Work and Energy

11.1 Work

When a force acts upon an object while it is moving, work is said to have been done upon the object by that force.

11.1.1 Not Much ‘Work’ in Spite of Working Hard!

The way we understand the term ‘work’ in science, work is not done. In day-to-day life, we consider any useful physical or mental labour as work. Activities like playing in a field, talking with friends, humming a tune, watching a movie, attending a function are sometimes not considered to be work.

1.1.2 Scientific Conception of Work

If satisfied for work to be done: (i) a force should act on an object, and (ii) the object must be displaced.

If any one of the above conditions does not exist, work is not done. This is the way we view work in science.

11.1.3 Work Done By a Constant Force

The work done will be equal to the product of the force and displacement. In such situations, the work done by the force is taken as positive.

Work done is negative when the force acts opposite to the direction of displacement. Work done is positive when the force is in the direction of displacement.

11.2 Energy

Many of our energy sources are derived from the Sun. We can also get energy from the nuclei of atoms, the interior of the earth, and the tides.

The word energy is very often used in our daily life, but in science we give it a definite and precise meaning.

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.

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.

11.2.1 Forms Of Energy

The various forms include mechanical energy (potential energy + kinetic energy), heat energy, chemical energy, electrical energy and light energy.

11.2.2 Kinetic Energy

A moving object can do work. An object moving faster can do more work than an identical object moving relatively slow. A moving bullet, blowing wind, a rotating wheel, a speeding stone can do work. Objects in motion possess energy. We call this energy kinetic energy.

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.

The energy transferred to an object is stored as potential energy if it is not used to cause a change in the velocity or speed of the object.

The energy transferred to the spring inside is stored as potential energy. The potential energy possessed by the object is the energy present in it by virtue of its position or configuration.

11.2.4 Potential Energy of an Object at a Height

An object increases its energy when raised through a height. This is because work is done on it against gravity while it is being raised. The energy present in such an object is the gravitational potential energy. 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. It is easy to arrive at an expression for the gravitational potential energy of an object at a height.

Work done on the object is equal to mgh, an energy equal to mgh units is gained by the object. This is the potential energy (EP) of the object.

Ep = mgh

11.2.5 Are Various Energy Forms Interconvertible?

In nature a number of instances of conversion of energy from one form to another.

11.2.6 Law of Conservation of Energy

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.

An object of mass, m be made to fall freely from a height, h. At the start, the potential energy is mgh and kinetic energy is zero. Why is the kinetic energy zero? It is zero because its velocity is zero. The total energy of the object is thus mgh.

As it falls, its potential energy will change into kinetic energy. If v is the velocity of the object at a given instant, the kinetic energy would be 1/2mv2. As the fall of the object continues, the potential energy would decrease while the kinetic energy would increase. When the object is about to reach the ground, h = 0 and v will be the highest. Therefore, the kinetic energy would be the largest and potential energy the least. However, the sum of the potential energy and kinetic energy of the object would be the same at all points. That is, potential energy + kinetic energy = constant

or

mgh + 1/2mv2 = constant.

The sum of kinetic energy and potential energy of an object is its total mechanical energy.

11.3 Rate of Doing Work

The power of an agent may vary with time. This means that the agent may be doing work at different rates at different intervals of time.

Therefore the concept of average power is useful. We obtain average power by dividing the total energy consumed by the total time taken.

11.3.1 Commercial Unit of Energy

The unit joule is too small and hence is inconvenient to express large quantities of energy. We use a bigger unit of energy called kilowatt hour (kW h).