49-kg woman cheats on her diet and eats a 582-Calorie (582 kcal) jelly doughnut for breakfast.
(a) How many joules of energy are the equivalent of one jelly doughnut?
J
(b) How many stairs must the woman climb to perform an amount of mechanical work equivalent to the food energy in one jelly doughnut? Assume the height of a single stair is 15 cm.
stairs
(c) If the human body is only 28% efficient in converting chemical energy to mechanical energy, how many stairs must the woman climb to work off her breakfast?
stairs
4.184 J = 1 calorie
To answer these questions, we need to understand the energy conversions involved.
(a) To determine how many joules of energy are in one jelly doughnut, we need to convert from calories to joules. One calorie is equivalent to approximately 4.184 joules. So, to calculate the energy in joules, we multiply the calorie value of the doughnut by the conversion factor:
Energy (joules) = Calories x Conversion factor
Energy (joules) = 582 Calories x 4.184 joules/Calorie
(b) The mechanical work required to climb a set of stairs can be calculated by multiplying the weight of the woman by the height of the stairs. The weight can be converted from kilograms to newtons using the acceleration due to gravity (approximately 9.8 m/s²).
Work (joules) = Weight (newtons) x Height (meters)
First, we need to convert the weight of the woman from kilograms to newtons:
Weight (newtons) = Mass (kilograms) x Acceleration due to gravity (m/s²)
Weight (newtons) = 49 kg x 9.8 m/s²
Now we can calculate the work in joules:
Work (joules) = Weight (newtons) x Height (meters)
Work (joules) = Weight (newtons) x (Height per stair (meters) x Number of stairs)
(c) To determine the number of stairs the woman must climb, taking into account the human body's efficiency in converting chemical energy to mechanical energy, we need to adjust the work calculation.
Work (joules) = (Work (joules) / Efficiency)
Now we can calculate the number of stairs:
Number of stairs = Work (joules) / (Weight (newtons) x Height per stair (meters))
By plugging in the values and following these steps, we can find the answers to all three questions.