# Work

### Work is said to be done when a force applied on an object causes it to move in the direction, the force is applied.

Let a constant force, F act on an object. Let the object be displaced through a distance, s in the direction of the force

Work done=Force x Displacement

w=F x s

• Work done by a force acting on an object is equal to the magnitude of the force multiplied by the distance moved in the direction of the force.

• Work has only magnitude and no direction.(It is a scalar quantity)

• SI unit of work is Joule(J)

### What is 1 Joule of work?

1 J is the amount of work done on an object when a force of 1 N displaces it by 1 m along the line of action of the force.

### Work done may be positive or negative

• Consider a situation in which an object is moving with a uniform velocity along a particular direction. Now a retarding force, F, is applied in the opposite direction.Let the object stop after a displacement s.

• In such a situation, the work done by the force, F is taken as negative and denoted by the minus sign. The work done by the force is F × (–s) or (–F × s).

• It is clear from the above discussion that the work done by a force can be either positive or negative.

# Energy

### Energy is the capacity to do work.

• An object having a capability to do work is said to possess energy.

• The object which does the work loses energy and the object on which the work is done gains energy.

• An object with energy can apply force to another object. Energy is moved from the former to the latter when this occurs. As the second object absorbs energy, it might move and so perform some work. The first object therefore had the capacity to do work. This suggests that any thing with energy has the ability to perform work.

• The energy possessed by an object is thus measured in terms of its capacity of doing work. The unit of energy is, therefore, the same as that of work, that is, joule (J).

• 1 J is the energy required to do 1 joule of work. Sometimes a larger unit of energy called kilo joule (kJ) is used. 1 kJ equals 1000 J.

## Kinetic energy

### By definition, we say that the kinetic energy of a body moving with a certain velocity is equal to the work done on it to make it acquire that velocity.

• It is the energy possessed by an object due to its motion.

• The kinetic energy of an object increases with its speed.

• Kinetic energy=0.5 x mass x velocity^2

• KE=0.5mv^2

## Potential Energy

### The energy possessed by a body by virtue of its position is known as Potential Energy

A spring has potential energy when it is compressed or stretched. A ball has potential energy,when raised above the ground.

## Potential energy of an object at a height

The gravitational potential energy of an object at a point above the ground is defined as the work done in raising it from the ground to that point against gravity.

• When an object is raised through a height, its energy increases. This is due to the fact that as it is being raised, work is done on it against gravity. The gravitational potential energy is the energy that such an object possesses.

• The potential energy of an object at a height depends on the ground level or the zero level you choose. An object in a given position can have a certain potential energy with respect to one level and a different value of potential energy with respect to another level.

• Consider an object of mass, m. Let it be raised through a height, h from the ground.

• A force is required to do this.

• The minimum force required to raise the object is equal to the weight of the object, mg.

• The object gains energy equal to the work done on it.

• Let the work done on the object against gravity be W.

W is equal to:

• W=mg x height(h)

• W=mgh

So potential energy of an object raised at height h is mgh where m is the mass of the body, h is the height at which the object is raised, g is the accleleation due to gravity

## Law of conservation of energy

• According to this law, energy can only be converted from one form to another; it can neither be created or destroyed. The total energy before and after the transformation remains the same.

• The law of conservation of energy is valid in all situations and for all kinds of transformations.

• potential energy + kinetic energy = constant

• If a ball is raised at a height h then its potential energy is mgh and when it falls on the ground the kinetic energy will be 0.5mv^2,so the entire potential energy will get converted to kinetic energy so potential energy at height h=kinetic energy possessed when ball falls on the ground.