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Unformatted text preview: Physics 103H/105 Problem Set 4 Solutions Problem 1 (3 pts) (a) A strong human cyclist, weighing about 110 kg (including bicycle), can bicycle up a 3.1 percent grade at about 30 km/h. What is her or his power output in watts? in horsepower? If θ is the angle the slope makes with the flat ground, tan θ = 0 . 031. Thus sin θ ≈ . 031. 1 hp = 746 W. P = mgv sin( θ ) ≈ 280 W ≈ . 37 hp (1) (b) How does this compare to a typical human office worker climbing stairs in an office building at a rate of one floor every 20 s? Let us assume that the mass of a typical human worker m is 65 kg. The height of an office floor is y = 15 feet = 4.5 m. v y = 4 . 5 / 20 = 0 . 225 m/s. P = mgv y ≈ 143 W ≈ . 19 hp (2) (c) How many kilocalories (which are known as “calories” in nutritional information) would you have to eat every day to sustain each of these (relatively high) levels of activity for 3 hours per day? W = P Δ t where Δ t = 3 h = 10800 s . As there are 4184 J per 1 kcal, the work in case (a) is 720 kcal and in case (b) 370 kcal. (d) A person with an active lifestyle eats 3 to 5 thousand kilocalories per day. Do you think that the production of mechanical work is the primary use of food calories? It takes only 600 kcal or so to maintain these levels of daily activity, yet we take in 3000-5000 kcal per day. Most of our energy goes not to mechanical work but to our metabolism (primarily maintaining our high body temperature). If al you did was sit all day, you’d still need about 2000 kcal per day. If your average power input is 2000 kcal/day, your average power output must also be 2000 kcal/day or about 100 W. Thus, if 50 students are in Jadwin 303 on a Wednesday night and it feels hot in the room, it’s because there is the equivalent of a 50 × 100 = 5 kW heater in there!heater in there!...
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