Sunlight on a roof Suppose that a house has a flat (not peaked) but slanted roof

Question

Sunlight on a roof

Suppose that a house has a flat (not peaked) but slanted roof in the shape of a rectangle withdimensions 10. m by 24 m.
(a) The angle of the roof is such that at noon in midsummer, the sunlight hits the roof at normalincidence, i.e. face-on. Estimate the total power of the sunlight falling on the roof. (To do that,you’ll have to look up the intensity of sunlight – state what value you use and where you got itfrom.)
(b) Calculate the radiation pressure (with appropriate units) and the total force on the roof fromthe sunlight, assuming that half of the light is absorbed and half is reflected.
(c) Later in the day, the Sun is lower in the sky (but assume it is equally bright) and the sunlighthits the roof not at normal incidence, but 35º away from normal incidence. What is the totalpower of the sunlight falling on the roof at this time? (Hint: This is like a flux calculation.)

Explanation / Answer

a) Power is

P = IA = (1360)(10x24) = 3.264x10^5 W

b) Radiation presssure is

P = I /C = 1360 / (3x 10^8) = 4.53x10^-6 N/m^2

c) P ' = P cos 35

  P ' = (3.264x10^5 ) cos 35 = 2.674x10^5 W

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