Question

1. The motion of a particle of mass mm is described by y = ut+ 1/2gt^2. Find the force acting on the particle.
2. A batsman hits back a ball straight in the direction of the bowler without changing its initial speed of 12 m s^{-1}.
If the mass of the ball is 0.15 kg, determine the impulse imparted to the ball. (Assume linear motion of the ball)

Answer 1

$\mathbb{ANSWER:}$

1.

We know,

              $y = ut + \frac{1}{2} gt^2$

Now,

              $v = \frac{dy}{dt} = u + gt$

acceleration, $a = \frac{dv}{dt} = g$

Then the force is given by Eq.

      $F = ma = mg$

Thus the given equation describes the motion of a particle under acceleration due to gravity and y is the position coordinate in the direction of g.

2.

Change in momentum

             $= 0.15 \times 12 - (-0.15 \times 12)$

             $= 3.6 \text{ N s},$

$\text{Impulse} = 3.6 \text{ N s},$

in the direction from the batsman to the bowler.

This is an example where the force on the ball by the batsman and the time of contact of the ball and the bat are difficult to know, but the impulse is readily calculated.