Why do point particles never collide according to Young and Freedman?

[hasan_researc]

Homework Statement

Young and Freedman: pg 700, Paragraph 1, line 2

Point particle never collide. I don't understand why that is so?

Homework Equations

The Attempt at a Solution

Actually, I thought of one point particle being placed at the origin of a Cartesian coordinate system, and the other particle moving in the positive x-direction towards the first particle. If that's the case, then the two particles will eventually meet. If two particle meet, then by definition that's a collision. So point particles collide. But Young and Freedman have said that they don't. Surely, the authors can't be wrong!

So, how do I solve the problem, then?

 

[rock.freak667]

A point particle (ideal particle[1] or point-like particle, often spelled pointlike particle) is an idealized object heavily used in physics. Its defining feature is that it lacks spatial extension: being zero-dimensional, it does not take up space. A point particle is an appropriate representation of any object whose size, shape, and structure is irrelevant in a given context

That is why they never truly collide in a real sense.

 

[hasan_researc]

But that avoids answering the problem I posed about the cartesian system where the two particles collide!

Let's think of the point particle as a geometric entity. I can't visualise a geometric entity as not taking up any space. Surely, an entity, even if it is infinitesimally small, should take up some space?

 

[Phrak]

I think I can state this in a more precise manner than your text, unless you've left a great deal out.

The probability of a collision in a finite collection of idealized point particles having random trajectories, in a finite volume and over finite time, is vanishingly small.

 

[gabbagabbahey]

I have a different edition of Young and Freedman than you, so page 700 just has some problems on E&M...what section is the quote you referred to in (eg. 22-9)?

 

[hasan_researc]

I think I can state this in a more precise manner than your text, unless you've left a great deal out.

The probability of a collision in a finite collection of idealized point particles having random trajectories, in a finite volume and over finite time, is vanishingly small.

But that depends on the volume of the container, right? If the volume is comparable to the size of the point particles, then the probability is very large, right?

And that brings me to the question of the size of a point particle. Wikipedia states that a point particle has no spatial extension. That means that the probability of collisions should be zero, not vanishingly small. (Right??)

I have a different edition of Young and Freedman than you, so page 700 just has some problems on E&M...what section is the quote you referred to in (eg. 22-9)?

yOUNG AND FREEDMAN 10TH EDITION. Chapter name: Thermal Properties of matter. Section name: Kinetic molecular model of ideal gas. See below heading "Collisions between molecules".