ICSE Class 6 Physics Chapter 04 Work and Energy

Work and Energy

'Work' and 'energy' are two words we often use. We usually associate energy with work. For example, we may say, "I don't have the energy to do this work right now." In science, too, work and energy are closely related. Let us see what these two words mean in science and how they are related.

Work

When we speak of 'work', we mean doing something. This 'doing' may have different descriptions or forms. You do your class work and homework, and know of people working (doing things) in offices, factories, and on farms.

In physics, however, work does not have different descriptions. It is a physical quantity that can be measured. Its magnitude can be expressed in terms of numbers and units. It has a precise definition. Work is done when the point of application of a force moves through some distance. To put it simply, work is done when a force acts on a body and moves the body through some distance.

Let us try to understand this with the help of an example. Figure 4.1 shows a cart being drawn by a horse. The horse applies a force F₁ at the point A. As the cart moves, this point (of application of F₁) moves to B. We say that the horse has done some work.

To take another example, the child in Figure 4.2 applies an upward force F₂ on the handle of the bucket. As the bucket moves up, this point on the handle moves up. This means the child does some work, or rather the force applied by the child on the handle does some work.

Fig. 4.1 The horse does some work because the point where it applies force moves from A to B.

Amount of Work

Since work is a physical quantity, it must have a clearly defined magnitude. The work done by a force is equal to the product of the force and the displacement of its point of application in the direction of the force.

This can be expressed as

work = force × distance

We can also use symbols to write it as

\[W = F \times d\]

where F is a force, d is the displacement of its point of application in the direction of F and W is the work done.

In Figure 4.1

force = F₁, displacement = d.

\[\therefore \text{work done} = F_1 \times d\]

In Figure 4.2

force = F₂, displacement = h.

\[\therefore \text{work done} = F_2 \times h\]

To find the amount of work done by a force you must consider whether

1. the point of application of the force is displaced, and

2. the displacement is in the direction of the force.

No work is done if there is no displacement or if the displacement is at right angles to the direction in which the force is applied. A few examples will make this clear.

In Figure 4.3(a), the man pushing the box towards the left is applying a horizontal force P to the left. This force moves the box through a distance d, so the work done by this force is P × d. There is another force acting on the box. This is its weight M acting downwards. M does no work because the point C, where M acts, moves horizontally, while M acts vertically.

In Figure 4.3(b), a man is pushing against a wall with a force F. He does not do any work because the point on the wall where he applies the force does not move.

In Figure 4.3(c), a man is carrying a load on his head. He is applying an upward force W to overcome the weight of the load, which acts downwards. If he is standing, he does not do any work because the point D, where he is applying the force W, does not move. Even if he walks, he does not do any work on the load. This is because though D moves, its displacement is at right angles to W.

Unit of Work

Since work = force × distance,

the unit of work = the unit of force × the unit of distance

= newton × metre.

This unit of work is called the joule. Its symbol is J.

Thus, joule = newton × metre, or J = N × m or N m.

Example 1. A man pushes a cart with a horizontal force of 20 N. How much work does he do in moving the cart through a distance of 50 m?

Work = force × distance. Here, force = 20 N, distance = 50 m.

\[\therefore \text{work} = 20 \text{ N} \times 50 \text{ m} = 1000 \text{ N m} = 1000 \text{ J}\]

Example 2. A boy has to apply an upward force of 4 N on a book to lift it from the floor to a desk. If he does 3 J of work in the process, what is the height of the desk?

Here, work = 3 J, force = 4 N.

Since work = force × distance,

distance = work ÷ force = 3 J ÷ 4 N = 0.75 m = 75 cm.

\[\therefore \text{the height of the desk} = 75 \text{ cm}\]

Teacher's Note

Work in everyday life includes household chores and exercises, while in physics, work is only done when force causes displacement in the direction of that force.

Energy

When a person is tired or lacks energy, he is unable to work. In other words, a person needs energy to be able to work. This everyday meaning of energy is very close to the definition of energy in physics. Energy is the ability to do work.

Unit of Energy

Energy, like all other physical quantities, has a clearly defined magnitude that can be measured. Since the energy of something has is defined as the amount of work it can do, energy is measured in the same unit as work, i.e., the joule (J).

Mechanical Energy

Energy can exist in many forms. The energy stored in food and fuels (such as petrol and coal), and the energy we receive from the sun are two forms of energy. The two most common forms of energy around us are:

1. The energy a body has due to its motion, called kinetic energy

2. The energy a body has due to its position or condition, called potential energy

Kinetic energy and potential energy are together known as mechanical energy. Let us study these two forms of energy in greater detail.

Kinetic Energy

A moving body is capable of doing work. Suppose a box is resting on a floor. To move it, someone will have to apply some force. He will do some work as the point where he applies force moves along the floor. Now, if a heavy ball rolls along the ground and collides with the box, the box will move. Thus, the ball is able to do some work on the box because of its motion. Similarly, a moving striker is able to move counters on a carom board because of its motion.

Anything that has mass and is moving has some kinetic energy. This is true not only of solids, but of liquids and gases as well. The kinetic energy of moving air makes clothes and leaves flutter. It helps to move kites and sailing boats. Earlier, this energy was used to turn windmills.

Water flowing down mountains can move rocks and wash away soil. The kinetic energy of flowing water was earlier used in watermills to grind grain and do other kinds of work. Now we use the energy of wind and water to generate electricity.

Amount of kinetic energy Common sense would tell you that all moving bodies do not have the same amount of energy. For instance, when you throw a stone into a pool, the size of the ripples it makes depends on how big the stone is and how hard you throw it. The bigger the stone, the greater will be its kinetic energy, and so, the bigger will be the ripples. Also, if you throw stones of the same size (same mass), the size of the ripples will depend on the speed with which each stone moves. This applies to the kinetic energy of any moving body. In general, the kinetic energy of a body depends on its mass and its speed. The actual relationship between these quantities is

\[\text{kinetic energy} = \frac{1}{2} \text{mass} \times \text{(speed)}^2\]

This relation shows that

1. if two bodies move with the same speed, the one with greater mass has more kinetic energy, and

2. if two bodies have the same mass, the one moving faster has greater kinetic energy.

Teacher's Note

A moving car has kinetic energy and can do damage or work. A car moving faster causes more damage, similar to how a heavier vehicle at the same speed does more damage.

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