## 2. Work and Energy

Generally, any mental or physical activity is referred to as work. When we walk or run, the energy in our body is used to do the necessary work.

We say that a girl who is studying is working or performing work. But that is mental work. In physics, we deal with physical work. Work has a special meaning in physics.

‘Work is said to be done when a force applied on an object causes displacement of the object.’

You have already learnt that the work done by a force acting on an object is the product of the magnitude of the force and the displacement of the object in the direction of the force. Thus, Work = force × displacement

Minakshee wants to displace a wooden block from point A to point B along the surface of a table as shown in figure 2.2A. She has used force F for the purpose. Has all the energy she spent been used to produce acceleration in the block? Which forces have been overcome using that energy?

You must have seen the events depicted in the pictures B and C above. When a child pulls a toy with the help of a string, the direction of the force is different from that of displacement. Similarly, when a large vehicle tows a small one, the directions of force and the displacements are different. In both these cases, the direction of force makes an angle with the direction of displacement. Let us see how to calculate work done in such cases.

When a child pulls a toy cart, force is applied along the direction of the string while the cart is pulled along the horizontal surface. In this case, in order to calculate the amount of work done, we have to convert the applied force into the force acting along the direction of displacement.

Let F be the applied force and F1 be its component in the direction of displacement. Let s be the displacement. The amount of work done is given by

W = F 1 .s …………………………… (1)

The force F is applied in the direction of the string i. e. at an angle with the horizontal. Let q be the angle that the string makes with the horizontal. We can determine the component F1 , of this force F, which acts in the horizontal direction by means of trigonometry.

Positive, negative and zero work

You will notice that in some of the above examples, the direction of the force and displacement are the same. In some other cases, these directions are opposite to each other, while in some cases, they are perpendicular to each other. In these cases, the work done by the force is as follows.

Take a plastic cup and make a hole in the centre of its bottom. Take a long thread, double it and pass it through the hole. Tie a thick enough knot at the end so that the knot will not pass through the hole, taking care that the two loose ends are below the bottom of the cup. Tie a nut each to the two ends as shown in figure 2.4. Now do the following.

As shown in figure ‘A’, put the cup on a table, keep one of the nuts in the cup and let the thread carrying the other nut hang down along the side of the table. What happens?

As shown in figure ‘B’, when the cup is sliding along the table, stop it by putting a ruler in its path. As shown in figure ‘C’, keep the cup at the centre of the table and leave the two nuts hanging on opposite sides of the table.

Questions:

1. Figure A- Why does the cup get pulled?
2. Figure B- What is the relation between the displacement of the cup and the force applied through the ruler?
3. In figure C- Why doesn’t the cup get displaced?
4. What is the type of work done in figures A, B and C? In the three actions above, what is the relationship between the applied force and the displacement?

Energy

Why does it happen?

1. If a pot having a plant is kept in the dark, the plant languishes.
2. On increasing the volume of a music system or TV beyond a limit, the vessels in the house start vibrating.
3. Collecting sunlight on a paper with the help of a convex lens burns the paper. The capacity of a body to perform work is called its energy. The units of work and energy are the same. The unit in SI system is joule while that in cgs system is erg. You have learnt that energy exists in various forms like mechanical, heat, light, sound, electro-magnetic, chemical, nuclear and solar. In this chapter, we are going to study two forms of mechanical energy, namely, potential energy and kinetic energy.

Kinetic energy

What will happen in the following cases?

1. A fast cricket ball strikes the stumps.
2. The striker hits a coin on the carom board.
3. One marble strikes another in a game of marbles.

From the above examples we understand that when a moving object strikes a stationary object, the stationary object moves. Thus, the moving object has some energy, part or all of which it shares with the stationary object, thereby setting it in motion. ‘The energy which an object has because of its motion is called its kinetic energy’. The work done by a force to displace a stationary object through a distance s is the kinetic energy gained by the object.

Kinetic energy = work done on the object

K.E. = F × s

Expression for kinetic energy :

Suppose a stationary object of mass m moves because of an applied force. Let u be its initial velocity (here u = 0). Let the applied force be F. This generates an acceleration a in the object, and, after time t, the velocity of the object becomes equal to v. The displacement during this time is s. The work done on the object,

W = F . s W = F × s

According to Newton’s second law of motion,

Potential energy

Which words describe the state of the object in the above examples? Where did the energy required to cause the motion of objects come from? If the objects were not brought in those states, would they have moved?

‘The energy stored in an object because of its specific state or position is called its potential energy.’

1.Hold a chalk at a height of 5 cm from the floor and release it.

1. Now stand up straight and then release the chalk.
2. Is there a difference in the results of the two activities? If so, why?

Expression for potential energy

To carry an object of mass ‘m’ to a height ‘h’ above the earth’s surface, a force equal to ‘mg’ has to be used against the direction of the gravitational force. The amount of work done can be calculated as follows.

Work = force x displacement W = mg × h \ W = mgh \ The amount of potential energy stored in the object because of its displacement P.E. = mgh (W = P.E.) \ Displacement to height h causes energy equal to mgh to be stored in the object.

Transformation of energy

Which are the different forms of energy? Which type of energy is used in each of the following processes?

1. A stretched piece of rubber
2. Fast moving car
3. The whistling of a cooker due to steam
4. The crackers exploded in Diwali
5. A fan running on electricity
6. Drawing out pieces of iron from garbage, using a magnet
7. Breaking of a glass window pane because of a loud noise.

Energy can be transformed from one type to another. For example, the exploding firecrackers convert the chemical energy stored in them into light, sound and heat energy.

Observe the above diagram (figure 2.5) and discuss how tranformation of energy takes place, giving example of each.

Law of conservation of energy

‘Energy can neither be created nor destroyed. It can be converted from one form into another. Thus, the total amount of energy in the universe remains constant’.

Tie the two pendulums to this horizontal thread in such a way that they will not hit each other while swinging. Now swing one of the pendulums and observe. What do you see? You will see that as the speed of oscillation of the pendulum slowly decreases, the second pendulum which was initially stationary, begins to swing. Thus, one pendulum transfers its energy to the other.

Free fall

If we release an object from a height, it gets pulled towards the earth because of the gravitational force. An object falling solely under the influence of gravitational force is said to be in free fall or to be falling freely. Let us look at the kinetic and potential energies of an object of mass m, falling freely from height h, when the object is at different heights

As shown in the figure, the point A is at a height h from the ground. Let the point B be at a distance x, vertically below A. Let the point C be on the ground directly below A and B. Let us calculate the energies of the object at A, B and C. 1. When the object is stationary at A, its initial velocity is u = 0

Thus, every object has potential energy when it is at a height above the ground and it keeps getting converted to kinetic energy as the object falls towards the ground. On reaching the ground (point C), all the potential energy gets converted to kinetic energy. But at any point during the fall the total energy remains constant.

i.e., T.E. = P.E. + K.E.

T.E. at A = mgh + 0 = mgh

T.E. at B = mgx + mg (h – x) = mgh

T.E. at C = 0 + mgh = mgh

Power

In the above examples, the work done is the same in each example but the time taken to perform the work is different for each person or each method. The fast or slow rate of the work done is expressed in terms of power. ‘Power is the rate at which work is done.’ If W amount of work is done in time t then,

In the above examples, the work done is the same in each example but the time taken to perform the work is different for each person or each method. The fast or slow rate of the work done is expressed in terms of power. ‘Power is the rate at which work is done.’ If W amount of work is done in time t then,

An introduction to scientists

The steam engine was invented in 1781 by the Scottish scientist James Watt (1736 – 1819). This invention brought about an industrial revolution. The unit of power is called Watt in his honour. James Watt was the first to use the term ‘horse-power’