FORCE AND LAWS OF MOTION, Class IX, Part 3

 

                                     

In order to understand Newton’s second law of motion, we should first know the meaning of the term momentum of a moving body (or moving object).

We know that a cricket ball is much heavier than a tennis ball. Suppose we throw a cricket ball and a tennis ball, both with the same speed or velocity. It will be found that more force is required to stop the cricket ball (Which has more mass) and less force is required to stop the tennis ball (which has less mass). We conclude that the force required to stop a moving body is directly proportional to its mass.

If we throw two cricket balls of the same mass at different speeds or velocities, it will be found that more force is required to stop that cricket ball which is moving with higher velocity and less force is required to stop that cricket ball which is moving with higher velocity and less force is required to stop the cricket ball moving with lower velocity. So conclude that the force required to stop a moving body is also directly proportional to its velocity. Thus the quantity of motion in a body depends on the mass and velocity of the body. This given us another term knows as “momentum” the momentum of a body is defined as the product of its mass and velocity.

 Thus,                                 Momentum = Mass x velocity.

Or                                       P = m x v

Where                                P = momentum

                                           M = mass of the body

and                                      v = velocity (or speed) of the body                              

It is clear that if a body is at rest, its velocity is zero and hence its momentum is also zero. Thus the total momentum of the gun and bullet before firing is zero because their velocity is zero.

Momentum is a vector quantity and takes place in the direction of velocity. We have just seen that momentum is equal to the product of mass and velocity. Now mass is measured in kilograms (kg) and velocity is measured in meters per second (m/s) so the SI unit of momentum is kilogram meters per second which is written as kg m/s.

Every moving body possesses momentum. Since momentum depends on the mass and velocity of a body so a body will have a large momentum.

(a) If its mass is large

 (b) If its velocity (speed) is large

(c) If both its mass and velocity (speed) are large.

For example

1. A karate player can break a pile of tiles or a slap of ice with a single blow of his hand. This is because a karate player strikes the pile of tiles or the slab of ice with his hand very, very fast.

2. Though a cricket ball is not very heavy but when it is thrown with a high speed (or high velocity) it acquires a very large momentum and sometimes hurts the batsman.

3. A car or bus may not be running at a high speed ( or high velocity) but because of its high mass, it has a very high momentum which may hunt the person coming in its way.

From above examples we conclude that the combined effect of mass and velocity of a body is called momentum.  

 When two bodies a heavy one and a light one, are acted upon by the same force for the same time the light body attains a higher velocity or higher speed than the heavy one. But the momentum gained by both the bodies is the same. The link between force and momentum is expresses in Newton’s second law of motion.

          According to Newton’s second law of motion

The rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction in which the force acts. The rate of change of momentum of a body can be obtained by dividing the change in momentum by time taken for change.

For example let us consider a body of mass m having an initial velocity u. The initial momentum of this body will be mu. Suppose a force F acts on this body for time t and causes the final velocity to become v. The final momentum of this body will be mv. Now the change in momentum of this body is mv – mu and the time taken for this change is t.

So according to Newton’s second law of motion

Thus, Newton’s second law of motion gives us a relationship between ‘force’ and acceleration. When a force acts on a body, it produces acceleration in the body.

 The acceleration produced may be positive or negative. Newton’s second law of motion also gives us a method of measuring the force in terms of mass and acceleration. This is another definition of Newton’s law of motion.

The acceleration produced in a body is directly proportional to the force acting on it and inversely proportional to the mass of the body.

The acceleration produced is inversely proportional to the mass of body therefore if the mass of a body is doubled its acceleration will be halved. If the acceleration produced is inversely proportional to the mass of the body it means that it will be easier to move light bodies having less mass than having bodies having large mass.

The SI unit of force is Newton which is denoted by N.

A Newton is that force which when acting on a body of mass 1 kg produces an acceleration of 1 m/s² in it.

           Applications of Newton's Second Law of Motion

We can take some of the examples from our daily life. Can explain the Newton’s second law of motion.                                            

                               Catching a Cricket Ball

A cricket player (or fielder) moves his hands backwards on catching a fast cricket ball. This is done to prevent injury to the hand. We can explain it as follows a fast moving cricket ball has a large momentum in stopping or catching. The cricket ball Momentum has to be reduced to zero. Now when a cricket player moves back his hand or catching the fast ball then the time taken to reduce the momentum of ball to zero the increased due to more time taken to stop the ball the rate of change of momentum of ball is decreased and hence a small force exerted on the hands of player. So the hand of player does not get hurt.

 If however a cricket player stops a fast-moving ball suddenly keeping his hand is stationary  than the large momentum of the balls will be reduced to zero is in a very short time, due to this the rate of change of momentum of cricket ball will be very large and hence it will be exert a large force on. Players’ hands. The player’s hands will get hurt.

                                The Case of a High Jumper

During athletics meet a high jumping athlete is provided either a cushion or a heap of sand of the ground to fall upon. This is down to prevent injury to the athlete when he falls down after making a high jump. We can explain it when the high jumper falls on a soft landing sites (such as cushion or heap of sand) then the jumper takes a longer time to come to a stop. The rate of change of momentum of athlete is less due to which a smaller stopping force act and the athlete and that does not get hurt. Thus the cushion or sand being soft reduces the athlete momentum more gently.

 If however a high jumping athlete Falls from a  height on  to hard ground, then his momentum will be reduced to zero in a very short time. The rate of change of momentum will be large due to which a large opposing forces will athlete. This can cause serious injuries of the athlete.

                              The use of seat belt  in cars

 In a car accident a fast running car stops suddenly. Due to this car's large Momentum is reduced to zero in a very short time. The slightly stretchable seat belt worn by the passenger of the car increase that time taken by the passengers to fall forward. Due to longer time that rate of change of momentum of passenger is reduced and hence less stopping force acts on them. So the passengers may either not get injured at all or may get less injuries. It is obvious that seat belt reduces the passengers Momentum more gently and hence prevents injuries.