Numerical Problems Based on Impulse of a Force for Class 11 Physics

Mass of the ball, $m = 150\text{ g} = 0.15\text{ kg}$

Initial velocity, $u = 12\text{ ms}^{-1}$

Final velocity, $v = -20\text{ ms}^{-1}$ (negative sign indicates opposite direction after being hit)

Time interval, $t = 0.01\text{ s}$

Using Newton’s second law, Force ($F$) is the rate of change of momentum:

The magnitude of the average force exerted by the bat is $480\text{ N}$.

Mass, $m = 1\text{ kg}$; Initial speed, $u = 10\text{ ms}^{-1}$; Final speed, $v = 0$; Distance penetrated, $s = 10\text{ cm} = 0.1\text{ m}$

(i) Acceleration ($a$): Using the third equation of motion:

(ii) Time interval ($t$): Using the first equation of motion:

(iii) Impulse ($J$): Impulse is the change in momentum:

Mass of each ball, $m = 50\text{ g} = 0.05\text{ kg}$

Initial velocity of the first ball, $u_1 = 16\text{ ms}^{-1}$

Final velocity of the first ball after rebound, $v_1 = -16\text{ ms}^{-1}$

Impulse imparted to the first ball is equal to its change in momentum:

By Newton’s third law of motion, the impulse imparted to the second ball is equal in magnitude and opposite in direction:

Mass of a single bullet, $m = 30\text{ g} = 0.03\text{ kg}$

Velocity of the bullet, $v = 400\text{ ms}^{-1}$

Number of bullets fired per second, $n = 400\text{ s}^{-1}$

The force required to hold the gun in position must balance the rate of change of momentum of the bullets being fired. Force = total mass of bullets fired per second $\times$ velocity:

Mass, $m = 1500\text{ kg}$

Initial velocity, $u = 90\text{ km/h} = 90 \times \frac{5}{18}\text{ ms}^{-1} = 25\text{ ms}^{-1}$

Final velocity, $v = 0$ (since the car is stopped)

Impulse ($J$) is equal to the change in momentum of the car:

Mass, $m = 0.25\text{ kg}$; Initial velocity, $u = 12\text{ ms}^{-1}$; Final velocity, $v = 0$

Retarding Force, $F = -0.6\text{ N}$

1. Time taken to stop ($t$):

First, calculate the acceleration using Newton’s second law:

Now, use the first equation of motion to find time:

2. Impulse ($J$):

Impulse is the change in momentum (the question implies finding the magnitude):

Alternatively, $J = |F \times t| = |-0.6 \times 5| = 3\text{ Ns}$.