An estimated force-time curve for a baseball struck by a bat is shown in the fig

Question

An estimated force-time curve for a baseball struck by a bat is shown in the figure below. F_max = 15 000 N, t_a = 1.5 ms, and t_b = 3 ms. From this curve, determine each of the following. (a) the magnitude of the impulse delivered to the ball____________n middot s (b) the average force exerted on the ball____________kN A railroad car of mass 2.48 times 10^4 kg is moving with a speed of 3.84 m/s. It collides and couples with three other coupled railroad cars, each of the same mass as the single car and moving in the same direction with an initial speed of 1.92 m/s. (a) What is the speed of the four cars after the collision?____________m/s (b) How much mechanical energy is lost in the collision?____________J

Explanation / Answer

Impulse = integral F dt

Impulse = A under curve

= 1/2 * ( tb-ta) 15000 N

= 1/2 * 1.5 * 10^-3 * 15000 N

= 11.25 N

(b)

Impulse = Favg t

Favg = 11.25/1.5 * 10^-3

=7.5 kN

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Pfinal = 4 M vfinal

Pinitial = M (3.84 m/s) + 3 M (1.92m/s)

Pfinal = 4 M vfinal = M (3.84m/s) + 3 M (1.92 m/s) = Pinitial

4 vfinal = (3.84 m/s) + 3 (1.92 m/s) = 9.6m/s

4 vfinal = 9.6 m/s

vfinal = 2.4 m/s

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E'lost' = Einitial - Efinal

Einitial = (1/2)(2.48 x 104 kg)(3.84 m/s)2 + (1/2)(3 x 2.48 x 104 kg)(1.92m/s)2

Einitial = 3.199 x 105 J

Efinal = (1/2)(4 x 2.48x 104)(2.4 m/s)2

Efinal = 2.85 x 105 J

E'lost' = Einitial - Efinal

E'lost' = 0.349 * 10^5 J

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