# Newton's 3rd law and force equilibrium

• greypilgrim
In summary: However, we usually only consider the force on one side because the other side is usually attached to something that will balance it out. In summary, the spring will be compressed until the force exerted by the compressed spring balances out the gravitational attraction between the two mass points.
greypilgrim
Hi.

Assume a rock lying on the ground. Furthermore, let's assume both the rock and Earth to be rigid bodies. I'm a bit confused about force equilibrium and Newton's 3rd law here. There's Earth's gravity acting on the rock, and by Newton's 3rd law (or just by looking at the law of gravity) the rock's gravity acts on earth. But on the other hand, since the rock is at rest, the gravitational force pulling it towards the c.o.m. of Earth needs to be balanced by a normal force of the ground acting on the rock (which is probably due to electrostatic interactions between the two objects).

So what is the reactio to this normal force of the ground on the rock? Isn't it the rock pushing on the ground because of gravity? But then this force would have two opposing forces, first the attraction of the c.o.m. of the Earth and second the normal force of the ground. I guess there's a flaw in my train of thought, but where?

Thanks

Yes. There are two forces on the rock: The gravitational attraction by the Earth + the normal force by the ground. There are reactions to these two, the gravitational attraction by the rock on the Earth + the normal force exerted (downwards) by the rock on the ground. The two gravitational forces are an action-reaction pair, and the two nrmal forces are an action-reaction pair.

greypilgrim said:
Hi.

Assume a rock lying on the ground. Furthermore, let's assume both the rock and Earth to be rigid bodies. I'm a bit confused about force equilibrium and Newton's 3rd law here. There's Earth's gravity acting on the rock, and by Newton's 3rd law (or just by looking at the law of gravity) the rock's gravity acts on earth. But on the other hand, since the rock is at rest, the gravitational force pulling it towards the c.o.m. of Earth needs to be balanced by a normal force of the ground acting on the rock (which is probably due to electrostatic interactions between the two objects).

So what is the reactio to this normal force of the ground on the rock? Isn't it the rock pushing on the ground because of gravity? But then this force would have two opposing forces, first the attraction of the c.o.m. of the Earth and second the normal force of the ground. I guess there's a flaw in my train of thought, but where?

Thanks

It's not clear to me why you're getting confused. Gravity and the normal force are the equal and opposites that Newton's 3rd law demands.

If there were no gravity, then the rock would sit on the Earth without exerting a force and the normal force would be zero.

Note that bodies are not rigid at the molecular level, so gravity will have deformed the rock and the Earth to some degree, which is where the electrostatic repulsion comes from.

Chandra Prayaga said:
The two gravitational forces are an action-reaction pair, and the two nrmal forces are an action-reaction pair.

PeroK said:
Gravity and the normal force are the equal and opposites that Newton's 3rd law demands.

Those two statements seem to contradict each other, don't they?

PeroK said:
It's not clear to me why you're getting confused. Gravity and the normal force are the equal and opposites that Newton's 3rd law demands.

.
No, gravity and normal force are not part of a 3rd law pair.
The fact that gravity on the rock is balanced by the normal force on the rock does not make these two a pair in the sense of 3rd law.
The fact that they act on the same body is a hint. The forces in a 3-rd law pair newer act on the same body.

greypilgrim said:
Those two statements seem to contradict each other, don't they?
nasu said:
No, gravity and normal force are not part of a 3rd law pair.
The fact that gravity on the rock is balanced by the normal force on the rock does not make these two a pair in the sense of 3rd law.
The fact that they act on the same body is a hint. The forces in a 3-rd law pair newer act on the same body.

Very true!

I think I get it now, I forgot the normal force of the rock.

A related question: Assume two mass points separated by a spring of some spring constant. How do I correctly calculate how much the spring is compressed?

Why is the spring compressed?

Because the two mass points attract each other.

You need to know the spring constant. Then you can balance the gravitational attraction with the force exerted by the compressed spring. This gives the equilibrium configuration.

You also need the length of the spring in the relaxed (uncompressed) state.

Yes, suppose those quantities are given. What's unclear to me is if I need to consider the forces from both sides on the spring?

greypilgrim said:
What's unclear to me is if I need to consider the forces from both sides on the spring?
No, the F in the spring formula is the force at one side.

Correct. In fact, there are always two forces, one on each side of the spring, otherwise, the spring itself would run away.

## 1. What is Newton's 3rd law?

Newton's 3rd law states that for every action, there is an equal and opposite reaction. This means that every force has an equal and opposite force acting on a different body.

## 2. How does Newton's 3rd law relate to force equilibrium?

In a system where all forces are balanced, there is no net force acting on the system. This is known as force equilibrium, and it is a direct result of Newton's 3rd law. The equal and opposite forces cancel each other out, resulting in a state of equilibrium.

## 3. Can you provide an example of Newton's 3rd law in action?

One example is when you push against a wall. Your body exerts a force on the wall, but the wall exerts an equal and opposite force on your body, keeping you from moving through the wall.

## 4. Does Newton's 3rd law apply to all forces?

Yes, Newton's 3rd law applies to all types of forces, including contact forces (such as pushing or pulling) and non-contact forces (such as gravitational or electromagnetic forces).

## 5. Can Newton's 3rd law be violated?

No, Newton's 3rd law is a fundamental law of physics that has been proven to hold true in all observed situations. It cannot be violated or disproven.

• Mechanics
Replies
8
Views
520
• Mechanics
Replies
27
Views
417
• Mechanics
Replies
35
Views
3K
• Mechanics
Replies
31
Views
2K
• Mechanics
Replies
22
Views
2K
• Mechanics
Replies
6
Views
2K
• Mechanics
Replies
8
Views
318
• Mechanics
Replies
9
Views
1K
• Mechanics
Replies
10
Views
3K
• Mechanics
Replies
4
Views
798