# Is force an accelerating mass?

• TT0
In summary, the equation F = ma represents the net force acting on an object, which is the sum of all forces acting on the object. For an object traveling at a constant velocity, the sum of forces must be zero. This applies to both static and dynamic forces, with the exception of friction which can act as a dynamic force. Inertia and friction are examples of dynamical forces, while the sum of forces acting on an object can also be described as the equation of motion. However, the terminology surrounding these concepts is not unified and can vary, leading to confusion.
TT0
From the equation F = ma, is force an accelerating mass?

So if an object is traveling at constant speed it doesn't have a force attacking on it?

How about a car traveling at constant speed? A force will need to be applied to it otherwise the friction would stop it right? But it wouldn't accelerate.

TT0 said:
So if an object is traveling at constant speed it doesn't have a force attacking on it?

F in F = ma is the net force acting on an object, i.e., the sum of all forces. It is more accurate to say that if an object is traveling at constant velocity then the (vector) sum of the forces acting (not attacking) on it is zero.

TT0 said:
How about a car traveling at constant speed? A force will need to be applied to it otherwise the friction would stop it right? But it wouldn't accelerate.

If there is friction acting on the car, there needs to be a force in the opposite direction and with the same magnitude for the force sum to be zero - and thus for the car to travel at constant velocity. An object with constant speed may have net forces acting on it since speed does not specify the direction.

TT0
frish said:

Not a good source. Just an example:

frish said:
His third law, usually stated as "action equals reaction," means this:
"The sum of all forces (static and dynamic) acting on a body is zero"

This is a popular misconception of the third law.

TT0
DrStupid said:
Not a good source. Just an example:
This is a popular misconception of the third law.
Yes , I agree with you. Normally many people make this mistake.
The forces are of same magnitude and of opposite direction but they act on DIFFERENT BODIES!

TT0
TT0 said:
From the equation F = ma, is force an accelerating mass?

So if an object is traveling at constant speed it doesn't have a force attacking on it?

How about a car traveling at constant speed? A force will need to be applied to it otherwise the friction would stop it right? But it wouldn't accelerate.
That is for the net/total force on an object.
A force is usually described by a field, which gives a value to every point in space or spacetime. Based on the force, a different type of field is required. When using F=ma, you are probably thinking about vector fields, which are represented by a vector/line segment (most fields that include velocity/acceleration are vector fields, because velocity and acceleration are vectors themselves).

If some mentor corrects me, believe them- I'm not an expert!

Orodruin and TT0
You would have to read the whole essay to understand the third law.

The 'two different bodies' is a popular misconception, found even in some textbooks.

Consider Moon. One force is gravity, other is inertia. Both act on the Moon.

Put their sum to zero and you get the equation of motion. That is what Newton discovered.

PF

TT0
frish said:
The 'two different bodies' is a popular misconception, found even in some textbooks.

This "misconception" found even in Newton's original publication:

"Lex III: Actioni contrariam semper et æqualem esse reactionem: sive corporum duorum actiones in se mutuo semper esse æquales et in partes contrarias dirigi."

That means

"Law III: To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts."

and leaves no scope of interpretation. Force and counter-force always act on different bodies.

TT0
You can think about forces as some unknown physical conditions by which two or more systems interacts each other. Because all systems are equivalent (there is no classes of systems acts forces and systems accept forces) we assume that physical conditions acts by pairs action-reaction forces.
We define work by forces, so these pairs must be opposite so the total interaction be zero. We define energy by work to use like a common coin to calculate systems interactions. All these thinks works together in one whole frame.

TT0
OK thanks everyone for the explanations!

frish said:
Consider Moon. One force is gravity, other is inertia. Both act on the Moon.

Put their sum to zero and you get the equation of motion. That is what Newton discovered.
This is not the standard physics nomenclature. In standard texts, inertia is not a force, it is the resistance to acceleration which appears in Newton's second law. It does not deal directly with the third law, as quoted by DrStupid.

frish said:
Consider Moon. One force is gravity, other is inertia. Both act on the Moon. Put their sum to zero and you get the equation of motion. That is what Newton discovered.
That isn't Newtons 3rd Law. That's a transformation into a non-inertial frame, where the Moon is not accelerating, because an inertial force cancels Earth's gravity. Newtons 3rd Law doesn't apply to such inertial forces.

frish said:
Consider Moon. One force is gravity, other is inertia. Both act on the Moon.

Put their sum to zero and you get the equation of motion. That is what Newton discovered.

No. The only force acting on the Moon is the gravitational force exerted on it by the Earth. (Assuming we're considering the Earth-Moon system in isolation, without taking the Sun into account.) Therefore a net force acts on the moon, which causes it to accelerate: namely, the centripetal acceleration (v2/r) of its circular orbit around the Earth.

[QUOTE="Orodruin, post: 5129121 inertia is not a force,

Type into Google 'force of inertia' and you get
what then are they talking about?

Whe Earth attracts Moon, there is a force 1) of Earth to Moon and 2)Moon attracts Earth.
Those are two forces acting on two bodies, action and reaction.
In addition, each mass has an equation of motion - which says 'sum of all forces' (dynamical and static) is zero.

Inertia and friction are dynamical forces ; static forces depen on position only.
Terminology is not unified, but it is confusing (as some bad textbooks say) to say that F-m*a
is DEFINITION of force. It is definition of inertial force only. There are other forces, e.g. spring
or gravity ...
Newton generalized the condition of equilibrium by including dynamical forces. That's how he was
able to derive the elipse.

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frish said:
what then are they talking about?
Typically, they will be talking of a fictitious force resulting from a transformation to an accelerating reference frame. The ma in Newton's second law is not a force in normal physics terminology, it is equal to the net force acting on a system. In the case of the moon, the force acting on it is gravity and the result is an acceleration of the moon since the net force is not zero.

frish said:
Whe Earth attracts Moon, there is a force 1) of Earth to Moon and 2)Moon attracts Earth.
Those are two forces acting on two bodies, action and reaction.
Yes, that is Newtons 3rd Law.

frish said:
In addition, each mass has an equation of motion - which says 'sum of all forces' (dynamical and static) is zero.
No, in the inertial frame the sum of all forces is not zero on each mass, because each mass undergoes non-zero acceleration.

frish said:
it is confusing (as some bad textbooks say) to say that F-m*a
is DEFINITION of force.
There two similar definitions:

Fnet = m * a is the sum of all forces on an object with mass m and acceleration a.

Finertial = - m * a is an inertial force that appears in frames of reference accelerating at a and applies to all objects according to their mass m

Also, engineers sometimes use "quasi static analysis" in inertial frames, where you analyze multiple accelerating bodies at one time point, by bringing the m*a to the side of forces and calling it "inertial force", to have zero on the other side of the equation.

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Can someone explain the third law? If a ball is traveling through the air.
Action = ball's force on the air molecules
Reaction force = air molecule's force on the ball
Since every action has an equal opposite reaction then won't the forces cancel out?
I know there is something wrong with my understanding, but I have searched on the internet and the main explanation people give is that "they apply on different bodies". Isn't the forces applying on different bodies? Thanks

TT0 said:
Since every action has an equal opposite reaction then won't the forces cancel out?

No, one of the forces is accelerating the ball and the other is accelerating the air molecules. The net force on the ball is therefore not zero.

TT0
But won't the ball hit the air molecules with an equal amount of force as it has applied to it?

Yes, but that is not accelerating the ball, that force is acting on the air molecules and accelerating them. There is a force from the air molecules on the ball, which accelerate the ball, and an equal and opposite force from the ball on the air molecules, accelerating the air molecules.

TT0
TT0 said:
Isn't the forces applying on different bodies?
Yes, that's the explanation why they don't cancel out in terms of acceleration.

TT0
frish said:
Newton generalized the condition of equilibrium by including dynamical forces. That's how he was
able to derive the elipse.

Can you provide a proper reference?

Thanks guys

text Ohanian (not currently on me to state page and edition) physics demonstrates how magnetic forces are not always equal and opposite using the cross-product.

kind of relevant to what some were saying about the third law.

## 1. What is the relationship between force and acceleration?

According to Newton's second law of motion, force is directly proportional to acceleration and inversely proportional to mass. This means that as force increases, acceleration also increases, but as mass increases, acceleration decreases.

## 2. How does force affect an object's acceleration?

Force causes an object to accelerate by imparting a change in its velocity. This can either be an increase or decrease in speed or a change in direction.

## 3. Is force necessary for an object to accelerate?

Yes, force is necessary for an object to accelerate. Without any force acting on an object, it will either remain at rest or continue moving at a constant velocity.

## 4. Can an object's acceleration be greater than its force?

No, an object's acceleration cannot be greater than its force. As mentioned before, the two are directly proportional, so if the force increases, the acceleration will also increase. However, the acceleration can be less than the force if the mass of the object is high.

## 5. How does mass affect an object's acceleration?

Mass has an inverse relationship with acceleration, meaning that as mass increases, acceleration decreases. This is because a larger mass requires more force to accelerate compared to a smaller mass.

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