force, can be used to calculate the work. For the special case where the force is constant, the work may be computed as:

W(work done) = [F]. ds.cos $\theta$ where $\theta$ is the angle between force and displacement.

One question may be raised as to how /where the "work performed" resides in the body on which it was done?

If the body has been only shifted in position in the field of force -then the energy may reside in the body to have such potential capacity to do work. In the above example the body acquired a Potential Energy = W.h

This was termed as "Potential Energy" of a body -an energy which may appear/can be used when we need to perform work.

A load of W if moved to a height h on earth has some potential to perform work and some machine can be built which can derive the full energy from it.

The Energy concept actually came out of the human's desire to build ideal machines to do work.Or some innovative ideas to have a perpetual motion machine for doing work-in these one tries various state of motion and rest and deal with conversion of work in energy and vice versa.

The idea of "energy of bodies "due to state of its motion /rate of change of displacement(velocity) and our efforts working on a body to have more and more speeds- developed the concept of 'kinetic energy'.

The momentum of a body and its rate of change could define the force experienced by a body ,thereby the action of forces in changing the momentum equivalent to change in state of motion i.e. the Kinetic energy could be defined and it could get the form of 1/2 (mass).(sq. of velocity)-

So in two ways our effort to perform work led to changes in the energy content of a body in our physical/mechanical world.

And the conservation of mechanical energy will require to put a condition that if no energy dissipation is being observed the total work done on a body should be equivalent to the total mechanical energy ( potential+Kinetic energy) of the body.