## Truck and Bicycle

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Goemon
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### Truck and Bicycle

Theoretically speaking, when any object is slowed by static friction, its acceleration is independent of its mass:

Frictional force = (normal force = [imath]mg[/imath]) * (coefficient of friction = [imath]\mu[/imath])
[imath]F = mg\mu[/imath]

acceleration = (frictional force) / mass
[imath]a = g\mu[/imath]

So, for example: You're riding your bicycle down the highway at 100km/h directly in front of a large truck. A chipmunk runs across the road in front of you. You slam on the brakes, locking up the wheels. The truck does the same.

According to the above equations, you and the truck decelerate at the same rate, so long as your tires are made out of the same material. You and the truck screech to a halt at the same rate, and you come safely to a stop with the truck maintaining the same distance behind you.

Anyone trust their theoretical physics enough to try this little experiment?

If not, why?
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Klotz
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### Re: Truck and Bicycle

With trucks and vehicles and general, a huge factor is viscous dampening/air resistance, which increases with surface area and velocity and decreases with mass.

Seraph
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### Re: Truck and Bicycle

If you lock up the wheels why do you think that static friction would apply?

Static friction requires non-moving surfaces. In the case of brakes the energy disipation is either being done by the brakes sliding across a disk or drum, or by the wheels sliding across the ground. Both of those involve surfaces moving relative to each other and therefor are outside the relm of static friction.
Last edited by Seraph on Sun Feb 01, 2009 7:26 pm UTC, edited 1 time in total.

Klotz
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### Re: Truck and Bicycle

I'm pretty he meant kinetic friction. He's talking about a fixed coefficient of friction multiplied by the normal force.

Seraph
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### Re: Truck and Bicycle

Klotz wrote:I'm pretty he meant kinetic friction. He's talking about a fixed coefficient of friction multiplied by the normal force.

That doesn't make any sense to me.

Kinetic friction requries that you account for the forces that are orthogonal to the contact plane, in addition to the forces that are perpendicular to the contact plane (including the ones you mentioned in your first post). It looks to me like he's calculating the maximum force that you can generate from static friction, which is the coefficient of static friction multiplied by the normal force. Kinetic friction is a lot more complicated then that, and he doesn't seem to be taking any of that into account.

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### Re: Truck and Bicycle

I find this entirely believable, but I'm not going to try the experiment. Why not? I really don't think I could peddle my bike at 100 km/h, and the premise rather requires that I'm moving at exactly the same speed as the truck, and the truck driver has perfect reflexes. I'll stick with Feynman's bowling ball example if I want to prove that I trust the laws of physics. (For that matter I have a lot more faith in conservation of energy, which is exact, than in the law that friction is proportional to normal force, which is a first order approximation to a phenomenon where the details really are quite messy.)

Seraph: orthogonal and perpendicular are synonyms.

Theoretically, you can get the full force of static friction when braking: the idea is to break just enough so that your tires don't lock up, and your wheels are rolling rather than sliding. In practice this is very hard to achieve, but you can come close with an antilock breaking system. I'm guessing that this is also why they tell you to pump the brakes rather than slamming on them.
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Rentsy
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### Re: Truck and Bicycle

I think a truck's brakes have a higher coefficient of friction than my bike's brakes.

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### Re: Truck and Bicycle

Rentsy wrote:I think a truck's brakes have a higher coefficient of friction than my bike's brakes.

Both the truck and the bike's breaks are locked. The idea is sound though. The friction coefficient is a very complicated variable that potentially depends on a whole host of other variables, including in this case thread pattern and material.
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### Re: Truck and Bicycle

Meteorswarm wrote:Wouldn't the truck's tires present a greater area to the road, thereby having a higher coefficient of friction? Or does the less normal pressure counter that?

In friction that way they teach it in high school physics, normal pressure would counteract that effect. Think about it this way: having weight evenly distributed among two pieces of tire with friction constant k provides the same total friction force as having all weight concentrated on the same piece, if force is exactly proportional to normal force.

I'm not sure how exact this is. They make racecar tires gigantic compared to ordinary tires, which could suggest that increasing area increases traction. However, it could also be that it doesn't increase traction at all, and the reason they do it is because spreading the force out more allows tires to last longer.
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Sockmonkey
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### Re: Truck and Bicycle

The large surface area of racing tires is to spread out the friction enough to keep the tires from eroding and melting. Melting and/or eroding rubber particles provides a certain amount lubrication.

DysfunctionalGroup
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### Re: Truck and Bicycle

mathematically, everything makes sense, but logically, and actually in practice is where there are discrepancies.

ideally, if both bike and truck lock brakes, they will both decelerate at the same rate.

however, if you're on a bike, you'd never lock both wheels - either you'll flop over if both wheels are sliding long enough, or you'd flip your shit.

so.... in all situations, if the truck locks all brakes:

bike locks just the rear brake, and (we'll assume ideal weight distribution as even on each wheel), the bike will actually decelerate at half the rate of the truck (even slower in reality considering weight shifts forward while breaking and off of the rear wheel)

if the bike locks the rear brake and also applies the front brake, if the deceleration due to static friction of the bike's front tire + kinetic friction from rear > deceleration of truck (which is very possible) then things will get ugly.

hope that makes sense... i'd go into a little more detailed math/physics, but im also supposed to be doing a chem lab report right now...
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IHOPancake
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### Re: Truck and Bicycle

DysfunctionalGroup wrote:however, if you're on a bike, you'd never lock both wheels - either you'll flop over if both wheels are sliding long enough, or you'd flip your shit.

In an ideal world, it would be possible to maintain your balance even with both tires locked. If you lean to the left, the bike will tilt left, and leaning right will cause the bike to tilt right. Therefore, there must be some position where the bike will tilt neither to the left nor the right.
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quintopia
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### Re: Truck and Bicycle

i wouldn't try it with a loaded reefer on my tail. i know that driver can't swerve and he's not gonna lock the brakes because jackknifing could just hurt even more people.

Allenr
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### Re: Truck and Bicycle

I think I remember learning that the surface area in contact with the ground doesn't effect the friction force.

I would think the truck would still slow down faster, mainly from common sence. If you had an ideal truck and bike though and no forces other than friction, the mass does seem like it would be irrelevent.
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### Re: Truck and Bicycle

The problem with bikes is that they have a maximum deceleration (on the order of 1g) dictated by their center of gravity. At some point you just go over the handlebars. Trucks have that too, but it's rather a lot higher.

But it would be interesting to just build some identical sleds and measuring the distance of deceleration for various weights of blocks.
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Goemon
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### Re: Truck and Bicycle

I'd also like to know how drag racing cars manage to accelerate on the order of 4g when starting from the line, when every elementary physics student will do the math and find that the acceleration can't be more than one g.

What's with the coefficient of friction on a drag car? Is it something more like glue?

Does that mean cars can pull more than a g in a tight turn as well?
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Rentsy
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### Re: Truck and Bicycle

I want to point out that when I pull on my bike's brakes, the tires don't stop. They keep rotating. And when I do try to stop quickly on a wet day, I start to skid.

When braking a car, the same thing happens. The wheels keep moving.

And even when the tires are held to a stop and the car skids across the pavement, a car has alot more surface area of its wheels making contact with the ground.

But, yes. Two objects of the same coefficient of friction moving at the same speed will decelerate at the same rate, regardless of weight.

but "coefficient of friction" becomes the fudge factor. So keep that in mind.

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### Re: Truck and Bicycle

Goemon wrote:I'd also like to know how drag racing cars manage to accelerate on the order of 4g when starting from the line, when every elementary physics student will do the math and find that the acceleration can't be more than one g.

What do you mean? The coefficient of friction is not necessarily bounded by 1.

On the other hand, Wikipedia says, "under good conditions, a tire on concrete may have a coefficient of friction of 1.7." This would suggest that drag racing cars shouldn't be able to accelerate at more than 1.7g.
I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.

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SonicIce
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### Re: Truck and Bicycle

skeptical scientist wrote:
Goemon wrote:I'd also like to know how drag racing cars manage to accelerate on the order of 4g when starting from the line, when every elementary physics student will do the math and find that the acceleration can't be more than one g.

What do you mean? The coefficient of friction is not necessarily bounded by 1.

On the other hand, Wikipedia says, "under good conditions, a tire on concrete may have a coefficient of friction of 1.7." This would suggest that drag racing cars shouldn't be able to accelerate at more than 1.7g.

Drag racing tires are very soft and sticky. They are so soft that their life span is only about 2 miles! Also, the starting line has a layer of rubber from all of the burnouts which makes it also very sticky. In fact, if you walk around on the starting line, your shoes will stick to the ground as you walk and make a noise like pulling 2 peices of tape apart. This grip gives the ability to do wheel stands. If a dragster was using standard road tires and on a normal road, it wouldn't accelerate nearly as fast because the tires would be so easy to spin.