Forces, vectors and straight lines

[Studiot]

Where is it writ that forces must act in straight lines?

 

[I like Serena]

Where is it writ that forces must act in straight lines?

It's an observation of nature.
Newton was the first to put it into words.

Actually there's no real reason why an apple would fall straight down from a tree.
It's just that it works best to explain what we see around us.

 

[Studiot]

I am aware that we count tangents as straight, but what of ring forces?

 

[Pythagorean]

Magnitude and direction. Direction is a straight line.

Circular forces act in a straight line at any given moment in time (tangential) but that direction changes as a function of time. It's not pushing in all directions at once or it wouldn't go anywhere.

 

[Studiot]

Circular forces act in a straight line at any given moment in time (tangential) but that direction changes as a function of time. It's not pushing in all directions at once or it wouldn't go anywhere.

That's my point.
Ring forces act in every direction at once.

 

[Pythagorean]

I've never heard of a ring force, I guess. What is it?

 

[Studiot]

A 2D example would be the force within a journal containing a heated metal shaft.
A 3D example would be the membrane force in a balloon under pressure.

 

[Pythagorean]

Each force term acts orthogonal to the membrane surface in a single direction. They're not all one force.

 

[Studiot]

They're not all one force.

Why not, there is a continuous force all the way round the circle?

Would you also suggest that a circle is not one line, but an assembly of straight lines?

 

[Pythagorean]

Why not, there is a continuous force all the way round the circle?

Would you also suggest that a circle is not one line, but an assembly of straight lines?

No; in differentation, a circle is an assembly of infinitesimal points.

Yes, continuous, so at each infinitesimal chunk of surface area:
$$P = \vec{A} \cdot \vec{F}$$

the surface area vector (the "normal") and the force acting on that that surface have a single direction associated with them.

 

[Studiot]

1)

No; in differentation, a circle is an assembly of infinitesimal points.

By that reasoning so is a straight (or any other) line.

2)I'm sorry what surface?

 

[cjl]

1)



By that reasoning so is a straight (or any other) line.

Very true.

2)I'm sorry what surface?

I assume the surface of the balloon that you used as a 3d example.

 

[Studiot]

I assume the surface of the balloon that you used as a 3d example.

The discussion had moved on to circles by then.

Whilst I'm sure we can regard circles and other lines, for some purposes, as just an assemblage of points I maintain that they have a existence all of their own.

Lines, including straight lines and circles, have zero thickness, zero cross sectional area and zero surface area.

All that has been offered here is to say that we can assign vectors to each point along a curve or across an area.

But for this to be possible, both the curve and area must have an existence separate from and the assigned vectors.

No answer has been offered to the question as to why a force cannot follow such a curve.

 

[Pythagorean]

I was referring to the balloon for surface area.

In classical physics, spacetime is "smooth"