Mechanical Energy Staircase Problem

In summary: TME is PEIn summary, the conversation is discussing the mechanics and energy expenditure of climbing stairs. The participants discuss how to estimate the mechanical energy needed for climbing and how it relates to potential energy and work. They also touch on the concept of power and its relation to energy expenditure. They then move on to discussing the conversion of energy to Calories and how it relates to a person's daily diet. The conversation ends with a discussion about the limitations of the human body in converting food energy into mechanical energy and the different bodily processes that use energy.
  • #1
kimberlyphys
3
0

Homework Statement



Problem 1: A standard-sized and typically able college-age human walks
into a building for an appointment on the 10th story. The elevator is broken.
She walks up the 9 stories. Roughly speaking:

(a) How much mechanical energy does she need to expend to climb those
9 stories?

(b) How much time do you think it takes her to climb those stairs? As-
sume she is at least somewhat motivated to get to her appointment. If you
are having trouble estimating this, hire a friend to time themselves climbing stairs. Use that time and the total energy from part (a) to get a power, and express the power in horsepower. Are you surprised? Why is horsepower defi ned as it is?

(c) Now convert the energy you got in part (a) to what dieticians call "Calories", which are really SI kcal units. What fraction of a standard human 2000 kcal diet was this stair climbing exercise? Does this make sense given what you know about programs of "exercise"?

(d) How many flights of stairs could our subject climb in a day if all her body did was convert a 2000 kcal input of food into stair-climbing energy? Why is that not at all a realistic description of the body? On what bodily processes is energy spent in forms other than mechanical forms?

Homework Equations



TME = PE + KE

The Attempt at a Solution



I'm pretty sure I can do all of the calculations in the final parts, I'm just extremely confused as to how to estimate the mechanical energy she needs to climb the staircase.
 
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  • #2
Work equates to energy. How is work defined (mathematically)? If she goes up 9 stories, has she changed her potential energy by doing work?
 
  • #3
Well, I suppose her potential energy has increased, and the work would be the change in the total amount of energy? Thank you.
 
  • #4
You've got it.
 
  • #5
I'm still about confused as to how I would calculate this!
 
  • #6
kimberlyphys said:
I'm still about confused as to how I would calculate this!

Well the work is force x distance right? Each step has a vertical distance associated with it, so each step you are expending energy to increase your potential energy. What specifically are you having trouble grasping?
 
  • #7
at top when at rest i think PE=mgh and KE=0
 

1. What is the Mechanical Energy Staircase Problem?

The Mechanical Energy Staircase Problem is a physics problem that involves calculating the amount of potential and kinetic energy at different points along a staircase. It is used to demonstrate the conversion and conservation of energy in a real-world scenario.

2. How do you solve the Mechanical Energy Staircase Problem?

To solve the Mechanical Energy Staircase Problem, you need to first identify the total mass of the object, the height of the staircase, and the distance traveled along the staircase. Then, you can use the equations for potential and kinetic energy to calculate the energy at each step and compare it to the starting and ending energy values.

3. What are the key concepts involved in the Mechanical Energy Staircase Problem?

The key concepts involved in the Mechanical Energy Staircase Problem are potential energy, kinetic energy, gravitational potential energy, and conservation of energy. These concepts help us understand how energy is converted and conserved in a system, such as an object moving along a staircase.

4. What are some real-life examples of the Mechanical Energy Staircase Problem?

Some real-life examples of the Mechanical Energy Staircase Problem include a person climbing a flight of stairs, a rollercoaster moving up and down hills, and a ball rolling down a ramp. These scenarios all involve the conversion and conservation of energy as objects move along a height or incline.

5. How is the Mechanical Energy Staircase Problem relevant in everyday life?

The Mechanical Energy Staircase Problem is relevant in everyday life because it helps us understand how energy is used and conserved in various situations. It also demonstrates the relationship between potential and kinetic energy, which is important in fields such as engineering, architecture, and sports. Understanding this problem can also help us make more energy-efficient choices in our daily lives.

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