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NEWTON’S SECOND LAW OF MOTION

“The rate of change of linear momentum of a body is directly proportional to the external force applied on the body, and this change takes place in the direction of the applied force”

Mathematically:

Consequences of Newton second law of motion

1. No force is required to move a body uniformly in a straight line

According to Newton’s second law of motion

F = ma

If F = 0, then a = 0 Thus velocity of body is constant.

2. Accelerated motion is always due to an external force

Force is required for acceleration i.e. for changing speed, direction or both.

Question 1. An object is accelerating at 2 m/s2. If the net force is tripled and the mass of the object is halved, what is the new acceleration?

a will become 6 times i.e. 6 x 2 = 12m/s²

Impulse

The forces which act on a body for a short time are called impulsive forces. Impulse of a force is a measure of total effect of a force. It is given by the product of force and time for which the force acts on the body.

Impulse = force x time = change in momentum

Applications of the Concept of Impulse

1. A cricket player lowers his hands while catching a cricket ball to avoid injury. In this way, he increases the time of catch to reduce the momentum of the ball to zero. As

Impulse = force x time = change in momentum

Or force = change in momentum/time, thus player has to apply a smaller force against the ball in order to stop it.

2. An athlete is advised to come to stop slowly, after finishing a fast race, so that time of stop increases and hence force experienced by him decreases.

Question 1. If the net force of 10 N was continuously applied on 5 kg object at rest, how long will it take to raise its velocity to 80 m/s?

Ans. u = 0, v = 80 m/s, F = 10 N, m = 5 kg, t =?

F = ma = m (v-u)/t

t = m (v-u)/F = 5x (80-0)/10 = 40s

Question 2. A batsman hits back a ball straight in the direction of the bowler without changing its initial speed of 12 m/s. If the mass of the ball is 0.15 kg, determine the impulse imparted to the ball.

Ans. m = 0.15 kg, u = 12 m/s, v = - 12 m/s

Impulse = m (v-u) = 0.15(-12 – 12) = - 3.6 Ns

*The negative sign indicates that the direction of the impulse is from batsman to the bowler.

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