Question

3. ∗ The food calorie (also known as nutritional calorie and large calorie) is a quantity equal to a kilocalorie (kcal). Not surprisingly, the food calorie is used to represent units of energy associated with eating, as in "An average hot dog with ketchup and a bun contains 315 calories." You woke up hungry this morning so you ate a breakfast of hotcakes, eggs, and a large biscuit. An online application indicates that this meal contains 1090 calories (meaning food calories). (a) How many flights of stairs in a typical office building would you have to climb to burn off the calories you consumed? Make a reasonable assumption about the height of a flight of stairs, and state any other assumptions you make. (b) The required height of the climb would almost certainly be different from the number calculated in Part (a), even if your assumption about the height of a flight of stairs is correct. Explain why you think it would be more or fewer stairs.

Answer 1

Part a: There will be 30976 stairs of height 7.25 inches each to be climbed if 180 lbm person wants to consume 1090 calories.

Part b: As the average mass of the person is also assumed, thus the height will also be dependent on mass of the person in addition to the stair height.

Step-by-step explanation:

Part a:

The amount of energy consumed = 1090 food calories = 1090 X 10^3 Calories = 1090 X 10^3 X 4.184 Joules= 4560.56 X 10^3 Joules

Mass of person = 180 lbm = 0.4536 X 180 Kg = 81.647 Kg

Gravitational Force on the person with given weight = Mass X acceleration due to gravity = 81.647 X 9.8 m/s^2 = 800.14 N

The work done in climbing height "h" = 800.14 X h Joules

So height that can be climbed to burn the calories = The energy intake in Joules / force = 4560.56 X 10^3 Joules / 800.14

Height = 5699.70 meters

the height of each stair = 7.25 inches = 7.25 X 0.0254 meters = 0.184 meters

So number of stairs = 5699.70 / 0.184 = 30976 stairs

Part b:

The mass of person = 210 lbm = 95.25 Kg

Gravitational force on person = 95.25 x 9.8 = 933.25 Newton

Energy to be burned = 4560.56 X 103 Joules

Height that can be climbed = Energy / Force = 4560.56 X 103 Joules / 933.25 Newton = 4886.75 Meters

Height of each each flight = number of stairs X height of each stair = 12 X 7.25 inches = 2.2098 meters

So number of flight = 4886.75/ 2.2098 = 2211.39

Height would also be different as the mass of the person is varied as indicated in the above calculation.

Answer 2

a. If the height of a flight of stairs is assumed to be 9 inch rise, the average calories burned per step is 0.17 calories, Total calories to be burned= 1090 cal, 1 step burns 0.17 cal Therefore total stairs to be climber = 1090/0.17 = 6411 stairs b. The required height of the climb would be different because burning calorie by climbing stairs depends on other factors also like: Weight( more heavy you are the more weight u loose), age, angle of stairs, the speed of climbing stairs, general state and age.