Answer to Question #104302 in Classical Mechanics for Franco Joco

Question

1.What is the average force between a cricket bat and ball during collision? Let's assume that the ball's initial and final velocities with respect to the bat are anti parallel and have magnitudes of about 100 kph. Suppose the collision lasts about 1 ms. A cricket ball has a mass of 0.16 kg. What is average force between bat and ball ?

Bowlers bowl at over 150 kph and, even though air resistance slows the ball down considerably by the time it reaches the batsman, the bat is often traveling rapidly in the other direction. So both velocities used here are probably exceeded substantially in professional games. I'm guessing that, because the cricket ball is hard, the collision might last less about 1 ms.

2. Parachutist and parachute have a combined mass of 93 kg. They are traveling vertically downwards at a constant speed of 0.30 m.s^-1. What is the magnitude of the force of air resistance on them ( in newtons and correct sig fig).

Answer 1

a)

As per the question,

Velocity of the ball =100kph=$100\times\dfrac{1000}{60\times 60}=\dfrac{1000}{36} m/sec$

Mass of the ball=0.16Kg

duration of collision =1ms=$1\times10^{-3}$ sec

Force = Rate of change of momentum=$\dfrac{mv-(-mv)}{t}=\dfrac{2mv}{t}$

Now, substituting the values in the above equation,

$F=\dfrac{2\times0.16\times1000}{36\times1\times 10^{-3}}=8.89\times 10^{3}N$

b)

Mass of the Parachutist and parachute(m)=93kg

downwards Speed(v) $=0.3m/sec$

Let the resistive force =$F_s$

​ and the gravitational acceleration =g

As per the question, they are moving with the constant speed,

So, net force must be zero,

$mg-F_s=0$

$F_s=mg=93\times 9.8 N=911.4N$