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.
Let us go to the basics first.
We know that
Impulse = Favg.t = m (Vi - Vf) .......................Eqn.1
From Newton's Eqn:
Vf = Vi + at [ Vi = 79.2 mi/h = 35.4 m/s; Vf = 0 since rest]
=>0 = 35.4 + at
=> at = - 35.4.....................Eqn.2
Also, S = Vit + 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:
Favg.*0.00994 = 0.14 (35.4- 0) [m = 140 g = 0.14 kg]
=> Favg.= 498.6 N (Answer)
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