Question

The density of air at sea level is 1.3 kg /m. Assume that the average density of a human body is 1,050 kg/m. Approximate the average human body as a cylinde of length 5 feet 7 inches and a cross sectional circumference of 27 inches. (a) Approximate the volume of an average human body. Vhody Number Units (b) Estimate air's buoyant force on an average body. Number Units (c) What is the apparent weight and true weight of an average body in vacuum(g 9.81 m/s Wbodly Number Units Wappurnt Number Units

Answer 1

First of all convert the units inches and feet into meters for simplicity of the solution.

Length of the cylinder, L = 5 feet 7 inches = 5 x 0.3040 + 7 x 0.0254 = 1.524 + 0.1778 = 1.7018 m

Circumference of the cylinder = 2pi*r = 27 inch = 27 x 0.0254 m = 0.6858 m

=> Radius of the cylinder = r = 0.6858 / (2pi) = 0.11 m

(a) Average volume of the human body, V = volume of cyliner = pi*r^2*L = 3.141*0.11^2*1.7018 = 0.0647 m^3

(b) Air buoyant force on human body = V * density of air * g = 0.0647*1.3*9.81 = 0.825 N

(c) True weight of human body = Wbody = V*(density of human body) = 0.0647 * 1050 = 67.94 kg

Apparent weight of human body = True weight - buoyant weight = 67.94 - 0.0647*1.3

= 67.86 kg