A student evaluates a weight loss program by calculating the number of times he would need to climb a $13\mathrm{.}0$ m high flight of steps in order to lose one pound $(0\mathrm{.}45$ kg$)$ of fat. Metabolizing $1\mathrm{.}00$ kg of fat can release $3\mathrm{.}77107$ J of chemical energy and the body can convert about $21\mathrm{.}4\%$ of this into mechanical energy $($the rest goes into internal energy.$)$

HINT

$($a$)$

How much mechanical energy $($in J$)$ can the body produce from $0\mathrm{.}450$ kg of fat?

J

$($b$)$

How many trips up the flight of steps are required for the $54\mathrm{.}0$ kg student to lose $0\mathrm{.}450$ kg of fat? Ignore the relatively small amount of energy required to return down the stairs.

trips