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What is the Magnitude of the Impulse Delivered?

In a Little League baseball game, the 145 g ball enters the strike zone with a speed of 15.0 m/s. The batter hits the ball, and it leaves his bat with a speed of 20.0 m/s in exactly the opposite direction.

1) What is the magnitude of the impulse delivered by the bat to the ball?

Known Variables:

(ball) mass (m1) : .145 kg

initial velocity (v1): 15 m/s

final velocity (v2): -20 m/s

magnitude of the impulse equation:

m(vf – vi) =

(0.145 kg)[20.0 m/s – (-15.0 m/s)] =
5.08 kg*m/s

2) If the bat is in contact with the ball for 1.5 ms, what is the magnitude of the average force exerted by the bat on the ball?

We know the equation of Impulse:

I= F(t)

5.08 kg-m/s = (F)(t)

Convert milliseconds(ms) to proper units, seconds(s).

1.5ms/1000= .0015 s

5.08 kg-m/s = (F)(.0015 s)

Solve for F

F= (5.08 kg-m/s)  /(.0015 s)

F = 3380 N

rounded would yield

F= 3400 N

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