Question

A student evaluates a weight loss program by calculating the number of times he would need to climb a 16.0 m high flight of steps in order to lose one pound (0.45 kg) of fat. Metabolizing 1.00 kg of fat can release 3.77 ✕ 10⁷ J of chemical energy and the body can convert about 18.8% of this into mechanical energy (the rest goes into internal energy.)

HINT

(a)

How much mechanical energy (in J) can the body produce from 0.450 kg of fat?

J

(b)

How many trips up the flight of steps are required for the 94.0 kg student to lose 0.450 kg of fat? Ignore the relatively small amount of energy required to return down the stairs.

trips

Answer 1

Mechanical energy needed to climb 16m by a man of 94kg

= mgh

= 94 x 9.8 x 16

= 14739.2 J

(A)

1 Kg of fat releases 3.77 x 10⁷ J of energy

.45 kg of fat releases 1.6965 x 10⁷ J of energy

18.8% is converted into mechanical energy.

so, 18.8% of 1.6965 x 10⁷ J

= 3189.42x 10³ J , of mechanical energy will be available for mechanical work.

(B)

one trip of climbing of 16m requires 14739.2J of mechanical energy.

Now number of such trip possible with given mechanical energy .

n= 3189.42x10³ / 14739.2

= 216 trips