Gravitation (Potential Energy)

In summary: To find the distance from the surface, you need to subtract the radius of the asteroid from the value of r. Therefore, the correct answer is 59315 meters. In summary, to find the distance a particle will go from the surface of an asteroid with a radial speed of 1000 m/s, you need to calculate the mass of the asteroid using the gravitational acceleration near the surface and the radius of the asteroid. Then, using the energy conservation principle, you can find the distance from the surface by subtracting the radius of the asteroid from the value of r. The correct answer is 59315 meters.
  • #1
Oijl
113
0

Homework Statement


How far from the surface will a particle go if it leaves the asteroid's surface with a radial speed of 1000 m/s?

The radius of the asteroid is 565000 m, and the gravitational acceleration near the surface is 2.7 m/s^2


Homework Equations





The Attempt at a Solution


I would have thought I could just see how much energy a particle of mass m has moving at 1000 m/s, and then see what radius r would be necessary to produce the gravitation potential energy of the asteroid-particle system equal to the initial kinetic energy. When I do this, solving for r gives me a very small number.
 
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  • #2
Oijl said:

Homework Statement


How far from the surface will a particle go if it leaves the asteroid's surface with a radial speed of 1000 m/s?

The radius of the asteroid is 565000 m, and the gravitational acceleration near the surface is 2.7 m/s^2

Homework Equations


The Attempt at a Solution


I would have thought I could just see how much energy a particle of mass m has moving at 1000 m/s, and then see what radius r would be necessary to produce the gravitation potential energy of the asteroid-particle system equal to the initial kinetic energy. When I do this, solving for r gives me a very small number.
Note that the gravitation field is only valid near the surface of the asteroid. When you move away from the surface you need to use the full gravitational potential formula,

[tex] U = \frac{GM}{r}[/tex]
 
Last edited:
  • #3
I know; isn't gravitational potential energy described by

U = -(GMm)/r ?

So can't I say that plus (1/2)mv^2 equals zero, and solve for r? When I do that, I get 1158815 meters, but that's not the right answer.
 
  • #4
Hi,
"The radius of the asteroid is 565000 m, and the gravitational acceleration near the surface is 2.7 m/s^2"
With this information You can find the mass of the asteroid.
F=mg , F=GMm/R^2 --> g=GM/R^2 while g=2.7,R=565000.and G=6.67*10^-11 You can find M.

now, the initial energy of the body is the kinetic energy+potential energy, when the potential energy as stated in the post above is U=-GMm/R.
What happens in the highest point?
The body's kinetic energy=0 and he has potential energy equal to -GMm/R+h(max).
by the energy conservation------> Ei=Ef while i=initial and f=final.
note:the little m, aka the mass of particle goes away.
note 2:sometimes i wrote body instead of particle.
Good luck! Tell me if You get the wrong answer
note 3: I've seen Your message and You wrote that Ke+Up=0,seems logical, but I don't think its right...well what is the right answer?
 
  • #5
Oijl said:
I know; isn't gravitational potential energy described by

U = -(GMm)/r ?

So can't I say that plus (1/2)mv^2 equals zero, and solve for r? When I do that, I get 1158815 meters, but that's not the right answer.
The question asks for the distance from the surface, whereas r is the distance from the centre of the asteroid.
 

1. What is gravitation potential energy?

Gravitation potential energy is the potential energy that an object possesses due to its position in a gravitational field. It is the energy that is required to move an object from one position to another against the force of gravity.

2. How is gravitation potential energy calculated?

The formula for calculating gravitation potential energy is E = mgh, where E is the potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the height or distance from the reference point.

3. What is the relationship between gravitation potential energy and height?

The higher an object is positioned in a gravitational field, the greater its gravitation potential energy. As the object moves closer to the reference point, its potential energy decreases.

4. Can gravitation potential energy be converted into other forms of energy?

Yes, gravitation potential energy can be converted into kinetic energy when an object is in motion. This is evident in objects falling from a height, where potential energy is converted into kinetic energy as the object accelerates towards the ground.

5. How does mass affect gravitation potential energy?

The greater the mass of an object, the greater its gravitation potential energy. This is because a heavier object has a greater gravitational force acting upon it and therefore requires more energy to move against this force.

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