A force platform is a tool used to analyze the performance of athletes measuring

Question

A force platform is a tool used to analyze the performance of athletes measuring the vertical force that the athlete exerts on the ground as a function of time. Starting from rest, a 59.0-kg athlete jumps down onto the platform from a height of 0.590 m. While she is in contact with the platform during the time interval 0 < t < 0.800 s, the force she exerts on it is described by the function F = 9 200t ? 11 500t^2 where F is in newtons and t is in seconds. (a) What impulse did the athlete receive from the platform? _______________N

Explanation / Answer

a)

J = F.dt = (9200t 11500t^2) dt = 9200/2 t^2 - 11500/3 t^3

J = 9200/2 *(0.8*0.8) - 11500/3 *(0.8*0.8*0.8) = 981.33

J = 981 N.s

b)

0.5 m vi^2 = m g h

==> vi = (2gh) = (2*9.8*0.590) = 11.564

==> vi = 11.6 m/s

c)

m (vf - vi) = J

vf = J/m + vi

vf = 981.33/59 - 11.564 = 5.0687

vf = 5.07 m/s

d)

0.5 m vf^2 = m g h'

h' = 0.5 vf^2/g = 0.5 * 5.0687*5.0687/9.8

h' = 1.31 m

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