What is the scientific definition of work?

Answer 1

The scientific definition of work is the transfer of energy from one object to another, especially in order to make the second object move in a certain direction. Work is equal to the amount of force multiplied by the distance over which it is applied. If a force of 10 newtons, for example, is applied over a distance of 3 meters, the work is equal to 30 newtons per meter, or 30 joules. The unit for measuring work is the same as that for energy in any system of units, since work is simply a transfer of energy.

Answer 2

The definition of work is deceptively simple, but for accuracy it is perhaps better to approach this in stages.

It is often stated too simply, i.e. "Work equals force times distance."

It is necessary to clarify the vector nature in order to get the "scientific" definition. Both force and distance are vectors and to emphasize that, the term displacement is used instead of distance since distance is often used as the magnitude of how far something has gone. Displacement is more clearly understood to mean the vector difference between to positions in space, in this case from the stat position of the action of the force and the end position. Then, we need to be precise in saying that the work is done only by the component of force acting in the direction of movement.

Given a displacement vector, d, and a constant force vector, F, the product of the magnitude of the force parallel to the displacement and multiplied by the magnitude of the displacement is just the vector dot product of the vector force and vector displacement.

W = F .d

In words, work, W, equals vector force dotted with vector displacement.

That is a correct scientific statement. For many cases, one can stop at this point and consider themselves well informed.

But what if the force is not constant, but changes as the object being acted on moves through a path that may not be a straight line between the starting point and ending point of the displacement?

Alas, we are led to the general scientific statement of work, valid in every case except when the theory of relativity has to be considered. (That is beyond this discussion.)

One needs integral calculus to properly write the equation and that generalizes to a variable force along a path that is not straight. That can not be written with the character set available a on this interface, but we can say it, less elegantly, in words.

Given a starting point A and an ending point B an a path P of any shape between A and B, if we know the force F as a function of position along that path, then the work performed by the force on an object moved along that path is given by the integral of the force, F, dotted into the vector differential length element, dl, and integrated along the path from A to B.

W = integral (from A to B) F.dl

That is it. With a few months studying calculus and a semester learning mechanics, one can actually use this to calculate work done and understand how that relates to energy supplied or expended by a system. Fortunately, the simple case of the constant force and a straight line displacement is enough to give one the foundational understanding without the mathematical sophistication.

Force times distance.
Work is the product of a force and a distance. If force and distance don't act in the same direction, the dot product must be used. If the force varies over the distance it acts, an integral must be used.
The scientific definition of work is the scalar product of vector force times displacement, work= F.D = FDcos(FD).

The scientific definition is defines work as a scalar.

The definition of Work should recognize the Quaternion nature of Work,

W = Wscalar + Wvector =[f,F] [d, D] = [fd -F.D, fD + Fd + FxD] .