I told this problem to my buddy and he swears I am wrong. I have no one else around that he thinks is smart enough to believe, hence I turn to you all. Here it goes:
There is a part of a car that is going ~0mph at all times, no matter how fast the car is going. 1st Hint: It is more than one part. 2nd Hint: This part changes every instance.
Answer: When they contact the road, the molecules of rubber on the outermost tread of the tire are going ~0mph at any given speed. With a car speed of 50 mph, these molecules are going ~100mph at the top of the rotation, and ~0mph as they contact the road.
Please provide plenty of assurance to my buddy that he is dead wrong in disagreeing with my answer. Thank you.
*I understand that the tires and road to not perfectly grasp each other at such high speeds, that is why I used the “~” sign.
Somebody is confusing angular velocity with linear velocity. If the car is going at a constant forward speed, the outermost part of of the tire will have the same angular velocity at the bottom of the tire that it does at the top, if my rather fuzzy recollection of physics isn’t too far off the mark.
This concept is why anti-lock brakes work. Kinetic friction is always lower than the highest possible static friction. When a wheel is rolling, the static friction coefficient can be used, but when the wheel starts sliding, you can’t stop as fast, because the kinetic friction coefficient is used.
It would be nice if you could get him to resolve the matter by considering the details of the problem, rather than by consulting some “expert”. The physics of the case don’t defer to anyone’s opinion.
You might try asking him to say how fast he thinks the bottom of each tire is moving relative to the pavement. If not zero, there should be friction, heat, skid marks, etc.
OK upon further thought, I take my previous post back. I over simplified the problem, ignoring things like friction and elasticity.
There is a point where the surface of the tire touching the ground has zero velocity relative to the ground. I found an article that sums this up nicely:
Although, you’re right, it’s not “a” part, but “part of a” part (if, by part, a complete piece is meant. The “part of a” part is the small ammount of rubber that’s touching the road).
Yes, “wrt the road” is not necessary. My point was that it should be “At all times, there is part of the car that is going ~0mph”, rather than “There is a part of a car that is going ~0mph at all times”.
With respect to the road is necessary because there are plenty of parts that will be going zero mph with respect to say, the driver of the car. To easy of a loophole for an argumentative person, best to make that point clear!
Under what conditions? Sure, if the car is travelling at a constant speed along a level road, then it may be true that there will at any moment be a piece of the car that is not in motion with respect to the road…
But travelling in straight lines isn’t all that cars do; what if it’s performing a power slide around a wet corner? What if it’s them pesky Duke brothers and the General Lee is in the middle of an implausibly large jump? Or what if, yes, it’s on a treadmill?
Have the parameters of the scenario been rigidly defined?
Actually, there’s the mechanical solution to this problem (i.e. part of the tyre is touching the road without skidding, so it must be going the same speed), but there’s also a mathematical solution:
Given a disc of radius r, rotating at one revolution per second, there will at any given moment be points on the disc that are moving anywhere between 0 and 2Πr metres per second in a direction equivalent to any vector you choose, within the plane of rotation. So as long as the car is not braking in a slight skid, there will have to be a point on the wheel that is not in motion WRT the road.
If the car is accelerating in a skid, there will still be a point that is stationary WRT the road, but it will not be on the outside surface of the tyre.
What Fuel is looking for is a simple and clear explanation of why this is true, not simply an argument from authority. At least, that’s what he should be looking for. So here goes:
Any point on the contact patch of the tire has a horizontal velocity of zero, correct? If it had a non-zero horizontal velocity, it would be sliding on the pavement, and it’s not, so the velocity is zero.
Now to the vertical component of its velocity. That point of the tire had previously been heading down, with a negative velocity (if up is positive). It’s about to be going up with a positive velocity. At the short interval where it contacts the road, its velocity is passing through zero. It has a significant amount of acceleration, but its vertical velocity is zero.
So its horizontal velocity is zero, its vertical velocity is zero, and there is obviously no speed sideways, therefore its overall velocity is zero. QED.
Well yes and no.
I often ask a version of this in my ABS class when we discuss the theory of how ABS brakes work.*
If you are towing a trailer the speed of the tread of the trailer tire w.r.t. the pavement is zero.
If you driving a car the drive wheels have to overcome wind resistance,** and that will cause the tires to slip somewhat w.r.t. the pavement. Driving down the highway, there is about 1-2% slip due to wind resistance. If you step the brakes there will be some additional slip as the wheel and tire slows down. As the amount of brake retardation increases the slip increases up to a point. After about 12% -14% slip the braking force goes down. This is a skid. ABS limits how much slip and prevents you from getting into a skid.
Anytime you steer the car, accelerate the car, or brake the car there is some slip. If you just coast (see trailer example above) there is no slip.
*One of the statements I will make is: Most people think that the brakes stop the car, the steering wheel steers the car, and the gas pedal makes the car accelerate. Do you agree with this?
If they answer yes, I ask them what happens if they raise the car on the lift putting the tires 1" off the ground, does the car still accelerate when you step on the gas?
Why not?
Physics? Shoot, just watch the treads on a tank or other tracked crawler. Those segments what ain’t moving up at the back end, or getting lad down at the front are wither moving forward (the top part of the track loop) or holding their position on the ground a.k.a. not moving relative to the road.
A tire is basically a crawler track in the shape of a circle. The top of the tire/track is moving twice as fast as the vehicle, and the part that contacts the road is moving at 0. Otherwise the wheel would just spin on the pavement. The bottom bit has to be stationary in order to push against the road and move the vehicle forward.
IMO the answer is not limited to “the molecules of rubber on the outermost tread of the tire” but includes the entire thickness of the material making the footprint.
Sorry!
