Ok so say you're pushing hard (really hard) on a huge crate to make it budge, but it's not moving. You can make your case that you're exerting a lot of "energy" and putting a lot of effort into the task, but the fact is, you're not displacing it one bit. That's why, by scientific standards, you aren't doing any work.

When you are doing work in that sense, net displacement of the object has to occur. By definition:

where F is the component of the force in the axis of movement and d is the displacement of the object. Work is a scalar quantity.

What is meant by "the component of the force in the axis of movement?" Try studying this example:

If a block is displaced in the shown direction but the force is directed at an angle of Ø degrees, what is the work done on the object by the constant force F if it is displaced a distance of d?

Well, Fx points in the direction that the block is moving. (That is the only part of the force that makes the block move...Fy is totally unrelated to the horizontal motion). So what is Fx in terms of F and Ø?

With the right triangle "SOHCAHTOA" rule Fx is FcosØ. Therefore the work done is:

According to either equation,

The Work-Energy Theorem

With uniform acceleration, F = ma holds true.

Thus, W = Fd = (ma)d

Recalling the equations of uniform acceleration we can re-express

as

Therefore,

The (1/2)mv2 is a type of energy called Kinetic Energy (KE or simply K) Any object with a mass of m and a velocity of v has kinetic energy of (1/2)mv2. It is a scalar quantity and has the same units as work.

Therefore, the equation above can be expressed as

where /\K is the change in K.

Potential Energy

Potential energy is another form of energy which is associated with the position of the object. When you drop a heavy rock over a nut, will not only smash it, but flatten it to the ground. What gave it its energy to do that? Its weight, by the pull of gravity, but also because of its height above the ground. It has more time to accelerate if it is dropped at a point higher above the ground, thus gaining a greater kinetic energy.

As such, potential energy, PE or simply U, is

Work can be considered the gravitational force, which is pulling the object that is in the air toward the ground. Falling, the object is displaced a distance, which we can call height h. Therefore, displacement = h, force of gravity = weight and

So wait? Isn't W = KE too? Yeah, so W = /\KE = /\PE. But kinetic energy and potential energy work in opposing ways.