Work, Power, Energy and Force

Work (W)

When force acts on a body and the body undergoes some displacement, then work is said to be done. The amount of work done is equal to the product of force and displacement in the direction of force. Let, ‘P’ be the force acting on the body and ‘s’ be the distance through which the body moves, then, 

Fig.1 Body moves in the direction of application of force

                                         Work done by the force, P = Force × Distance

                                                                               W = P × s

Sometimes, the force P does not act in the direction of motion of the body, or in other words, the body does not move in the direction of the force as shown in figure. In such a case, work done is expressed as the product of the component of the force in the direction of motion and the displacement.

Fig. 2 Body is not moving in the direction of application of force

Hence,

                                                         Work done W = P cos θ × s

If θ = 90⁰, cos θ = 0 and there will be no work done i.e. if force and displacement are at right angles to each other, work done will be zero. Similarly, work done against the force is taken as negative.

When the point of application of the force moves in the direction of motion of the body, work is said to be done by the force. Work done by the force is taken as +ve.

As work is the product of force and displacement, the units of work depend upon the units of force and displacement. Work is expressed in N-m or kN-m. One Newton-meter is the work done by a force of 1N in moving the body through 1m. It is called Joule. 

                                                                   1J = 1 N-m. 

Similarly, 1 kilo Newton-meter is the work done by a force of 1 kN in moving a body through 1m. It is also called kilojoules. 

                                                                  1kJ = 1 kN-m

Power (P)

Power is defined as the rate of doing work. It is thus the measure of performance of engines. For example, an engine doing a certain amount of work, in one second, will be twice as powerful as an engine doing the same amount of work in two seconds. In SI units, the unit of power is watt (W) which is equal to 1 N-m/s or 1 J/s. It is also expressed in Kilowatt (kW), which is equal to 10³ W and Megawatt (MW) which is equal to 10⁶ W. In case of engines, the following two terms are commonly used for power.

                                                                    Power = Work / Time

                                                                            P = W / t

Another unit of power (In British engineering) is Horsepower (hp). Where 

                                                                          1hp = 746 W

Energy (E)

Energy may be defined as the capacity for doing work. Since energy of a machine is measured by the work it can do, therefore unit of energy is same as that of work. In S.I system, energy is expressed in Joules or Kilojoules. It exists in many forms i.e., mechanical, electrical chemical, heat, light etc. There are two types of mechanical energy.

1) Potential Energy(PE or U)

It is the energy possessed by a body by virtue of its position. A body at some height above the ground level possesses potential energy. If a body of mass (m) is raised to a height (h) above the ground level, the work done in rising the body is

                                        Work done = Weight of the body × distance through which it moved

                                                               = (mg) ×h

                                                         PE = mgh

This work (equal to mgh) is stored in the body as potential energy. The body, while coming down to its original level, can do work equal to mgh. Potential energy is zero when the body is on the earth. 

Compressed air also possesses potential energy because it can do some work in expanding, to the volume it would occupy at atmospheric pressure. A compressed spring also possesses potential energy because it can do some work in recovering to its original shape.

2) Kinetic Energy (KE)

It is the energy possessed by a body by virtue of its motion. It is the energy, possessed by a body, for doing work by virtue of its mass and velocity of motion. We can measure kinetic energy of a body by finding the work done by the body against external force to stop it.

Let, m= Mass of the body

u= Velocity of the body at any instant

P= External force applied

a=Constant Retardation of the body

s= distance travelled by the body before coming to rest

As the body comes to rest its final velocity v = 0

Work done, 

                                               W = Force × Distance = P × s ..….... (1)

Now substituting value of (P = m.a) in equation (1),

                                               W = ma × s = m.a.s ...…....(2)

But, v²-u²= -2as (for retardation)

                                                    0 – u²= -2as

                                                          u²= 2as

                                                         as =1/2 u²

Now substituting value of (a.s) in equation (2) and replacing work done with kinetic energy

                                    Kinetic Energy KE = 1/2mu²

If initial velocity is taken as v instead of u then

                                                            KE =1/2 mv²

Force (F)

Force is that which changes or tends to change the state of rest of uniform motion of a body along a straight line. It may also deform a body changing its dimensions. The force may be broadly defined as an agent which produces or tends to produce, destroys or tends to destroy motion. It has a magnitude and direction. The unit of force is N or kgm/s². Mathematically,

                                                       Force = Mass× Acceleration

Where

F-Force, m-Mass and a-Acceleration