Susan, whose mass is 68 kg, climbs 59 m to the top of the Cape hatters lighthous
ID: 1589635 • Letter: S
Question
Susan, whose mass is 68 kg, climbs 59 m to the top of the Cape hatters lighthouse. During the climb, by how much does her potential energy increase? For a typical efficiency of 25%, what metabolic energy does she require to complete the climb? If Susan takes 1hr to climb to the top, what is her metabolic power? When exercising, the body must perspire and use other mechanisms to cool itself to avoid potentially dangerous increases on body temperature. If we assume that Susan doesn't perspire or otherwise cool herself and that all of the "lost" energy goes into increasing her body temperature, by how much would her body temperature increase during this climb? What happens to the thermal energy lost by Susan? Explain. If Susan is losing heat at a rate of 300W, does she feel hot, chilly or neither?Explanation / Answer
(i)
Increase in Potential Energy = m*g*h
Increase in Potential Energy = 68 * 9.8 * 59 J
Increase in Potential Energy = 39317.6 J
(ii)
Metabolic Energy Needed = x
25 % of x = 39317.6 J
x = 39317.6 * 100/25 J
x = 157270.4 J
Metabolic Energy Needed, x = 157270.4 J
(iii)
time = 1hr = 3600 s
Power = Work/time
Power = 157270.4/3600 W
Metabolic Power = 43.68 Watt
(iv)
75% of the energy used is wasted and goes to thermal energy so,
Eth = 0.75 * 157270.4 J
Eth = 117952.8 J
Rise in Body temp is given by, T = Eth/(mc)
T = (117952.8 J)/(68 Kg * 3400 J/Kg k )
T = 0.51 k
T = 0.51 c
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