WORK AND ENERGY

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POINTS TO REMEMBER

Work done on an object is defined as the magnitude of the force multiplied by the distance moved by the object in the direction of the applied force. The unit of work is joul :

1 joule = 1 newton x 1 metre.

Work done on an object by a force would be zero if the displacement of the object is zero. •
An object having capability to do work is said to possess energy. Energy has the same unit as that of work.
An object in motion possesses what is known as the kinetic energy of the object. An object of mass m moving with velocity v has a kinetic energy K = 1/ 2 mv²
The energy possessed by a body due to its change in position or shape is called the potential energy. The gravitational potential energy of an object of mass m, raised through a height, h from the earth’s surface is given by U = mgh.
If a force changes the velocity of the body from u to v then total work done is:

W = 1/2mv² – 1/2mu²

According to the law of conservation of energy, energy can only be transformed from one form to another, it can neither be created nor destroyed. The total energy before and after the transformation always remains constant.
Energy exists in nature in several forms such as kinetic energy, potential energy, heat energy, chemical energy etc. The sum of the kinetic and potential energies of an object is called its mechanical energy.
Power is defined as the rate of doing work power P= W/T. The S.I. unit of power is watt. IW=1J/s.
The energy used in one hour at the rate of 1 kW is called 1 kWh or 1 unit.

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WORK AND ENERGY

A porter lifts a luggage of 15kg from the ground and puts it on his head 1.5 m above the ground. Calculate the work done by him on the luggage.

Solution: Mass of the object, m = 10kg, displacement (height), h = 6m and acceleration due to gravity, g = 9.8 ms^-2

Potential energy = mgh

= 10 kg

9.8ms^-2

6 m

= 588 J

4.An object of mass 12 kg is at a certain height above the ground. If the potential energy of the object is 480J, find the height at which the object is with respect to the ground. Given, g = 10 ms^-2.