Point objects

We talked about gravitational potential energy earlier, for moving objects around in a uniform gravitational field. Now, we'll be more general.

There is a gravitation potential energy associated with a pair of interacting objects. For two objects, with charges of m and M$,$ separated by a distance r$,$ the potential energy is given by:

$$U$=$GmMrU$=$rGmM$$

G is the universal gravitational constant: G $=6\mathrm{.}67$ x $10-11$ N m$2/$kg$2$

Note that the potential energy is negative $-$ this is associated with the attractive nature of gravity. Also, unlike an object with mass in a uniform field, you are not free to define your own zero for potential energy in the case of two point objects. The potential energy is zero when the distance between the objects is infinite $($this makes sense, seeing as the two objects are really no longer interacting with one another when the distance between them becomes infinite$).$

Don't worry too much about the negative sign. It is important but what is most important is the change in potential energy. Also, even though this may not be obvious to you, this more general form of the potential energy equation is consistent with the mgh form, in the sense that they give the same change in energy when h is small.

What happens if there are more than two objects interacting via the force of gravity? To find the total potential energy of such a system, simply add up the potential energies from each interacting pair.

$$It is also good to remember that when two objects have a gravitational interaction, each one feels a gravitational force but there is just one potential energy. Neither object owns the potential energy by itself $-$ the energy is associated with the interaction between the objects.$$

$$

How many pairs

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Imagine a system consisting of four objects that each have mass, so they are all interacting via the force of gravity. How many pairs of interacting objects are there in this system?

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a

$2$

b

$4$

c

$5$

d

$6$

Your answer

e

$8$

f

$12$

Explanation

Here are the six pairs: $1-2,1-3,1-4,2-3,2-4,3-4$

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Explanation

Explanation

Calculate the potential energy

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You have four identical objects, each with a mass M$.$

You arrange the objects so that there is one object at each corner of a square. Each side of the square measures a distance L$.$ What is the total gravitational potential energy of this set of objects?

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a

b

c

d

zero

e

None of the above

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