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.

Question

02-07-2020
Physics

contestada

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.

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Round 1,129.872 To The Nearest Tenth

tochjosh tochjosh · Answer 1 · 2020-07-03T03:22:01+02:00

Answer:

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