A 53 kg student eats a 200 Calorie doughnut.
To “burn it off”, he decides to climb the
steps of a tall building. (1 food Calorie = 103
Calories.)
How high would he have to climb to expend
an equivalent amount of work? The accelera-
tion of gravity is 9.8 m/s2 .
Answer in units of m.
i have no attempt. i have no idea what to do. and there are many where that came from
To solve this problem, we need to calculate the work done in climbing the stairs. We can then equate this work to the energy contained in the doughnut.
First, we need to convert the energy content of the doughnut from Calories to Joules. Since 1 food Calorie equals 103 Calories, the energy content of the doughnut is:
200 Calories * 103 Calories = 20600 Calories
To convert the energy from Calories to Joules, we can use the conversion factor 1 calorie = 4.184 Joules. Therefore, the energy content of the doughnut is:
20600 Calories * 4.184 Joules/calorie = 86174.4 Joules
Now, we can calculate the work done in climbing the stairs. The work done against gravity is equal to the change in potential energy:
work = mass * gravity * height
Given that the mass of the student is 53 kg and the acceleration due to gravity is 9.8 m/s^2, we can substitute these values into the equation:
work = 53 kg * 9.8 m/s^2 * height
We can set the work done in climbing the stairs equal to the energy content of the doughnut:
work = 86174.4 Joules
53 kg * 9.8 m/s^2 * height = 86174.4 Joules
Simplifying the equation gives us:
height = 86174.4 Joules / (53 kg * 9.8 m/s^2)
height = 161.43 meters
Therefore, the student would have to climb approximately 161.43 meters to burn off the energy equivalent of the doughnut.