please show steps and equations used 3. An estimated force-time curve for a base

Question

please show steps and equations used

3. An estimated force-time curve for a baseball struck by a bat is shown in the graph. Determine, (a). the magnitude of the impulse delivered to the ball (b). the magnitude of the peak force exerted on the ball, (c). the magnitude of the average force exerted on the ball (d). Compare your result in (c) with the weight of the ball and determine whether or not the impulse approximation is valid in this situation. Take the mass to be 145 grams (kiloNewtons) 15.0 5.0 f (milliseconds) 5.

Explanation / Answer

a) Impulse delievered to the ball = F*dt , since fro 3 different intervals, there are different forces, the impulse is sum of all these 3 impilses ;which is area under the curve. = 0.5*1.2*13 + (1.8-1.2)*13 + 0.5*(3.8-1.8)*13 = 28.6 kN-ms

b) From the graph, maximum value of F is 13 kN

c) 28.6kN-ms is exerted on the ball over 3.8ms, so average force = 28.6/3.8 = 7.526 kN

d) Weight of the ball = 0.145kg*9.8m/s^2 = 1.421 N, which is far less than the impulse calculated in (c), so it is valid in this situation to approximate.

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