Question

A 90-kg person steps on a scale in Salem, Oregon where g = 9.806 m/s^2. The scale reads in newtons down to the tenth of a newton.

a) What is the volume of the person, assuming that the person has the same density as water?

b) Describe a free-body diagram for the person including the small buoyant force by the air. Each force must include type, source, receiver, and direction.

c) Determine the magnitudes of each of the forces in your free-body diagram.

d) What is the reading of the scale?

Answer 1

a)

m = mass of person = 90 kg

_p = density of person = density of water = 1000 kg/m³

Volume of person is given as

V_p = m/_p = 90/1000 = 0.09 m³

b)

c)

F_g = mg = 90 x 9.806 = 882.54 N

_a = density of air = 1.23

F_b = _a V_p g = (1.23) (0.09) (9.8) = 1.085 N

normal force is given as

F_n = F_g - F_b = 882.54 - 1.085 = 881.46 N

d)

reading of scale = F_n =  881.46 N