A new record for running the stairs of the Empire State Building was set on February 3, 2003. The 86 flights, with a total of 1576 steps, was run in 9 minutes and 33 seconds. Consider a scenario where a man ran up 1600 steps of the Empire State Building in 10 minutes and 59 seconds. If the height gain of each step was 0.20 m, and the man's mass was 61.0 kg, what was his average power output during the climb? Give your answer in both watts and horsepower.
Help if you can please.
2007-10-18 04:49:11 · 3 answers · asked by Imagine 1 in Science & Mathematics ➔ Physics
Work done = potential energy gained
W=Fs=mgh
W=mgh=61.0x 9.81 x 1600 x 0.2=19149120 joules
Power=Energy/time
P=W/t=19149120/(10x60 + 59)=29058 Watts
since 1HP=745.7 Watts
P(in hp)=39 hp
2007-10-18 05:04:30 · answer #1 · answered by Edward 7 · 1⤊ 0⤋
P = W/T W=F*S F=M*A 1Hp = 745.7 watts
given: M=61kg A=9.8m/s^2(he's under constant acceleration of gravity) S= 1600*0.2m(# of steps * height gain gives vertical displacement) T=659s
W= (61kg*9.8m/s^2)*(1600*0.2) = 191040 N*m
T=659s
P = 191040N*m/659s = 289.894watts
289.894watts*1hp/745.7watts = .38875 Hp
2007-10-18 05:19:39 · answer #2 · answered by DBL-G 3 · 0⤊ 0⤋
1600*.20m = 320m
total work done was
PE gained = mgh = 9.8 m/s * 61 kg * 320 m
Average Power = Energy/ time = mgh/659 s
Will give you an answer in watts.
Use google to convert to horse power
2007-10-18 05:05:29 · answer #3 · answered by Blank 2 · 0⤊ 0⤋