Work, Power and Energy

Question : 22

Total: 30

A person trying to lose weight (dieter) lifts a 10 kg mass, one thousand times, to a height of 0.5 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 gravitationalforce?
(b) Fat supplies 3.8×107J of energy per kilogram which is converted to mechanical energy with a 20% efficiency rate. How much fat will the dieter use up?

Solution:

Here, m = 10 kg, h = 0.5 m, n = 1000
(a) Work done against gravitational force
W=n(mgh) =1000×(10×9.8×0.5)=49000 J
(b) Mechanical energy supplied by 1 kg of fat
=3.8×107×

100

=0.76×107J∕kg
∴ Fat is used up by the dieter =

1‌kg

0.76×107

×49000 =6.45×10−3kg

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