How Do You Calculate Potential Energy on Each Step of Stairs?

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SUMMARY

The discussion focuses on calculating gravitational potential energy (PE) for a person ascending a staircase with a total height of 1.10 meters using the formula PE = mgh. The mass is specified as 50 kg, and the acceleration due to gravity is given as 9.81 m/s². Participants clarify that the height of each individual step is 0.22 meters, leading to a potential energy calculation of approximately 103.005 joules for each step. The final answer requires calculating PE for all five steps, resulting in a total of 539.55 joules for the entire ascent.

PREREQUISITES
  • Understanding of gravitational potential energy (PE) formula: PE = mgh
  • Basic knowledge of units in the MKS (meters, kilograms, seconds) system
  • Familiarity with the concept of height and mass in physics
  • Ability to perform unit conversions and calculations
NEXT STEPS
  • Research the concept of gravitational potential energy on Wikipedia
  • Learn about unit conversions in the MKS system
  • Practice calculating potential energy for different masses and heights
  • Explore how potential energy relates to kinetic energy in physics
USEFUL FOR

High school students studying physics, educators teaching potential energy concepts, and anyone needing to understand energy calculations in mechanics.

WMM
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Homework Statement


Using the diagram of the set of stairs below calculate your potential energy as you stand on each step. The total rise of the stairs is 1.10 meters.
Please use 50kg for your mass. Hint: The total rise is 1.10 meters so you need to find the rise of each individual stair, from top of that stair to the floor.

http://bransonschoolonline.blackboard.com/@@/95FF19D3DD07724BF160723B05C8FB1A/courses/1/10-11PhysicalScience1/content/_285561_1/embedded/Homework%201.gif




The attempt at a solution
I don't know where to begin...

Thanks for any help!
I'm new here hope I posted everything right...
 
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WMM said:

Homework Statement


Using the diagram of the set of stairs below calculate your potential energy as you stand on each step. The total rise of the stairs is 1.10 meters.
Please use 50kg for your mass. Hint: The total rise is 1.10 meters so you need to find the rise of each individual stair, from top of that stair to the floor.

http://bransonschoolonline.blackboard.com/@@/95FF19D3DD07724BF160723B05C8FB1A/courses/1/10-11PhysicalScience1/content/_285561_1/embedded/Homework%201.gif




The attempt at a solution
I don't know where to begin...

Thanks for any help!
I'm new here hope I posted everything right...

Welcome to the PF.

What is the equation that relates the gravitational potential energy "PE" to the mass and height of a raised object? The acceleration of gravity comes in there someplace as well...
 
berkeman said:
Welcome to the PF.

What is the equation that relates the gravitational potential energy "PE" to the mass and height of a raised object? The acceleration of gravity comes in there someplace as well...
I honestly have no idea... I'm still in high school so not like I'm in college...
 
WMM said:
I honestly have no idea... I'm still in high school so not like I'm in college...

Well, if you were given this problem, then you have also been given the applicable equation. It should be right there in that section of the textbook, before that problem is given to you.

Alternately, go to www.wikipedia.org, and search on gravitational potential energy. That should also show you the forumula to use. Post your work with that formula, and we can check your work.
 
U = mgh
Would that be the equation I use?
There are several equations...
0.9090909090909091
If you divide 1 by 1.10 meters you get what's above.
But I don't get what to do with the mass and the 3 1/2 inches...
 
WMM said:
U = mgh
Would that be the equation I use?
There are several equations...
0.9090909090909091
If you divide 1 by 1.10 meters you get what's above.
But I don't get what to do with the mass and the 3 1/2 inches...

Good! Yes, that is the equation.

There are 5 steps in 1.1m, so each step is 1.1m/5. That is the rise for each step, which is the h in the equation above. The mass is the m, and g is the acceleration of gravity which is a constant. Your answer should have units of energy. Do you know what they should be?

And your 0.909 answer isn't correct. How did you get that? Can you show how you filled out the quanties in the PE = mgh equation? Include units with each quantity, and stay in a consistent system of units, like the mks (meters kilograms seconds) system.

BTW, the only thing you need for this question is the mass and how high it's going for each step. The "run" and other numbers do not come into play here...
 
I'm pretty sure each step is about 0.1818 meters or 7.15818 inches.
50kg x gravity x 7.15818 inches
What's the gravity?
 
WMM said:
I'm pretty sure each step is about 0.1818 meters or 7.15818 inches.
50kg x gravity x 7.15818 inches
What's the gravity?

You are mixing units. Stay in units of meters, kilograms and seconds.

The acceleration of gravity is the constant "g" at the surface of the Earth. Does your textbook list it? If not, back to wikipedia (part-way down this page)...

http://en.wikipedia.org/wiki/Acceleration_of_gravity

.
 
g = 9.81 m/s2 = 32.2 ft/s2
So now how would I go about this equation with that?
Of course with meters now to.
 
  • #10
WMM said:
g = 9.81 m/s2 = 32.2 ft/s2
So now how would I go about this equation with that?
Of course with meters now to.

You plug in your numbers into the equation:

PE = mgh

being careful to keep each number in mks units. Mass is in units of kg, g is in units of m/s^2, and height is in units of meters. The final units are the multiplication of each quantity's units. And if you look up the units of energy, you will find there is a shorthand name for units of kg * m/s^2 * m = kg * m^2 / s^2...
 
  • #11
88.29
So now what unit would I measure that in?
 
  • #12
WMM said:
88.29
So now what unit would I measure that in?

I already indicated what the primitive units are for the multiplication. You need to actually read your book or wikipedia to figure out what the units of potential energy are in the mks system of units.

Oh, and I get a different answer than you. That's why we ask here that you show your work. Write out what you multiplied, including units, and what the final answer is including units.
 
  • #13
My schooling is online I don't have a textbook so keep that in mind.
I honestly have no idea what the measurement would be.
I did:
50 x 9.81 x 0.1818
Am I doing this wrong lol?
 
  • #14
WMM said:
My schooling is online I don't have a textbook so keep that in mind.
I honestly have no idea what the measurement would be.
I did:
50 x 9.81 x 0.1818
Am I doing this wrong lol?

How did you get 0.1818? There are 5 steps to make up the total of 1.1m ...

And you should include units in all of your calculations, like:

PE = 50kg * 9.81m/s^2 * (a corrected delta-height)m = ___ kg * m^2 / s^2

and then the final answer with the compacted units for energy. Hint -- the units of energy are named after a guy whose last name starts with J...
 
  • #15
Also, remember that the problem wants the PE for each step listed...
 
  • #16
50 kg x 9.81m/s^2 x 1.10 meters = 539.55 megajoules
Correct :D ?
 
  • #17
WMM said:
50 kg x 9.81m/s^2 x 1.10 meters = 539.55 megajoules
Correct :D ?

Except for the mega part :smile:

1 kg * m^2 / s^2 = 1 J (1 Joule)

Remember that's for all 5 steps, and they ask for the PE at each step. So you need 5 numbers for your answer (excluding the starting level, where we are taking the PE = 0J to start off).
 
  • #18
berkeman said:
Except for the mega part :smile:

1 kg * m^2 / s^2 = 1 J (1 Joule)

Remember that's for all 5 steps, and they ask for the PE at each step. So you need 5 numbers for your answer (excluding the starting level, where we are taking the PE = 0J to start off).
Now wouldn't I just divide 539.55 Joules by 5?
 
  • #19
WMM said:
Now wouldn't I just divide 539.55 Joules by 5?

You have calculated the PE for the last (highest) step #5. What is it for step #1, #2, #3, and #4?
 
  • #20
It doesn't say any where in the problem that each stairs are different heights. I'm pretty sure that each step is the same height.
If they aren't then how would I go about solving each different step when I'm only given the total height.
The only possible way would be to divide the total height by 5 and and then repeating the problem with the results from dividing by 5. Or couldn't you just divide my total 538.55 Joules by 5 and get the same answer?
 
  • #21
WMM said:
It doesn't say any where in the problem that each stairs are different heights. I'm pretty sure that each step is the same height.
If they aren't then how would I go about solving each different step when I'm only given the total height.
The only possible way would be to divide the total height by 5 and and then repeating the problem with the results from dividing by 5. Or couldn't you just divide my total 538.55 Joules by 5 and get the same answer?

The problem statement implies that the "unit rise" is the same from step-to-step. So you will calculate the 5 values of the PE as the mass (person) rises higher and higher with each uniform step.
 
  • #22
So now I need to.
1.10 meters divided by 5 (steps) = 0.22 meters
50 kg x 9.81m/s^2 x 0.22 m = 103.005 joules
Is that correct?
That would be for each step?
 
  • #23
WMM said:
So now I need to.
1.10 meters divided by 5 (steps) = 0.22 meters
50 kg x 9.81m/s^2 x 0.22 m = 103.005 joules
Is that correct?
That would be for each step?

Looks right. Make a small 5-entry table, and you're done.
 

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