Maharashtra Board Class 9 Science Chapter 2 Work and Energy PDF Download

2. Work And Energy

In this chapter we will learn about Work, Energy, Mechanical energy, Law of conservation of energy, and Free fall.

Can You Tell?

1. In which of the pictures above has work been done?

2. From scientific point of view, when do we say that no work was done?

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

Can You Recall?

What are different types of forces and their examples?

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?

Use Your Brain Power!

You have learnt how to calculate the work done on an object when the displacement is in the direction of the applied force. But if the displacement is not in the direction of the applied force, how do we calculate the amount of work done?

Teacher's Note

Work in physics means moving something by applying force. For example, pushing a heavy box across the floor is work.

Exam Trick

Remember: Work = Force × Displacement. If there is no displacement, there is no work, even if you use lots of force.

Points to Remember

Work happens when force moves an object.
Work = force × displacement.
The unit of work is joule (J).
Work can be positive, negative, or zero.
Direction of force and displacement matters.

Observe

2.1 Various activities

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 = F₁.s ................................. (1)

The force F is applied in the direction of the string i.e. at an angle with the horizontal. Let θ 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. (see figure2.3)

cos θ = base / hypotenuse

cos θ = F₁ / F

F₁ = F cos θ

Thus, the work done by F₁ is

W = F cos θ s

W = F s cos θ

Observe And Discuss.

Enter your conclusions about the work done for the specific values of θ in the following table.

2.2 Displacement of an object

Teacher's Note

When you pull a toy by a string at an angle, only the horizontal part of the force does the work. The vertical part does not help move the toy forward.

Exam Trick

Remember: W = F s cos θ. When θ = 0°, work is maximum. When θ = 90°, work is zero.

Points to Remember

Work depends on the angle between force and displacement.
Use W = F s cos θ to find work at any angle.
When force and displacement are same direction, θ = 0° and work is positive.
When they are opposite, θ = 180° and work is negative.
When they are perpendicular, θ = 90° and work is zero.

Positive, Negative And Zero Work

Unit Of Work

Work = Force × Displacement

In SI system, the unit of force is newton (N) and the unit of displacement is metre (m). Thus, the unit of force is newton-metre. This is called joule.

1 Joule: If a force of 1 newton displaces an object through 1 metre in the direction of the force, the amount of work done on the object is 1 joule.

∴ 1 joule = 1 newton × 1 metre

1 J = 1 N × 1 m

In CGS system, the unit of force is dyne and that of displacement is centimeter (cm). Thus, the unit of work done is dyne-centimetre. This is called an erg.

1 erg: If a force of 1 dyne displaces an object through 1 centimetre in the direction of the force, the amount of work done is 1 erg.

1 erg = 1 dyne × 1 cm

Relationship Between Joule And Erg

We know that, 1 newton = 10⁵ dyne and 1 m = 10² cm

Work = force × displacement

1 joule = 1 newton × 1 m

1 joule = 10⁵ dyne × 10² cm

= 10⁷ dyne cm

1 joule = 10⁷ erg

Think Before You Answer

Discuss the directions of force and of displacement in each of the following cases.

1. Pushing a stalled vehicle

2. Catching the ball which your friend has thrown towards you.

3. Tying a stone to one end of a string and swinging it round and round by the other end of the string.

4. Walking up and down a staircase; climbing a tree.

5. Stopping a moving car by applying brakes.

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.

1. When the force and the displacement are in the same direction (θ = 0°), the work done by the force is positive.

2. When the force and the displacement are in opposite directions (θ = 180°), the work done by the force is negative.

3. When the applied force does not cause any displacement or when the force and the displacement are perpendicular to each other (θ = 90°), the work done by the force is zero.

Teacher's Note

Work can be positive (like pushing a car forward), negative (like friction stopping a car), or zero (like carrying a book horizontally).

Exam Trick

Remember: Same direction = positive work. Opposite direction = negative work. Perpendicular = zero work.

Points to Remember

Positive work happens when force and displacement are in the same direction.
Negative work happens when they are in opposite directions.
Zero work happens when they are perpendicular to each other.
Work tells us how much energy was used.
The angle between force and displacement is very important.

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