A 50 kg person accelerates uniformyl from rest to 20m/s running up a flight of s
ID: 1602842 • Letter: A
Question
A 50 kg person accelerates uniformyl from rest to 20m/s running up a flight of stairs in 4.0 s. The stairs have a 37 degree angle with the horizonntal. Assume no air resistance.
a) Find the total work done on the person in this time. What forces does the work to accelerate the person?
b) Find the average power delivered ON the person (by himself and all other forces) over the 5 s. Would you say that your answer is an underestimation or an overestimation of the true poer output of the person? EXPLAIN!
c) Find the average power delivered BY the person (by himself) over the 5s. Now would you say that your answer is an underestimation or an overestimation of the true power output of the person? EXPLAIN!
d) Determine the instantaneous power generated BY the person at 2 sec.
Explanation / Answer
Total work done by all forces = change in KE
W - mgh = 0.5*mv^2
W = 50*9.8*(0.5*20*4)* sin 37 degree + 0.5*50*20^2
= 21795 J
Gravitational forces, force of man does the work to accelerate.
B) average power = KE/time
= 0.5*50*(20*5/4)^2 /5
= 3125 W
underestimation because of Gravitational power
C) power of himself = (50*9.8*(0.5*25*5)* sin 37 degree + 0.5*50*25^2 )/5
= 6811 W
It is true power
D) instantaneous power = Fv
= (50*20/4 + 50*9.8)*20*2/4
= 7400W
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