Work for 9th Class

Living beings have to perform several basic activities to survive. We call such activities ‘life processes’.

            The energy for these processes comes from food. We need energy for other activities like playing, singing, reading, writing, thinking, jumping, cycling and running. Activities that are strenuous require more energy.

            Animals too, get engaged in activities. For example, they may jump and run. They have to fight, move away from enemies, find food or find a safe place to live. Also, we engage some animals to lift weights, carry loads, pull carts or plough fields. All such activities require energy.

            Think of machines.  They too require energy.  They get energy from fuel like petrol and diesel, electricity, solar panels etc.

WORK

            Two conditions need to be 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.  In day-to-day life, we consider any useful physical or mental labour as work. So, many times not much work is done in spite of hard work. A few examples are given:

1. Kamali is preparing for examinations. She spends lot of time in studies. She reads books, draws diagrams, organises her thoughts, collects question papers, attends classes, discusses problems with her friends, and performs experiments. She spends a lot of energy on these activities. In common parlance, she is ‘working hard’; but scientifically not.
2. You are working hard to push a huge rock. Let us say the rock does not move despite all the effort. You get completely exhausted. However, you have not done any work on the rock as there is no displacement of the rock.
3. You stand still for a few minutes with a heavy load on your head. You get tired. You have exerted yourself and have spent quite a bit of your energy; but the way we understand the term ‘work’ in science, work is not done.

            On the other hand,

1. If you climb up the steps of a staircase and reach the second floor of a building just to see the landscape from there, we may think that no work has been done – we have only enjoyed the scenery; but If we apply the scientific definition, these activities involve a lot of work.
2. Push a pebble lying on a surface. The pebble moves through a distance. You exerted a force on the pebble and the pebble got displaced. In this situation work is done.
3. A girl pulls a trolley and the trolley moves through a distance. The girl has exerted a force on the trolley and it is displaced. Therefore, work is done.
4. Lift a book through a height. To do this you must apply a force. The book rises up. There is a force applied on the book and the book has moved. Hence, work is done.

            Whenever work is done three things occur and as a student of Science you have to observe them :

1. If work is done, there should be some force acting on the object?  Take note of it. Record it.
2. What is the object on which the work is done?
3. What happens to the object on which work is done? Is it displaced or stopped. The displacement etc.

WORK DONE BY A CONSTANT FORCE

            Work done by a Force may be either positive or negative. Example of positive is when we push something to make it move and negative is when we apply force to stop a moving object.

            Let a constant force, F act on an object. Let the object be displaced through a distance, s in the direction of the force.

            Let W be the work done. We define work to be equal to the product of the force and displacement.

             Work done = force × displacement      W = F s

              Force = Mass x Acceleration               F = ma 

             Weight is similar as it is the force exerted by gravity on a mass of body / matter / object. So,        Weight = Mass x gravitational pull      W = mg

             g though varies from place to place is considered to be 9.8 m/s²

Units:

            Unit of Mass is Kg & Acceleration is m/s²  (we write it as ms^-2).

            So Unit of Force is Kgms^-2 (also know as Newton, N).

            Hence unit of Work is Nm (Newton meter).  We also call it Joule, J

            Work has only magnitude and no direction. [ It is scalar as it is dot product of 2 vectors]

            1 J is the amount of work  done on an object when a force of 1 N displaces it by 1 m along the line of action of the force.

            [1 N is the force needed to accelerate 1 Kg of mass at the rate of 1 meter per second square in the direction of the applied force.

            1 m/s²  means increase in velocity by one meter every second.  So 9.8 m/s²  means the velocity will be 9.8 m/s after 1 second.

       It will be 19.6 m/s after 2 seconds.

       It will be 29.4 m/s after 3 seconds.]

Example 1  A force of 5 N is acting on an object. The object is displaced through 2 m in the direction of the force. If the force acts on the object all through the displacement, then

Work done is 5 N × 2 m =10 N m or 10 J.

Question 1. A force of 7 N acts on an object. The displacement is, say 8 m, in the direction of the force. Let us take it that the force acts on the object through the displacement. What is the work done in this case? 

Ans. (7 x 8 = 56 Nm or J)

Example of negative work done:

            Consider a situation in which a stone is rolling down the mountain. If a force is applied from the opposite direction (down) to stop it, it may stop after some time.  The Force applied here is called Retarding Force.  The work done here is F x (–s)  =  – (Fs)

            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.

Example 2 A porter lifts a luggage of 15 kg 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 luggage, m = 15 kg and displacement, s = 1.5 m

Work done , W = Fs = mg into s

= 15 Kg x 10 m/s²  x 1.5 m

= 225 Kg m/s² m

= 225 Nm

=225 J

Q. A pair of bullocks exerts a force of 140 N on a plough. The field being ploughed is 15 m long. How much work is done in ploughing the length of the field?

A. 140 x 15 = 2100 J.  (Work done by each bullock is 1050 J)