# A-level Physics/Forces, Fields and Energy/Work and energy

Doing Work:

Work is done whenever a force moves something over a distance. The force moves through a distance, and we say that it does work. The amount of work done tells us the amount of energy that has been transferred by the force. Thus:

work done (J) = energy transferred (J)

To calculate the amount of work done W, we need to know two quantities:

- The magnitude of the force F. - The distance, d, moved by the force, in the direction of the force/parallel to the force.

So Work done ${\displaystyle W}$ = force ${\displaystyle F}$ × distance moved in the direction of the force ${\displaystyle x}$.

${\displaystyle W=Fx}$

or, where ${\displaystyle \Theta }$ is the angle between the direction of the force and the distance,

${\displaystyle W=Fxcos\Theta }$

Force is measured in ${\displaystyle newtons}$ and distance travelled parallel to the force in ${\displaystyle metres}$. Thus, Work done is described in newton metres or ${\displaystyle Nm}$. This is the SI unit, joule, ${\displaystyle J}$. work done by tension &= T \times D\\ work done against friction &= -F \times D\\ work done by gravity &= -mg \times h\\ \end{alignat} [/itex]

Energy:

James Joule is the man, where the term 'the joule' comes from. His principle of conservation of energy states that:

While energy may be converted from one form to another, the total amount of energy in a closed system is always constant.

There are two main different types of energy; kinetic and potential. Kinetic energy (EK) is moving energy and potential energy (EP)is the energy that could be transferred to moving energy. The formula for these are:

Kinetic Energy: ${\displaystyle E_{K}={\frac {1}{2}}mv^{2}}$

Potential Energy: ${\displaystyle E_{P}=mg\Delta h}$

The relationship between work done and energy is:

Work done = Energy transferred