Measurement of force from Newton’s second law. Suppose a force F acts on a body of mass m and changes its velocity from u to v in t seconds. Then

According to Newton’s second law, the rate of change of momentum is directly proportional to the applied force, so

where k is a constant. The unit of force is so chosen that k is equal to one. If m = 1, a = 1 and F = 1, then

So a unit force is that force which produces a unit acceleration in a body of unit mass. The S.I. unit of force is newton. One newton is that force which produces an acceleration of 1 m/s² in a body of mass 1 kg.

Thus, the second law of motion gives us a method to measure force. If the mass and acceleration of a body are known, we can determine the force acting on it.

(i) A cricket player lowers his hands while catching a ball. By lowering the hands, he increases the time of catching the ball. As a result, the rate of change of momentum decreases and by Newton’s second law, the force exerted on his hands is less. So he is less likely to hurt.

(ii) Chinawares are wrapped in straw paper before packing. The straw paper between the chinawares increases the time of experiencing the jerk during transportation. Hence, they strike against each other with a less force and are less likely to be damaged.

(iii) We are hurt less when we jump on a muddy floor than on a hard floor. When we jump on a muddy floor, the floor is carried in the direction of the jump and the time interval for which force acts is increased. This decreases the rate of change of momentum and hence the force of reaction. Thus, we are hurt less.

Initial velocity, u = 0, s = 10 m, v = ?, a = 10 m/s²

The velocity of the man after he has descended 10 m vertically downward is given by

The acceleration produced during the period the net sags down by 2 m is given by

The negative sign shows that the friction force exerted by the table is opposite to the direction of motion of the ball.

Fig.9.13.

(b) It is clear from the graph that the velocity at the end of 5 s is 15 m/s. So