WORKWORK:When a force acts on an object causing the object to be displaced in the direction of force, then work is said to be done by the force.Work = Force x displacementW = F.SWork is a scalar quantity.Unit for work: N-m or JouleIf 1 N force displaces the object by 1 m in its direction, then the work done is said to be 1 Joule.Note: SI unit of work is JouleCGS unit of work is erg1 Joule = 107 ergWORKDONE BY A CONSTANT FORCE:If the force is making an angle with the direction of the displacement, then it is expressed as, Work = F S Cos Where = the angle between the force and the Displacement

Work is the dot product of force and displacement.

Case 1:If force and displacement are in the same direction, = 00Therefore, work done = F S cos 0W = F SCase 2:If force and displacement are perpendicular to each other, = 900Therefore, the work done = F S Cos 90Since Cos 900, W = 0 JCase 3:If force and displacement are in opposite directions, = 1800Since Cos 1800 = -1=> W = - F SWork done by the force is negative in this case. That means, here the force opposes the motion of the object.Force Displacement graph:Area under Force Displacement graph gives the work done.

ENERGY:An object which is capable of doing work has energy. Then the ability of doing work is called as energy.Energy and work are similar quantities.Unit of energy:Unit of energy is Joule same as that of work.FORMS OF ENERGY:In nature, energy appears in many forms namely light, sound, heat, electricity etc.KINETIC ENERGY:Energy possessed due to the motion of the objects is called kinetic energy.If an object of mass m is moving with a velocity of v, then

Kinetic energy Kinetic energy of an object increases with its velocity.POTENTIAL ENERGY:The energy possessed by a body due to its position or configuration is called potential energy.EXPRESSION FOR POTENTIAL ENERGY:When an object is lifted to a height from the ground, work is done against to gravity. This work done is stored in the object in the form of potential energy.Let the object is lifted to a height of h.Work done = force x displacement = mg x h PE = mgh

POTENTIAL ENERGY OF AN OBJECT MAXIMUM HEIGHT hThe object of mass m is at a height of hAt the maximum height, the object has zero initial velocity. So its kinetic energy at that position is zero.Hence the object possesses potential energy only.The work done to move the object to height h is given by F.hHere the force is equal to its weight. HenceP.E. = F.h = mg.h

Therefore, total energy at A is,

LAW OF CONSERVATION OF ENERGY:Energy neither be created nor be destroyed. It is transformed from one form to the other.The total energy is of the system is always constant. This is known as conservation of energy.TRANSFORMATION OF ENERGY:1. In fans, electrical energy is converted into mechanical energy2. In generators mechanical energy is converted into electrical energy3. In fire crackers, chemical energy is converted into sound, light and thermal energyAPPLICATION OF LAW OF CONSERVATION OF ENERGY:Let us consider an object which is under free fall described as shown in the figure.At point A:The object of mass m is at a height of hAt A, the object has zero initial velocity. So its kinetic energy at that position is zero.Hence at A, the object possesses potential energy only.

Therefore, total energy at A is,

At point B:

At point B, the object is fallen by x m and at a height of (h-x).

As the body is falling down, its potential energy decreases as the height from the ground is decreasing and kinetic energy increases since the velocity is increasing.At B, the object has a velocity of VB.

Therefore the object has both potential energy and kinetic energy at B.

The potential energy PE = mg (h-x)

The initial velocity of the object = 0Final velocity at B is = VBDistance travelled s = xAcceleration a = g

From the equation of motion,

The kinetic energy at B is,

Therefore total energy at B is

At point C:When the object strikes the ground, the entire energy of the object is converted into kinetic energy. At the ground, the potential energy is zero.If the object hits the ground with a velocity of vc

Total energy at C is,

From the equations of laws of motion,

Total energy at c,

Therefore for a freely falling object, RELATION BETWEEN KINETIC ENERGY & LINEAR MOMENTUM:Linear momentum P = mv

Kinetic energy

WORK-ENERGY THEOREM:To increase the kinetic energy of a body, net force has to be acted on it. Thus the work done by the force is equal to change in its kinetic energy. This is known as work energy theorem.Proof:Let the object is moving with an initial velocity of u.Due to the net force (F) acting on the object, the velocity changes to v and it moves a distance of S.

Then the work done is defined as

From the equations of motions,

And the net force, F = ma

Therefore, work done

POWER:Power is defined as the rate of doing work.

Since work = F.S, the above expression can be written as,

Therefore, If force is making an angle with the direction of displacement, then

Thus power is defined as the dot product of force and velocity.Power is a scalar quantity.Unit of Power:SI unit of power is J/sec or watt1 watt = 1 J/1 secIf one joule of work is done in one sec, then the power is said to be one watt.ELECTRICAL ENERGY:The energy possessed by an electron which in motion is known as electrical energy.It is measured in watt hour (Wh)

Generally, it is expressed in terms of kilo watt hour.

Note:Electron volt is also used to measure the energy.It is defined as the amount of energy required to move an electron/proton in an electric field of potential 1 V. it is denoted by eV.