Shoveling snow can be extremely taxing since the arms have such a low efficiency
ID: 1428148 • Letter: S
Question
Shoveling snow can be extremely taxing since the arms have such a low efficiency in this activity. Suppose a person shoveling a sidewalk metabolizes food at the rate of 900 W. (The efficiency of a person shoveling is 3%.) What is her useful power output? How long will it take her to lift 2500 kg of snow 1.20 m? (This could be the amount of heavy snow on 60.0 ft of sidewalk.) What is the relationship between power output, work output and the time needed to do the work? Can you express the power output in terms of the efficiency and the power input? Can you express the work output in term of the change in gravitational potential energy of the snow? s How much waste heat will she generate in the process? Can you find an expression relating the heat generated to the work output? JExplanation / Answer
(a) What is her useful power output?"
900W * 0.03 = 27 W
"(b) How long will it take her to lift 2500 kg of snow 1.20 m? (This could be the amount of heavy snow on 60.0 ft of sidewalk.)"
work = mgh = 2500kg * 9.8m/s² * 1.2m = 29400J
power = work / time
time = work / power = 29400J / 27W = 1088.88 s
"(c) How much waste heat will she generate in the process?"
If 3% of the input was useful, 97% was waste.
97 / 3 = waste / 29400J
waste = 950502J