Question

A 140-g baseball traveling at 79.2 mi/h strikes the catcher's mitt which, in bringing the ball to rest, recoils backward a distance of 17.6 cm. Determine the magnitude of the average force applied by the glove on the ball to bring it to a stop, in newtons.

Answer 1

Solution:

Let us go to the basics first.

We know that

Impulse = F_avg.t = m (V_i - V_f) .......................Eqn.1

From Newton's Eqn:

V_f = V_i + at [ V_i = 79.2 mi/h = 35.4 m/s; V_f = 0 since rest]

=>0 = 35.4 + at

=> at = - 35.4.....................Eqn.2

Also, S = V_it + 0.5at² [where s = distance = 17.6 cm = 0.176 m]

=>0.176 = 35.4t + 0.5at² [substituting the value of a from eqn.2 in eqn.1]

=>0.176 = 35.4t + 0.5(-35.4 / t)t²

=>0.176 = 35.4t - 17.7t

=> t = 0.00994 seconds

Substituting t and other given values in eqn.1, we have:

F_avg.*0.00994 = 0.14 (35.4- 0) [m = 140 g = 0.14 kg]

=> F_avg.= 498.6 N (Answer)

Thanks!!!