Question

A ball of mass 20 g is initially moving with a velocity of 100 $m{s}^{-1}$. On applying a constant force on the ball for 0.5s, it acquires a velocity of 150 $m{s}^{-1}$. Calculate the following : [5 MARKS]
(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

Formula = 0.5 Mark each
Calculation = 0.5 Mark each
Given , mass, $m=20g=0.02kg$,
initial velocity,$u=100m{s}^{-1}$
time interval, $t=0.5s$ and
final velocity,$v=150m{s}^{-1}$

(i) Initial momentum of the ball,$P_1=mass\times initialvelocity=mu=0.02\times 100=2kgm{s}^{-1}$.
(ii) Final momentum of the ball $P_2=mass\times finalvelocity=mv=0.02\times 150=3kgm{s}^{-1}$
(iii) $Rateofchangeofmomentum=\frac{(P_2-P_1)}{t}$
$=\frac{(3-2)}{0.5}=2.0kgm{s}^{-2}=2.0N$
(iv) $Acceleration,a=\frac{(v-u)}{t}$
$=\frac{(150-100)}{0.5}$
$=100m{s}^{-2}$
(v) Force, F $=mass\times acceleration=0.02\times 100=2.0N$.