Finding jumping height on an unknown planet given Mass/Radius

In summary: So, if you jump on the Earth, you would jump with the same energy on the Moon or the new planet.In summary, the gravitational potential energy on the Earth's surface can be calculated using the equation U=mgh, where m is the mass of the object, g is the gravitational acceleration, and h is the height. On the unknown planet, with a mass of 4.19*10^21kg and a radius of 1*10^6m, the gravitational acceleration can be calculated using the equation g=GM/R^2. This gives a value of 0.28m/s^2. Applying the conservation of energy principle, the height that a person can jump on the unknown planet can be calculated using the
  • #1
rkiecaboose
4
0

Homework Statement


Knowing you can jump about 1m high on Earth's surface, how high can you jump on the unknown planet.
Munknown= 4.19*10^21kg
Radius Unknown= 1*10^6m

Homework Equations


Not sure if can be used in this question
K1+U1 = K2 + U2
1/2MV2 + mgh = 1/2MV2 + mgh
U=-GM/r and U = mgh
g=GM/R2

The Attempt at a Solution


[/B]
I found the force of gravity on the unknown planet using GM/R2
Giving me 0.28m/s2
Can I just equate the two equations for Gravitional Potential energy (U) to find the new height? as in -GM/r = mgh?
 
Last edited:
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  • #2
rkiecaboose said:
Can I just equate the two equations for Gravitional Potential energy (U) to find the new height?

If you were to do that, you are saying that the initial energy on each planet is the same.
Is it?
 
  • #3
rkiecaboose said:

Homework Statement


Knowing you can jump about 1m high on Earth's surface, how high can you jump on the unknown planet.
Munknown= 4.19*10^21kg
Radius Unknown= 1*10^6m

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How do the mass & radius of Planet X compare to those of Earth?

Do you know Newton's law of universal gravitation ?

Added in Edit:

I see that you did add some information after I quoted the OP.
 
  • #4
Sorry I posted the question initially while I went and grabbed my work.
Newtons universal law of gravitation...
F=GM1M2/R2
Though I don't know where I would use it.
Am I on the right track using conservation of energy but instead of using mgh use -GM/r ?
 
  • #5
Villyer said:
If you were to do that, you are saying that the initial energy on each planet is the same.
Is it?

Well if we're considering the initial point to be grounded wouldn't the initial just be 0 on both planets? I'm lost as to how to relate Earth to the unknown
 
  • #6
rkiecaboose said:
Well if we're considering the initial point to be grounded wouldn't the initial just be 0 on both planets? I'm lost as to how to relate Earth to the unknown

Were does the energy that makes a person jump come from?

Does this source maintain its full potential when transferred to a planet with different gravity?
 
  • #7
I think the energy stored in one's muscle must be the same everywhere.
 
  • #8
So...can someone tell me if this is correct?
Since I know the gravitational potential energy (U) is mgh on earth. It gives me 490J assuming a mass of 50kg. I used the same equation U=mgh, solving for h gives: U/mg=h.
Since the gravitational acceleration is GM/R2 the acceleration on the new planet is 0.28m/s2. I just plugged it into give me a jump height of 35m.
 
  • #9
You can check about Apollo astronauts jumping on the surface of the moon.
Conservation of energy applies everywhere.
 

What is the formula for finding jumping height on an unknown planet given mass and radius?

The formula is h = (2GM/R)^(1/2) - R, where h is the jumping height, G is the gravitational constant, M is the mass of the planet, and R is the radius of the planet.

What unit of measurement should be used for mass and radius?

Mass can be measured in kilograms (kg) and radius can be measured in meters (m).

How does the mass and radius of a planet affect jumping height?

The larger the mass and radius of a planet, the stronger the gravitational pull, resulting in a lower jumping height. Similarly, a smaller mass and radius will result in a higher jumping height.

Can this formula be used for any planet in the universe?

Yes, as long as the planet's mass and radius are known, this formula can be used to calculate the jumping height on that planet.

Are there any limitations to using this formula?

This formula assumes that the planet has a uniform mass distribution and does not take into account other factors such as air resistance. It is also only accurate for small jumping heights compared to the planet's radius. For larger jumping heights, a more complex formula is needed.

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