Second Law of Motion

The rate of change of momentum of a moving body is proportional to and is in the same direction as the force acting on it

F = d(mv)/dt

where F is the applied force, v is the velocity of the body, and m its mass.

If mass remains constant

F = mdv/dt

or

F =ma

where a is the acceleration The direction of acceleration is the same as that of F.

As F = ma it follows that for a fixed mass, greater the force, greater the acceleration.

The SI unit of force is Newton. 1 Newton is equal to 1 kgm/sec2.

1 Newton is force which will cause an acceleration of 1 m/sec2 in a body of mass 1 kg.

How do we explain the behaviour of a ball which is hit by a bat instead of being thrown.

In the case of a bat the force acts for an extremely short duration. The effect of this force is called an impulse.

Which gives rise to the question. What is impulse?

What is impulse?

Impulse (J) is the product of a force F and the time t for which it acts.

If the force is variable, the impulse is the integral of Fdt from to to t1. The impulse of a force acting for a given interval is equal to the change in momentum produced over the interval.

J =m(v1 - v0),

assuming that mass (m) remains constant while the velocity changes from v0 to v1.

Solved Examples on Second Law of Motion

A bullet of mass 0.04 kg moving with a speed of 90 m/s enters a heavy wooden block and is stopped after it penetrates 60 cm into the block. What is the average resistive force exerted by the block on the bullet?

u = 90 m/s, v = 0, S = 60 cm = 0.6m

v2 - u2 = 2as

-902 = 2 x a x 0.6

a = -902 / 2 x 0.6 = -6750 m/s2

retarding force = m a = 0.04 x 6750 = 270 N

A base ball of mass 200 g moving with a velocity of 15 m/s is brought to rest by a player in 0.05 second. What is the impulse of the ball and the average force applied by the player?

m = 0.2 kg, u = 15 m/s, v = 0

Change in momentum = m(v - u) = -0.2 x 15 = -3 Ns

As change in momentum = impulse = -3 Ns

Impulse(J) = average force(F) x time(t)

F = J/t = 3/0.05 = 60 N

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