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)
height, h=135*16 cm = 21.6 m
Time taken, t= 5 min 40 sec
= 340 seconds
mass, m= 63.9 kg
g=9.81 m/s²
(note that all values are in SI units)
Work done, W = mgh J (joules)
= 13540.2 J
(multiply together m,g & h to get work done)
Power = work done per second, so
= W/t J/s
=13540.2 J/340s
=39.82 J/s (or watts)
Each Cal = 4.1868 kJ
= 4.1868*1000 J
= 4186.8 J (joules)
Number of food calories
= W/4186.8 Cal.
= 3.234 Cal.
To find the work done by the person, we can use the formula:
Work = force × distance
First, let's calculate the force exerted by the person while climbing the stairs. The force exerted is equal to the person's weight, which is given by:
Force = mass × gravity
where gravity is approximately 9.8 m/s².
Force = 63.9 kg × 9.8 m/s²
Force = 626.22 N
Next, we need to find the distance covered by the person. Since there are 135 steps and each step is 16.0 cm tall, the total distance climbed is:
Distance = 135 steps × 16.0 cm
Distance = 2160 cm or 21.6 meters
Now, we can calculate the work done:
Work = Force × Distance
Work = 626.22 N × 21.6 m
Work = 13500.10 Joules or 13.5 kJ (to 3 significant figures)
The work done by the person is 13.5 kilojoules (kJ).
To find the average power performed by the person during the walk, we can use the formula:
Power = work / time
The time taken is given as 5 minutes and 40 seconds, which is equal to 340 seconds.
Power = 13.5 kJ / 340 s
Power = 0.0397 kW or 39.7 watts (to 3 significant figures)
The average power performed by the person during the walk is 39.7 watts.
To calculate the number of food calories burned during the walk, we need to convert the work done to food calories. Given that 1 Calorie is equal to 4.1868 kJ, we have:
Calories = Work / 4.1868 kJ
Calories = 13.5 kJ / 4.1868 kJ
Calories = 3.23 food Calories (to 3 significant figures)
The person burned approximately 3.23 food Calories during the walk.
To calculate the work done by the person, we need to find the gravitational potential energy gained. The formula for gravitational potential energy is given by:
Potential energy = mass * gravity * height
First, let's convert the height of each step from centimeters to meters:
Step height = 16.0 cm = 0.16 m
Next, we need to find the total height climbed by multiplying the height of each step by the number of steps:
Total height climbed = 135 steps * 0.16 m/step
Now, let's calculate the work done by the person:
Work = mass * gravity * total height climbed
The value of gravity is approximately 9.8 m/s^2.
Next, let's calculate the average power performed by the person. Power is defined as work done divided by the time taken:
Power = Work / time
Now, for the calculation of the number of food Calories burned, we need to convert the work done (in joules) to kilojoules, and then to Calories:
Energy (in Calories) = Energy (in joules) / Conversion factor
The conversion factor is given as 1 Cal = 4.1868 kJ.
Let's perform the calculations:
Total height climbed = 135 steps * 0.16 m/step = 21.6 m
Work = 63.9 kg * 9.8 m/s^2 * 21.6 m
Average Power = Work / (5 minutes and 40 seconds) = Work / 340 seconds
Energy in joules = Work
Energy in calories = Energy in joules / 4.1868 kJ/Cal
By performing these calculations, you will find the answers to the questions.
Please note: The actual number of Calories burned during physical activity can vary depending on several factors such as individual metabolic rate, intensity of exercise, and efficiency of movement. The given calculation is an estimate based on the information provided.