Question

A ball of mass 20 g is initially moving with a velocity of 100 $\frac{m}{s}$. On applying a constant force on the ball for 0.5s, it acquires a velocity of 150 $\frac{m}{s}$. Calculate the following:
(i) Initial momentum of the ball
(ii) Final momentum of the ball
(iii) Rate of change of momentum
(iv) Acceleration of the ball
(v) Magnitude of the force applied

Answer 1

Given, m = 20 g = 0.02 kg

Initial velocity, u = 100 $\frac{m}{s}$

Time interval, t = 0.5 s

Final velocity, v = 150 $\frac{m}{s}$

(i) Initial momentum of the ball = mass $\times$ initial velocity

$P_1$ ​= mu = 0.02 kg $\times$ 100 $\frac{m}{s}$ = 2 kg ${ms}^{-1}$​

(ii) Final momentum of the ball = mass $\times$ final velocity

$P_2$​ = mv = 0.02 kg $\times$ 150 $\frac{m}{s}$ = 3 kg ${ms}^{-1}$​​

(iii) Rate of change of momentum = $\frac{3-2}{0.5}$ = 2.0 kg ${ms}^{-2}$​​​ = 2.0 N

(iv) Acceleration, a = 100 ${ms}^{-2}$​​​

(v) Force, F = mass $\times$ acceleration = 0.02 $\times$ 100 = 2.0 N