Car brakes and internal forces

[asterroc]

It is worth noting that for all vehicles that travel on wheels (such as cars and bicycles), the sum of rolling resistance and static friction is what causes the vehicle to slow when the brakes are applied. The actual force applied in braking (for example, clamps applied to disk brakes) is internal, and by Newton's First Law cannot cause a change in the vehicle's motion. [Source]

I added that to the (English) Wikipedia page on rolling friction, and it's now been called into question on the Polish version of the page. kadath or anyone else got a good resource I can use to back me up on that here? My explanation is below, but I'd really like an external confirmation on it to fit the way Wikipedia works.

The issue is that you need to take the car as a whole, that is the body of the car, plus the brakes, plus the wheels. This is the body. Newton's Laws say that the sum of the external forces (also called the net force) causes a change in the body's motion (Law #1), and this sum of forces is equal to the mass times the acceleration (law #3, ΣF = ma). When you draw a Free Body Diagram, all you draw are the external forces, not what's going on inside.

Consider Newton's Second Law in this context, that every action has an equal and opposite reaction. In this case, we can think of the two bodies as the brake pads and the disk of the brake itself. Whatever force the brake pads are applying to the disk is equal and opposite of the force the disk is applying on the brake pads. These cancel out, and the center of mass of the two objects will be unaffected. Compare it to the Earth and the Moon - they apply equal and opposite forces of gravity upon each other, and so their center of mass will not accelerate due to those two forces alone. You need an external force to cause a change in motion, and in the case of the car it's friction between the tires and the road (rolling or kinetic, depending upon whether the wheel is rolling or sliding).

Comments

[zandperl.livejournal.com]

Hee. I'm a Wikipedia editor, so ... yeah... :) I've found that the people who actually ask me to explain my reasoning are very nice - they don't always agree with me, but they care enough to want to understand why I said what I did. I've pretty much never gotten into an edit war or anything b/c I don't "camp" pages, and I don't feel a lot of ownership about my own words so if people change it I don't mind too much.

This one's a Physics I question, and one I teach all the time, so to me it's just "duh, that's the way it is, by definition," and yet it's not explicitly stated in textbooks that I can think of. The one thing I do get a little irritated at is when people tag "citation needed" on something that is obvious and by definition, but here I can definitely see where it's not obvious to some people, so finding a source would be nice. I tried googling things like "car brakes rolling friction" and didn't find anything good. It's really the net force = external force part that's in question anyway, not car brakes, though if we could find that specifically referenced it would be good.

[zandperl.livejournal.com]

My physics textbook talks about it a bit in the section on Center of Mass. I think I'll quote that there.

[kadath.livejournal.com]

H'okay, I think the problem is that you have to look at both the wheel as a system and the car as a system to understand the forces at work. My awesome FBD.

Friction with the brake pad stops the wheel. Friction with the ground stops the car. If there were no friction with the ground, the car would just keep sliding despite the wheels not turning (and also wouldn't start moving, but let's pretend friction magically went away halfway.)

I don't know where you'd find a cite for that. It's kind of high school physics.

[zandperl.livejournal.com]

Exactly, friction w/ brake pad stops the wheel relative to the car, not relative to the ground. I found a quote in my alg. phys textbook saying that for a group of point masses or for an extended body, the center of mass requires a net *external* force to change its motion. And I cited that for the person; I'm hoping that's sufficient for him to win the argument on my behalf on the Polish page. If they continue to argue and drag me in, may I point them to that FBD sketch of yours?

[kadath.livejournal.com]

Heh, sure. But ask 'em to stick it up on Wikimedia Commons or something if they plan on linking it.

[dirkcjelli.livejournal.com]

Why not try this simplified thought experiment:

The breaks have sufficient friction to stop the wheels instantly, but the car is on a perfectly polished plane of ice (with a coefficient of friction of zero).

The car continues with its present momentum forever.

[rosefox]

I was going to say "hurtling through space" rather than "on a perfectly polished plane of ice" but the idea is the same: brake all you want, it won't do nothin'.