A 57.0-kg woman takes 4.270 seconds to run to the top of the spectator stands at her local high school track. The top of the stands are 4.90 m above the level of the track from which she starts. Ignore air resistance during the climb. The runner starts and ends her climb at rest .As a preliminary exercise, make a free-body diagram for the runner during her climb. For the purpose of this diagram, simplify the situation by replacing the spectator stands with a ramp. Notice that only the height of the stands was given, because only the altitude change is needed for the energy calculation; but for these preliminary questions concerning forces, assume a ramp of length 9.80 m (measured along the ramp). Human locomotion is complex, but we would like to treat the runner as a particle; so draw the runner with one foot on the ramp directly under the runner's center of mass (the other foot will be off the ground at this instant). Since the runner starts and ends at rest, she must first speed up and then slow down, but draw the free-body diagram for an instant when she has a constant velocity up the ramp.

a.) What is the change in mechanical energy for the runner-Earth system as a result of her climb?

b.) What has been the average power output of the runner during the climb?

Assume the runner's efficiency as an engine is 15.5 percentpercent . If you are not familiar with the concept of efficiency, please see the note at the top of the introduction to this problem.

c.) How much stored food energy will the runner have converted into mechanical energy and thermal energy during the climb? And how many food calories (1.0 food calorie = 1.0 Calorie = 1.0 chemist's kcal = 4186.0 J will the runner have consumed during the climb?

d.) Assuming the runner burned only carbohydrate during her climb, how many grams of "carbs" will she have burned? Each grams of carbohydrate provide about 4.3 calories of energy.

e.) At what average rate will the runner need to have dissipated thermal energy during the climb if she is not to be warmer at the end of her climb than at the climb?