Sara, who weighs 66 kg, is on a guilt trip after eating a 788-Calorie (788 kcal) breakfast of pancakes loaded with fruits, cream, and syrup. She decides to work out before going to her weekly weight-watchers' meeting. If the height of a single stair is 12 cm, and her body is only 25% efficient in converting chemical energy to mechanical energy, determine the number of stairs Sara must climb to cancel out the Calories consumed.

Sara must climb 10609 stairs to burn this food.

Explanation:

Chemical energy content in Sara's body = 788 kCal x 4.184 = 3296.99 kJ = 3296990 J

her body is only 25% effective in converting chemical to mechanical energy, therefore,

available mechanical energy = 25% of 3296990 = 0.25 x 3296990 = 824247.5 J - -this is equivalent to the work she must do to burn this stored energy

flight of stairs = 12 cm = 0.12 m

Sara's mass m = 66 kg

Sara's weight = mg = mass x acceleration due to gravity 9.81 m/s^2

weight W = 66 x 9.81 = 647.46 N

work done = force x distance climbed d

putting in the necessary values, we have

824247.5 = 647.46 x d

d = 1273.05 m

the number of stairs Sara must climb is equal to the distance climbed divided by the height of a single stairs

number of stairs = 1273.05/0.12 = 10608.75 ≅ 10609 stairs