# Net Force of Equal and Opposite Gravitational Forces Don't Equal Zero? [duplicate]

I've come across this question, and I'm at at a loss.

Two masses, m and M, are in an isolated system. The gravitational forces, F (by M on m) and F (by m on M), are equal and opposite. Why do they not add to a zero net force? Explain your answer.

I approached the question by simply adding vectors. In the question F(1) and F(2) are defined as equal and opposite. Mathematically that is F(1) = -F(2). Hence, is stands to reason that F(1) + F(2) = 0.

If it's an isolated system there there should be no other forces present. Also, even if the forces are moving towards each other, then they could be at a constant velocity (zero acceleration).

Is this flawed reasoning, or is there another explanation?

• The gravity does accelerate them toward each other. Jan 27, 2020 at 11:35
• Does this answer your question? How to intuitively understand Newton's third Law? Jan 27, 2020 at 13:21
• This question is way too vague to properly answer IMO. When they say "why don't they add to a net zero force", what perspective are they talking about? In terms of the entire isolated system, the net force is zero... so I find the wording on this extremely poor.
– JMac
Jan 27, 2020 at 14:04
• Possible duplicate of With Newton's third law, why are things capable of moving? Jan 27, 2020 at 15:17

See this depends what are you considering as your system.

If you consider each ball separately as your system then there is a net force acting on the object.

But if you consider both balls together as your system then for sure no net force acts on the system.

I think you might be confused by the fact that both balls come towards one another and therefore the system might be accelerating. But I assure you that this is not the case. We define a quantity called centre of mass which is measure of the net translational effect of external force on the system and this fact that no net force acts on the system can be verified from the fact that the centre of mass does not accelerate even a bit.

The answer to the following question provides a mathematical treatment to the center of mass:

"Two masses, m and M, are in an isolated system. The gravitational forces, F (by M on m) and F (by m on M), are equal and opposite. Why do they not add to a zero net force? Explain your answer."

You are making the common mistake of thinking Newton's third means the forces "cancel" and that nothing will happen to each of the objects involved. Although the net force on the system as a whole is zero, the net force on each mass individually is not.

Since in this case the only force acting on each mass is the force applied by the other, you can assume the net force on each mass is F. To find the effect of that force F on each mass you need to apply Newton's second law to each mass individually. Then the magnitude of the acceleration of each towards the other will be

$$a_{m}=\frac{F}{m}$$ $$a_{M}=\frac{F}{M}$$

If the masses are the same, their accelerations will be the same. Otherwise, they will be different.

Hope this helps.

You must only add up forces that act on the same object (or system or particle etc.).

The two forces mentioned act on different objects, so the net force on either of them, is non-zero (since only one force in acting on each).

Your depicted question is about Newton third law, now problem is you need to define system before arriving at any conclusion , I mean if you consider the two ball together as system then both forces termed as internal and they cancel out each other, but if you separately consider the balls then force on the each ball is not zero, because

According to Newton's Law, we always consider forces on the body - not by the body - to calculate its acceleration

So to make the net force on the body zero we should have the situation like this! $$F_1- F_2 =ma$$ in this situation two forces cancel out each other. (where both $$F_1$$ and $$F_2$$ are equal in magnitude and are on the body m).