We have seen that a change occurs in the motion or the shape of a body when a force acts on it. Now let us see how work is done when a force acts.
Distance and displacement
A Ranjit’s house is at place A. The figure alongside shows the distance traversed by Ranjit to reach his school at D. If we do not take direction into account, we find that Ranjit traversed a distance equal to AB+BC+CD. However, on doing this, his displacement was equal to AD. Ranjit’s displacement from his house to the school is shown in the picture with the broken line AD. AD is the minimum distance along a straight line from Ranjit’s house to the school.
The minimum distance traversed in a particular direction along a straight line is called displacement.
Speed and velocity
- What is meant by speed?
2. What is the formula for calculating speed?
When we say that the speed of a car is 40 km per hour, there is no need to specify the direction, but, to predict whether a storm will reach a particular place or not, a mention of its direction is essential.
Let us now use the above formulae to find out Ranjit’s velocity and speed when he goes to school as shown in the figure 7.2. The actual distance traversed by Ranjit from home to school
= AB + BC + CD
= 500 m + 700 m + 300 m = 1500 m.
Total time from home to school = 8 minutes + 11 minutes + 6 minutes = 25 minutes
Ranjit’s displacement from home to school, AD = 1000 metres
Thus, Ranjit’s velocity when going from home to school
Ranjit did not take the straight route of minimum distance while going to the school. Therefore, the magnitudes of his velocity and speed came out to be different. Had Ranjit actually gone by the straight route AD, then the magnitude of his velocity and speed would have been the same.
Average velocity and instantaneous velocity :
The velocity of an object can change even while it is moving along a straight line. Suppose that a truck is covering a distance of 40 km from A to D in a straight line. That is, its displacement will be 40 km.
If it requires altogether 1 hour for this, its average velocity is 40 km/hour. However, if the truck traverses the 10 km distance AB in 10 minutes, BC in 20 minutes and CD in 30 minutes, then
Now deduce the velocities for the distances BC and CD. We see that the velocity of the truck is different in the different segments of the road AB, BC and CD. However, the average velocity for the entire route AD is 40 km/hour. The velocity at a particular moment of time is called instantaneous velocity. The instantaneous velocity can be different at different times.
In the previous example, the truck covered the distance AB at the velocity of 60 km/hour, BC at 30 km/hour and CD at 40 km/hour. It means that the velocity for the distance CD is greater than the velocity for the distance BC. From the number of seconds required for this change in velocity to take place, the change in velocity per second can be deduced. This is called acceleration. What is the cause of acceleration?
You know that the truck driver increases or decreases the velocity of the truck by means of the accelerator. You might have seen a toy car that runs on a clockwork spring. When it is released on a flat floor, after winding up the spring, it goes in a straight line. However, when it is hit on one side, it changes direction and keeps going. If it collides into a wall, it stops. It means that its velocity changes. How did this change take place? It happens because the car comes into contact with something external to it. On a football ground, how does the direction of the ball moving in a straight line, change ? We see some player changing its direction by kicking it. When its direction changes, the velocity of the ball changes, that is to say, an acceleration takes place. The interaction that brings about the acceleration is called force. Force acts on a body.
Force and acceleration
Take a glass marble and let it roll on a big smooth tabletop. After some time its velocity will decrease and it will stop. On a carrom board, too, the carrom coin, pushed by a striker will move forward some distance, and then come to a stop. If the coin is pushed after applying talcum powder to the carrom board, it will keep moving for a longer time and then come to a stop.
What can we infer from this ? The velocity of the coin decreases due to the force of friction, and the coin stops. If the friction between the carrom board and the coin is reduced, the coin keeps moving for a longer time. It would mean that, if no force of friction is acting on a moving body, it will keep on moving with a constant velocity. The scientist Sir Isaac Newton was the first to study force and the resulting acceleration.
Newton’s First Law of Motion :
If no force is acting on a body, its velocity does not change, i.e. the body does not accelerate. In other words, if a body is stationary, it will remain stationary. If it is in motion, it will continue moving with the same velocity and in the same direction. You have learnt what is meant by force. You have seen that a body is accelerated due to force. Suppose, you place the 1 kilogram standard weight (See the chapter on ‘Measurement’.) on a surface with no friction and pull it with an acceleration of 1m/s2 , the force applied is called 1N (1 Newton).
Force, displacement and work
In the figure alongside, a string, attached to a wooden block on a table, is passed over a pulley and tied to a weight. On applying a sufficient weight, the block will be seen to move. Which force is being applied here ? How can this force be increased ? What will happen on applying more force ? When can we say that work is done by the applied force ?
If the block moves forward, we can say that it has been displaced. Due to the displacement, we say that the force has done some work. Can we measure this work ? We know that work done depends on the force and the displacement. The following formula expresses this relationship : Work (W) done by the force = force (F) applied to the body Í displacement (s) of the body that takes place in the direction of the force, W = F * s
In the SI system, the unit of work is Joule (J), while the unit of force is Newton (N) and the unit of displacement is metre (m). In the CGS system the unit of work is erg.