A force platform is a tool used to analyze the performance of athletes measuring
ID: 1374500 • Letter: A
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 64.8-kg athlete jumps down onto the platform from a height of 0.690 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 500t2
where F is in newtons and t is in seconds.
(a) What impulse did the athlete receive from the platform?
magnitude N 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 64.8-kg athlete jumps down onto the platform from a height of 0.690 m. While she is in contact with the platform during the time interval 0Explanation / Answer
a) F = 9 200t ? 11 500t^2
Impulse for a time dt = F*dt = 9 200t dt ? 11 500t^2dt
Total impulse = integral( F*dt) = 4600t^2 - 11 500t^3/3+ C
Applying the limts 0 to 0.8
integral(F*dt) = 981.33 Ns
b) v =sqrt(2gh) =sqrt(2*9.8*0.69) =3.6775 m/s
c) Considering the downward direction as positive
mv - mu = - 981.33 Ns
mv - 64.8*3.6775= - 981.33
v = (- 981.33+64.8*3.6775) / 64.8
v = -11.466 m/s
d) h = v^2/ (2g) = 11.466^2/19.6 = 6.708 m/s
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