I have a physics question that I can't figure out. Thanks to everyone who can answer!!!
A record was set for stair climbing when a man ran up the 1600 steps of the Empire State Building in 10 minutes and 59 seconds. If the height gain of each step was .20 m, and the man's mass was 70 kg, what was his average power output during the climb? Give your answer in both watts and horsepower.
Thanks to everybody who can help me!!!
2006-09-25 10:13:54 · 6 answers · asked by serendipitousgirl 3 in Science & Mathematics ➔ Physics
power is energy or work divided by time. in this case, the man is gaining potential energy as he is increasing his height. this additional energy comes from the power he is exerting in climbing the stairs. (he is also expending power to move laterally, but the problem wants you to ignore that because it is much harder to calculate.) so if we take his total energy and divide it by the total time of his climb, we will find his average power output.
We will start in metric units (watts): the total height is 1600 steps * 0.20 m/step = 320 m
The formula for gravitational potential energy is E=mgh. His mass is 70 kg and gravity is 9.8 m/s^2. So we get
E = 70 kg * 9.8 m/s^2 * 320 m = 219,520 Joules.
The time is 10 min 59 s = 659 s so his average power is
P = 219,520 J / 659 s = 333 W
To find the answer in horsepower, simply divide by 746 (1 hp = 746 W). P = 0.45 hp.
2006-09-25 10:28:58 · answer #1 · answered by aryeh_cls 2 · 2⤊ 0⤋
What he did was change his potential energy.
The formula for potential energy is U=mgh
m is his mass of 70kg
g is the gravitational constant 9.8m/s^2
h is the height which would be 1600x.2m or 320 m
Multiply these together to get 219,520 kg m^2/s^2 which is joules
Multiply 219,520 by 0.0002778 for 610 Watts Hours(not Watts per Hour)
Since he took 10 minutes and 59 seconds to climb, that is 659/3600 of an hour, so multiply by 659 and divide by 3600 hours
This equals 111 watts for the entire trip used.
Horsepower is 746 W per horsepower so 111/746 is about 0.1488HP
2006-09-25 18:12:59 · answer #2 · answered by Dennis K 4 · 0⤊ 1⤋
(70*10*1600*.2)/(10*60+59) considering deceleration due to gravity as 10m/s^2. to get in hp divide by 746. if you know your definitions well you will have no problem in solving the problem.
2006-09-26 11:20:35 · answer #3 · answered by Anonymous · 0⤊ 0⤋
P = W/t
P = (F*d) / t
P = (m*g*d) / t
P = (70*9.80*1600*.20)/(659)
P = 333 watts = 0.45 hp
2006-09-25 17:24:47 · answer #4 · answered by عبد الله (ドラゴン) 5 · 1⤊ 1⤋
Hold on...I need a drink first!
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2006-09-25 17:21:17 · answer #5 · answered by Uncle Arthur 3 · 0⤊ 1⤋
I'm sorry
2006-09-25 17:16:30 · answer #6 · answered by koolguy 2 · 0⤊ 1⤋