# Potential energy and forces

1. Oct 27, 2014

### alba

If two bodies A (m = 1kg) and B (M = 2kg) are at height h from the earth, when they fall and reach the ground A will have KE = 1*gh and B = 2*gh, That means double energy.
Is the force FA = m*a that acted on A equal to the force FB = M*a that acted on B since a = 9.8 in both cases? FB should be 2 * FA, according to arithmetic, but is it possible that 2 different forces acted on the bodies?
Thanks for you help

2. Oct 27, 2014

### Staff: Mentor

Yes, the forces are different. The force of gravity is proportional to the mass, so the bigger mass has the bigger force.

3. Oct 27, 2014

### alba

I read hear:http://www.tutorvista.com/content/physics/physics-i/gravitation/force-and-gravitation.php that the force of g on an apple is a reaction according to 3rd law, I cannot under understand:
- isn't 3rd law about conservation of momentum? there is no momentum here
- how can it be a reaction? the apple exerts a force and the earth reacts? the earth doesn't know that the apple is there ( and the same applies to the apple). Each mass exerts a pull independently of what happens around.
- how do you establish which is the action and which the reaction? It seems absurd like the egg and the chicken

Thanks, Dalespam you are ever so kind!

Last edited: Oct 27, 2014
4. Oct 27, 2014

### Staff: Mentor

I think that you are misunderstanding the 3rd law part. The Newtonian gravity acting on some mass $m_1$ due to some other mass $m_2$ follows this force law:
$F=G\frac{m_1 m_2}{r^2} \mathbf{\hat r}$

Where $\mathbf{r}$ is the vector from $m_1$ to $m_2$. Clearly, since $m_1$ and $m_2$ are just labels, you can simply swap them to get the force acting on $m_2$ due to $m_1$. The force is equal and opposite, so they form a valid action reaction pair.

This has nothing to do with the problem in the OP. The problem is about the force acting on mass A from the earth and the force acting on mass B from the earth. We are not interested in either of the forces acting on the earth from mass A or mass B.

Last edited: Oct 27, 2014
5. Oct 27, 2014

### alba

Yes, it does not follow from F = ma, but yet concernes the relation between F and p, could you explain why the action of the earth is a reaction to the apple. Does not each mass in the Universe act independently?

- isn't 3rd law about conservation of momentum? there is no momentum here
- how can it be a reaction? the apple exerts a force and the earth reacts? the earth doesn't know that the apple is there ( and the same applies to the apple). Each mass exerts a pull independently of what happens around.
- how do you establish which is the action and which the reaction? It seems absurd like the egg and the chicken

6. Oct 27, 2014

### Staff: Mentor

I don't understand what you are asking here. Any valid force law in Newtonian mechanics must satisfy both Newton's 2nd and Newton's 3rd law. Newtonian gravity satisfies both.

As long as it starts with 0 momentum and ends with 0 momentum then momentum is conserved. You don't need a non-zero momentum for the 3rd law to apply, just a conserved momentum.

It is an absurd chicken and egg scenario. Together they form an action-reaction pair, but there is no sense in which either is specifically established as "action" and the other as "reaction". The action-reaction language is unnecessary and it forms no part of the actual mathematical formulation of the theory.

7. Oct 27, 2014

### A.T.

Any force represents a transfer of momentum. So the 3rd law just says that in interactions the net change of total momentum is zero, and therefore momentum is conserved.
You don't. These are meaningless lables.

8. Oct 27, 2014

### sophiecentaur

If you want an Action and a Reaction, you have the action of the Earth on the Apple and the Reaction of the Apple on the Earth. It could just as easily be a piece of elastic instead of gravity and the two masses could be more nearly equal. Same principle will apply. Without some force pulling on one end of the elastic, there's no force on the other end to pull the apple.

9. Oct 29, 2014

### alba

I think I understand now, g is not the force of gravity but the acceleration, whereas in electrostatic we refer to the whole force? Is that so? if the bodies in OP were 1 electron or two electrons and the force at the centre of the earth was electrostatic e with the same pull of g we would not say that force is me but e , right? and to get the acceleration we would divide e by m a = e/mA, is that right? I suppose that there is no equivalent to g (e/m)

10. Oct 29, 2014

### sophiecentaur

Interestingly, it is e/m (the charge per unit mass for an electron) that is easiest to measure and, affair, was the first quantity that Particle Physicists were able to measure (way back). It is referred to as the 'specific charge' of an electron. A (standard) mass spectrometer will gather all particles with the same specific charge into the same place because both the Coulomb or Lorenz force and the mass will determine the path of the particles..
But I think you are trying to draw distinctions where there really are none. We measure and use quantities that happen to be most convenient in their particular context. There are mathematical relationships between all those quantities and you can hop between them to suit - but there's no particular magic in which you choose to use. You just have to bear in mind what the names actually represent when you use the quantities.