2. Running up the stairs (5 pts). Time how long it takes for you (or a…

2. Running up the stairs (5 pts). Time how long
it takes for you (or a friend) to run as fast as possible up a
staircase. Measure the height of one step and count the steps to
find how high you climbed.
a) How much mechanical energy did you produce to climb the
stairs?
b) What was the average mechanical power produced during your
climb?
c) Estimate the muscle mass in your upper legs (quadriceps,
hamstrings, and buttocks). (Recall that biological tissue has about
the same density as water.) If each kilogram of muscle can produce
about 100 watts of mechanical power, are these muscles sufficient
to provide the power required for you to run up the stairs?
d) If you are 25% efficient at converting food energy to
mechanical energy, and there are about 4200 joules in one food
Calorie, how many Calories did you consume during your climb?
e) The food energy that was not converted into
mechanical energy was mainly turned into heat. If your body were
completely insulated (for instance, if you were wearing heavy
winter clothes), how much would your body temperature increase as a
result of running up the stairs? Assume that your entire body has a
specific heat equal to that of water, C = 4.18 J/g·°C.