Calculate an estimate of the average force exerted on the baseball by the pitche
ID: 1950097 • Letter: C
Question
Calculate an estimate of the average force exerted on the baseball by the pitcher. Don't reproduce the entire acceleration estimate, just use the result here. It should take only a sentence or two to show and explain your work, and interpret the result.Calculate an estimate of the average force exerted on the pitched baseball by the catcher. Make no assumptions about the time involved in catching the ball.
Briefly compare your results for the two average forces. Did you expect them to be equal, or not? Do your results make sense? Why?
Notes
Justify all assumptions, show and explain all calculations.
All quantities should be presented with their units (SI only for results).
Round all answers to 2 sig figs.
Explanation / Answer
v0 = 0 m/sec : speed before pitched v = 3 m/sec : speed after pitcher lets go of ball x = 2 m : basically assume pitcher's arm is a meter long, so throws by moving arm from behind him (1 meter) to arm is in front of him (1 meter), total distance 2 meters. General expression for acceleration x = 1/2 * acc * t^2 : acc is acceleration assumed constant (although pitch is not necessarily a constant acceleration), t is time to throw the ball Solve for t, get t = sqrt(2 *x / acc) where sqrt means square root. so simplifying this expressing gives t = sqrt(2*x)/ sqrt(acc) Next define the change in velocity of the ball as delv = v- v0 = 3 m/sec Meanwhile, for constant acceleration, this change in velocity is given by delv = acc * t Solve for acc, get acc = delv / t Now substitute t from above, we have acc = delv / (qrt(2*x)/ sqrt(acc)) or acc = (delv /sqrt(2 *x)) * sqrt(acc) Simplifying this gives sqrt(acc) = delv/ sqrt(2 * x) and squaring both sides give acc = delv^2 / (2 * x) so estimate is acc = (30^2)/(2 * 2) = 900/4 = 225 m/sec/sec
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