Gravity and Energy -- Two masses above two different planets

In summary, the conversation discusses finding the mass of a ball based on given information about a foreign planet and the conservation of energy and momentum. The speaker is looking for help with finding the mass of the ball and acknowledges that it may not be necessary to know the exact mass, only the ratio between the two objects.
  • #1
jstelpend
1
1
Homework Statement
Hello, I have been stuck on this problem.

A ball with an unknown mass (mA) is initially 11.9 meters above the surface of a foreign planet. A box with an unknown mass (mE) is initially some distance (hE) above the surface of the Earth. The ball and box both have the same GPE relative to the surface of their respective planets.

The foreign planet has a mass of 8.7 x 10^24 kg and its radius is 6.35 x 10^6 meters.

Both the ball and the box are dropped from rest and caught by someone on the surface of the respective planets. The person on the foreign planet and the person on the Earth both apply the same amount of impulse on their respective objects.

Find hE initially. (6.67*10^-11 to be used for G and 9.8 to be used for g of Earth. Also, ignore air resistance)
Relevant Equations
Conservation of energy, gravitational acceleration, Fg = GMm/d^2???, pi = pf
So far, I have found g of the foreign planet, Vf of the ball, and realize that GPEiA = KEfA (Am I right here?). Thus, since GPEiA = GPEiE, GPEiE also equals KEfE. I also understand that, since the same impulse is applied to catch the objects, both objects have the same momentum at the moment that they are caught.

I am stuck on finding the mass of the ball which, I believe, will allow for me to solve the entirety of the question.

I appreciate all help and thank, in advance, those who decide to reach out!
 
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  • #2
jstelpend said:
I am stuck on finding the mass of the ball
Seems to me that you don't need to know the two masses, only their ratio.
 

FAQ: Gravity and Energy -- Two masses above two different planets

How does gravity affect the energy of two masses above two different planets?

Gravity is a force that pulls objects towards each other. The strength of this force depends on the masses of the objects and the distance between them. As the two masses above two different planets are pulled towards each other by gravity, their potential energy increases. This potential energy can then be converted into kinetic energy as the masses move closer to each other.

What is the relationship between mass and gravitational potential energy?

The gravitational potential energy of an object is directly proportional to its mass. This means that the greater the mass of an object, the greater its gravitational potential energy will be. In the case of two masses above two different planets, the larger mass will have a higher gravitational potential energy compared to the smaller mass.

How does the distance between two masses affect their gravitational potential energy?

The gravitational potential energy between two masses is inversely proportional to the distance between them. This means that as the distance between the two masses increases, their gravitational potential energy decreases. In the case of two masses above two different planets, the mass that is further away from the planet will have a lower gravitational potential energy compared to the mass that is closer to the planet.

Can the energy of two masses above two different planets be converted into other forms of energy?

Yes, the potential energy of two masses above two different planets can be converted into other forms of energy, such as kinetic energy. This can happen when the two masses are allowed to move towards each other under the influence of gravity. The potential energy is then converted into kinetic energy as the masses gain speed and move closer to each other.

How does the force of gravity change as the distance between two masses increases?

The force of gravity between two masses decreases as the distance between them increases. This is because the gravitational force is inversely proportional to the square of the distance between the masses. So, as the distance between two masses above two different planets increases, the force of gravity between them decreases.

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