# Energy differences when climbing a flight of stairs

Hey
If I were to climb a flight of stairs I would gain potential energy because I would be moving further away from the centre of the earth. However would I have more, less or equal amounts of kinetic energy at the top of the flight of stairs, or at the base and why would this be so? If what I had previously stated is also incorrect, could an explanation be provided on what the correct thesis is and why.

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#### andrevdh

Homework Helper
Hey
If I were to climb a flight of stairs I would gain potential energy because I would be moving further away from the centre of the earth.
Correct. You raised your potential energy by doing work, that is your legs pushed you up the flight of stairs. This energy can be recovered if you were to slide down the stairs on a tray (or whatever else will do without getting you into too much trouble). The work that you did pushing yourself up the stairs were "stored" in the system formed by your body and the earth.

Kinetic energy is not stored. It can be increased or decreased depending on the application of an external force. If the force works in the direction of the motion of the object it will increase its kinetic energy (it will move quicker) and vice versa.

Now coming back to climbing the stairs you need to do additional work, that is your legs need to push extra hard, if you want to go quickly up the stairs - you need to raise your potential energy and increase your kinetic energy.

If you are not in such a hurry your legs only need to push moderately hard in order to raise only your potential energy.

So it is completely up to you by how much your kinetic energy will differ at the top and the bottom of the stairs - it all depends on how eager you are to get up there.

#### Andrew Mason

Homework Helper
Hey
If I were to climb a flight of stairs I would gain potential energy because I would be moving further away from the centre of the earth. However would I have more, less or equal amounts of kinetic energy at the top of the flight of stairs, or at the base and why would this be so? If what I had previously stated is also incorrect, could an explanation be provided on what the correct thesis is and why.
Your angular momentum increases when you move farther from the earth's centre. So your kinetic energy would increase by:

$$\frac{1}{2}m\omega^2\Delta r = \frac{1}{2}m\omega^2h$$

AM

thanks for the reply Andrew Mason and andrevdh

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