Question

The time taken to stop a ball rolling with velocity u is reduced to half,
find the change in values of
(a) initial and final momentum
(b)change in momentum
(c) rate of change of momentum.

Answer 1

Answer:

Let a body of mass m and velocity v is brought to test in time t.

Initial momentum = mv

Final momentum = m× 0 = 0 ( as the ball is brought to test its velocity is zero)

Change in momentum = final momentum - initial momentum= 0 - mv

Time in which ball is brought to rest = t

Rate of change in momentum = - m v/t

Force F = Rate of change of momentum =- mv/t

Impulse = Force F × t = change in momentum = -mv

When the time in which the ball is brought to rest is halved, there is no change in,

Initial momentum, it remains m v

Final momentum, it remains zero

Change in momentum, it remains - m v.

The only change is in the rate of change of momentum, which is doubled when the time is halved. Though impulse (=change in momentum) does not change, the force required is doubled.

Answer 2

let a body of mass M and velocity V is brought to test in time T.

(a) Initial momentum = mv

Final momentum= m×0=0(as the ball is brought to test its velocity is zero)

(b)Momentum change = final momentum, initial momentum=0-mv

Time in which ball is brought to test=T

(c) Rate of change in momentu= -m v/t

Force F= rate of momentum change= mv/t

Impluse= Force F×T= change momentum= -mv