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HW9-soln

HW9-soln - 6.P.49 Human energy consumption(a We will...

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6.P.49 Human energy consumption (a) We will estimate the amount of energy required to lift the upper part of the body in a situp. Let’s esti- mate that the upper part of the body (torso, head, and arms) has about half of the total mass M of the body, with . The center of this mass is raised about h = 0.3 m (about one foot). Take the Universe as the system of interest: 100 situps is roughly equivalent to this number of candy bars: Actually, the body is nowhere near 100% efficient, so it would take more chemical energy than this to replace the energy used. (b) All of the blood must be lifted once every 20 seconds. When lying down, the lift height is about the body thickness, or about 0.2 m, say. When standing up, the lift height is about the person’s height, or about 1.8 m. The increased lift height is about 1.6 m. The increase in the power is very roughly this: Increase in power = A major simplifying assumption here is that the power required to force the blood through the blood vessels is probably not very different whether you’re lying down or standing up, so that we can roughly estimate the increased power by considering only the change in how much additional lifting of the blood there is against gravity. Also, we assume that blood has a density similar to water, 1 gram per cubic centimeter. M 70 kg Δ E Universe 0 = ΔΣ mc 2 Σ KU g E chem ++ + () 0 = Δ E chem Δ U g Mgh == Δ E chem 1 2 -- 70kg 9.8 N/kg 0.3 m 100 joules ≈≈ = 100 100 joules of situps × 280 4.2 3 × 10 × joules/candy bar -------------------------------------------------------------------------------- 0.01 candy bar 70 kg 60 cm 3 kg ----------------- ⎝⎠ ⎛⎞ 1 3 × 10 kg cm 3 ------------------------ 9.8 N/kg 1.6 m 20 s --------------------------------------------------------------------------------------------------------------------------------- 3 watts

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6.P.45 Hot water Take the water plus the aluminum pan as the system of interest: By Q
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HW9-soln - 6.P.49 Human energy consumption(a We will...

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