Help! with Core-1.1 (1 Viewer)

[テリー]

Define gravitational potential energy as the work done to move an object from a very large distance away to a point in a gravitational field [Ep= G m1m2/r]

Can some1 pls explan it to me, thx!!

 

[Lucid Scintilla]

The expression for the grav. pot. energy of an object of mass m at a distance r from the centre of, say, a planet is given by the equation you have there:
E_p = -G(M₁M₂/r)

Now, what does this all mean? Well, E_p is the potential energy; G is the grav. constant; M₁ is the mass of the object; M₂ is the mass of the planet (or whatever); and r, of course, is the distance.

I hope this explains it all to you. If there's anything else, just ask.

Edit: Uh... okay... hehe, I sorta stuffed up. No problem, and sorry... Japanese characters... テリー.
I sorta didn't explain it, did I?

 

[alcalder]

Define gravitational potential energy as the work done to move an object from a very large distance away to a point in a gravitational field
[E_p= -G m₁m₂/r]
don't forget the negative sign

Gravitational Potential Energy is the potential a body has to do work on its own in a gravitational field. But to increase the GPE YOU must do work in order to do this (conservation and conversion of energy from KE to GPE) eg lift a ball up off the ground, you have added some GPE and when you release the ball it will fall back to the earth.

We can define GPE at any point as 0. In our exercises where GPE=mgh, we are effectively defining the Earth's surface as GPE=0.

However, when we talk more generally about GPE around a planet they like to define GPE=0 at a distance so far from the planet that a body is unaffected by the planet's graviational field. Essentially, this is where the GPE is a maximum (but 0). As we move closer to the planet, then, the GPE must reduce down to the value that it attains on the Earth's surface (because you really can't go lower than that without a drill). Hence the need for a negative sign in the equation.

E_p= -G m₁m₂/r

So, when you move a body in a gravitational field;

• if you move a body towards the planet you are doing negative work (ie the body does its own work)
• if you move a body away from the planet you do positive work.

So let's take something from so far away that the GPE is 0. If we move it closer to the planet we do negative work in the order of:

E_p= -G m₁m₂/r

How do we get this equation, I hear you ask?

The force on a mass m₂ distance r from a planet is defined by Newton to be:

F= G m₁m₂/r²

Where:
m₁ = mass of one body (eg planet)
m₂ = mass of other body (eg satellite)
r = distance between the centres of these masses
G = gravitational constant

At the surface of the Earth (ie where r = radius of Earth, r_o) Newton says:
F=mg_o

Where: g_o = 9.8 m/s²
So,
mg_o = G m₁m₂/r²
g_o = G m₂/r²

The Force on a body distance r from the planet is
F= G m₁m₂/r²

The work done to get it there (ie from the centre of the Earth)

W = Fr = G m₁m₂/r

BUT NOW the GPE = -W = - G m₁m₂/r
There is a more complicated explanation involving the integration of the W= Fs equation with respect to r, but I will not include that. It is a little confusing.

 

[テリー]

i copied that outa the syllabus!!!

n thx alcalder & Lucid