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# Work and Energy

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 Sub Topics The word 'energy' comes from the Greek word energia, vigor of expression, activity. The word was coined by philosopher Aristotle from the word elements en (in)+ ergon (work). The term energy presently connotes the capacity for doing work. Every work by body, mind or machine requires energy and as soon as the energy is exhausted it stops working. Now let us go through more terms related to this work and energy.

## Work-Energy Principle

The work done by the net force can be calculated using the laws of force. The change in kinetic energy of a particle can be expressed in terms of the particle's mass and its speed just before and just after the performance of the work.

The work energy principle states that, the work done on a particle by the net force equals the change in kinetic energy of the particle.

Wnet = $\Delta$K

where $W_{net}$ = $\int F_{net}$.ds is the work done by the net force.

The work-energy principle is an alternative to Newton's second law, both describe the influence of the environment on the particle.

## Units

Since work is equal to the change in kinetic energy, the units of energy are the same as that of work. In SI unit system, the unit of energy is therefore the joule, equal to 1 Newton-meter.

## Kinetic Energy and Work Energy Theorem

If a force is applied to a particle, it gets accelerated. Depending upon the nature of force the speed of the particle varies. If we apply a positive force the speed of the particle will increase and we apply a negative force, the speed of the particle will decrease. The work done by this particle cannot be measured using its change in speed, but it is measured using the change in kinetic energy. According to the work-energy principle, work done can be calculated as the change in kinetic energy. Kinetic energy involves the mass and velocity of the particle.

K = $\frac{1}{2}$m$v^{2}$

## Gravitational Potential Energy

Potential energy is the energy due to the position of an object. An object is placed at a height, it posses some potential energy under the influence of gravity. This is known as the gravitational potential energy. Gravitational energy can be calculated as the work required to lift an object from the earth surface. A force which is equal to the weight of the object is required to lift an object. But it is the opposite direction of the weight of the object.

## Conservation Laws

The work done on a particle by the sum of all forces, conservative and non conservative, acting on that particle is included in Wnet. To introduce potential energy we limit our consideration to systems experiencing conservative forces only. With this restriction we can state that Wnet equals the work done by the sum of all conservative forces acting. The conservation law is given as,
If only conservative forces act on the system, the sum of changes in the kinetic and potential energies of a particle equals to zero. The sum of the kinetic and potential energies of the particle is conserved.

## Power

Power is the rate at which work is done; it is measured in watts (W). One watt is equal to one joule of work done per second. Power can be calculated as follows.
Power = $\frac{Work}{Time}$

## Momentum

The product of the mass m of a particle and its velocity v is called the momentum or linear momentum. It is a vector quantity.

p = mv

Newtons second law can be expressed in terms of momentum. Newton's second law is given by

F = ma

F = m$\frac{\mathrm{d}v }{\mathrm{d} t}$

F = $\frac{\mathrm{d} }{\mathrm{d} t}$ (mv)

We know that mv = p

So, F = $\frac{\mathrm{d}p }{\mathrm{d} t}$ = rate of change of momentum