Calculate height given KE and mass

In summary, the nitrogen molecule at sea level with an average translational KE of 6.2x10^-21 J and a mass of 4.7x10^-26 kg, when shot straight up without striking other air molecules, will rise to a height of 13460.7m, as determined by the equation y=U/mg where U represents the initial KE, m represents the mass of the molecule, and g represents the constant acceleration due to gravity. This is based on the fact that in this scenario, the entire KE is converted into potential energy, as described by the formula KE + PE = constant.
  • #1
Sandman327
6
0

Homework Statement


At sea level a nitrogen molecule in the air has an average translational KE of 6.2x10-21 J. Its mass is 4.7x10-26 kg. If the molecule could shoot straight up without striking other air molecules, how high would it rise? Thanks for any help.

Homework Equations



I think to find height I should use the equation U=mgy but I'm not 100% sure because I don't understand how KE relates to U.

The Attempt at a Solution



I set the equation up so that y=U/mg and I get the answer 13460.7m which just seems to big to be right although I could be wrong about that.
 
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  • #2
Draw a diagram of the initial and final states of the nitrogen molecule.
What's the energy in the initial state, and what's the energy in the final state? How do these two relate?

Your final answer is most likely correct (Number crunching errors aside), and I'm glad you see the importance of understanding how you got to it.
 
Last edited:
  • #3
Welcome to PF!

Hi Sandman327! Welcome to PF! :smile:
Sandman327 said:
… I don't understand how KE relates to U.

It's very simple:

always remember this formula … KE + PE = constant :wink:
 
  • #4
since it doesn't loose any energy by striking the other molecules, the entire KE will be converted into PE by raising to the height 13460.7m...
 

FAQ: Calculate height given KE and mass

How do you calculate height given kinetic energy and mass?

To calculate height given kinetic energy and mass, you can use the formula h = KE / (m * g), where h is the height, KE is the kinetic energy, m is the mass, and g is the acceleration due to gravity (9.8 m/s^2).

What is the unit of measurement for height in this calculation?

The unit of measurement for height in this calculation is meters (m).

Does this calculation take into account air resistance?

No, this calculation does not take into account air resistance. It assumes that the object is in a vacuum and there is no air resistance acting on it.

Can this calculation be used for any object regardless of its shape or size?

Yes, this calculation can be used for any object regardless of its shape or size as long as the mass and kinetic energy are known.

How accurate is this calculation?

This calculation is accurate as long as the initial kinetic energy and mass are measured accurately. However, it does not take into account external factors such as air resistance and can only provide an estimate of the height.

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