Question

A person trying to lose weight(dieter) lifts a 10 kg mass 0.5 m, 1000 times. Assume that the potential energy lost each time she lowers the mass is dissipated. (a) How much work does she do against the gravitational force? (b) Fat supplies 3.8 x 10⁷ J of energy per kilogram which is converted to mechanical energy with a 20% efficiency rate. How much fat will the dieter use up?

Answer 1

Here m = 10 kg, h = 0.5 m, n = 1000

(a) Work done against the gravitational force,

W = n mgh

= 1000 x (10 x 9.8 x 0.5) = 49000 J

(b) Mechanical energy supplied by 1 kg of fat

= 3 x 10⁷ J x 20/100

= 0.76 x 10⁷ J/kg

Fat used up by the dieter = {1}/{0.76 x 10⁷} x 49000

= 6.45 x 10^-3 kg