A person trying to lose weight (dieter ) lifts a 10 kg mass , one thousand times , to a height of0.5 m each time .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 xx10^(7) J of energy per kilogram which is converted to mechanical energy with a 20 % efficiency rate . How much fat will the dieter use up ?

A person trying to lose weight (dieter ) lifts a 10 kg mass , one thou

1.	A person trying to lose weight (dieter ) lifts a 10 kg mass , one thousand times , to a height of0.5 m each time .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 xx10^(7) 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» SOLUTION :(a) Mass of the weight , m = 10 kg Height to which the person lifts the weight , h = 0.05 m Number of times the weight is lifted , n = 1000 ` :. ` Work done against gravitational force , = n (mgh) ` = 1000 xx10 xx 9.8 xx 0.5` ` = 49 xx10^(3) J = 49000 J ` (b) Energy equivalent of 1 kg of fat = `3.8 xx10^(7) J ` Efficiency rate = 20 % Mechanical energy supplied by the person.s body ` 20/100 xx3.8 xx10^(7) J ` ` = 1/5 xx3.8 xx10^(7) J ` Equivalent mass of fat lost by the dieter , ` m = 1/(1/5 xx3.8 xx10^(7)) xx49 xx10^(3)` ` m = 245/(3.8) xx10^(-4) = 0.0064 kg ` = `6.4 ` G