Question
Shoveling snow can be extremely taxing because the arms have such a low efficiency in this activity. Suppose a person shoveling a footpath metabolizes food at the rate of 800 W. (a) What is her useful power output? (b) How long will it take her to lift 3000 kg of snow 1.20 m? (This could be the amount of heavy snow on 20 m of footpath.) (c) How much waste heat transfer in kilojoules will she generate in the process?

a) $24 \textrm{ W}$

b) $24.5 \textrm{ min}$

c) $1.14 \times 10^6 \textrm{ J}$

Solution Video

OpenStax College Physics Solution, Chapter 7, Problem 51 (Problems & Exercises) (2:34) Sign up to view this solution video!

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This is College Physics Answers with Shaun Dychko. In Table 7.2 we can look up the efficiency of shoveling snow and it's three percent which has a decimal as 0.03. So this efficiency equals the power output divided by the power input and we'll solve for P out by multiplying both sides by P in. So we're told that the power input consumed by the person shoveling is 800 watts and multiply that by the efficiency of 0.03 gives us 24 watts is the useful power output of their shoveling. In part B, we're asked to find out how long it'll take this shoveler to lift 3000 kilograms of snow 1.2 meters. So, the power output equals the useful work out divided by time and we can solve this for t by multiplying both sides by t over P out. We're left with the time is the work output divided by the power output. Now the work output imparts the potential energy to the snow and so it's going to be mgh of the snow, mass times gravitational field strength times the height. So we substitute mgh in place of w out and so the time is going to be 3000 kilograms times 9.8 meters per second squared times 1.2 meters divided by 24 watts, which is 1470 seconds. It is easier to think about time in terms of minutes so we multiply by one minute for every 60 seconds which gives 24 and a half minutes. Then, what is the amount of energy wasted as heat is the question in part C. So, that's going to be the difference between the total energy consumed minus the total energy that went into useful work so, w in minus w out in other words. The amount of energy consumed is going to be the power input which we're told is 800 watts multiplied by the length of time that she spends shoveling which is 1470 seconds, and then minus the energy given to the snow. So that's 800 watts times 1470 seconds minus 3000 kilograms times 9.8 times 1.2 meters, which is 1.14 times ten to the six joules of energy wasted. So this gives you an idea of why you can probably take off some of your layers of fleece or something or maybe even take off your jacket depending on how cold it is outside when you're shoveling snow because you're going to get hot.