In the Biomedical and Physical Sciences building at MSU there are 135 steps from the ground floor to the sixth floor. Each step is 16.0 cm tall. It takes 5 minutes and 40 seconds for a person with a mass of 63.9 kg to walk all the way up. How much work did the person do? What was the average power performed by the person during the walk?How many food Calories did the person burn during the walk? (1 Cal = 4.1868 kJ)
work = m g h
= 63.9 * 9.81 * 0.16 * 135 Joules
power = work/time
here time = 5*60+40 seconds
Kjoules = Joules work/1000
food calories = KJoules *(1 Cal/4.1868 Kj)
To find the work done by the person, we need to calculate the gravitational potential energy gained in walking up the stairs. The work done (W) is given by the formula:
W = mgh
Where:
m = mass of the person (63.9 kg)
g = acceleration due to gravity (approx. 9.8 m/s^2)
h = height climbed (135 steps * 16.0 cm/step = 2160 cm = 21.6 m)
Substituting the values into the formula:
W = 63.9 kg * 9.8 m/s^2 * 21.6 m = 13,711.52 Joules (J)
Therefore, the person did approximately 13,711.52 Joules of work.
To find the average power performed by the person during the walk, we can use the formula:
Power = Work / Time
The time taken to walk up is given as 5 minutes and 40 seconds, which can be converted to seconds as:
Time = 5 minutes * 60 seconds/minute + 40 seconds = 340 seconds
Using the formula:
Power = 13,711.52 J / 340 s = 40.31 Watts (W)
Therefore, the average power performed by the person during the walk is approximately 40.31 Watts.
To calculate the number of food Calories burned, we need to convert the work done into kilojoules (kJ) and then divide by the conversion factor from kilojoules to Calories.
Work in kJ = 13,711.52 J / 1000 = 13.71 kJ
Finally, using the conversion factor:
Calories burned = 13.71 kJ / 4.1868 kJ/Cal = 3.28 Calories
Therefore, the person burned approximately 3.28 Calories during the walk.