Instead of hitting a baseball, a baseball player hits a very flexible, rubber ba
ID: 1452958 • Letter: I
Question
Instead of hitting a baseball, a baseball player hits a very flexible, rubber baseball (m = 0.13 kg) similar to the situation shown in the figure below. The ball is initially traveling horizontally with a speed of 40 m/s. The batter hits a fly ball as shown, with speed vf = 61 m/s.
If the contact time changes (increases) by a factor of 70 but the initial and final velocities are the same, by what factor does the force of the bat on the ball change? (F1 is the force with the original contact time and F2 is the force with the increased contact time.)
Explanation / Answer
given
m = 0.13 kg
vi = 40 m/s
vf = -61 m/s
delta_2 = 70*delta_1
use Impulse-Momentum theorem,
in the first case,
Impulse = change in momentum
F1*delta_t1 = m*(vf - vi) ---(1)
in the second case
F2*delta_t2 = m*(vf - vi) ---(2)
take equation(2)/equation(1)
F2*delta_2/(F1*delta_1) = 1
F2/F1 = delta_1/delta_2
= delta_1/(70*delta_2)
F1/F1 = 1/70 <<<<<-----------Answer