Question:
Physics Problem. What does Ms and Mk stand for?
anonymous
2009-10-04 08:29:18 UTC
I am confused about what these variables mean when talking about friction. For instance, the question states that a horizontal section of a road has snow with Ms= .6 and Mk = 0.1. how far will the driver travel before stopping.

Please explain the basic concepts of Ms and Mk.
Thanks!
Three answers:
chente
2009-10-04 08:34:52 UTC
marie



Ms probalby means static coefficient of friction, the amount which is overcome for a block at rest.

Mk probanly means kinetic coefficient of friction, the amount which is overcome for a block in motion.



chente
oldprof
2009-10-04 16:25:02 UTC
The subscripts, s and k, refer to static and kinetic. Static means the movable object (e.g., the tire treads) is not moving with respect to the surface the object is on (e.g., the road). Kinetic means the movable object (e.g., the tire treads) is moving with respect to the surface the object is on (e.g., the road).



It is an observation in physics that Ms > Mk always. That is, the static friction, all other things equal, will always.... always... be greater than its otherwise comparable kinetic friction. This is why we admonish drivers to not lock their brakes when trying to stop quickly. By locking the brakes, the tires stop rotating and their treads start to skid over the surface of the road and that's Mk < Ms, kinetic friction.



On the other hand, if the tires are kept rolling, the contacting surface of the tire treads against the surface is NOT moving with respect to the asphalt. That is, because the tires are rotating, where the rubber hits the road, those two surfaces are not moving (i.e., static) with respect to each other. And that's static Ms > Mk and better braking action. This is why, good drivers know to pump their brakes if they want to stop quickly.



In general, friction force is F = kN; where k = Ms or Mk depending on if the case is static or kinetic, and N = W cos(theta) is the so-called normal weight and theta is the slope angle of the surface. "horizontal" means theta = 0 degrees slope. W = mg is the weight of the movable object with mass m and g is g, what else?



A warning... you will hear or read the terms rolling friction and sliding friction. Rolling friction is actually static friction even though the object is rolling, without slippage, across its surface. This is like the rolling tires on your car, that's static friction and Ms should be used.



On the other hand, sliding friction is kinetic. This results because the movable object's area of contact with the surface is actually moving with respect to the surface the object is moving over.



One other note... it is not exactly clear why Mk < Ms always. But there seems to be a consensus that it has to do with the molecules in the movable object skipping over the molecules of the surface in the kinetic case versus, settling down and become entrapped or attracted by adhesion in the static case.



A typical HS physics problem, which I think you're trying to solve, is:



If the car of mass m = 1000 kg is going 100 kph when a deer passes in front at 200 meters, the reaction time is t = 1 sec before the brakes are applied and, as a smart driver, the brakes are pumped to make use of Ms = .6, will the car stop in time to avoid hitting the deer?



So, to miss the deer, the distance the car travels d < D = 200 m The distance the car travels is the reaction time distance vt + the braking distance v^2/2a; where a = F/m = Ms mg/m = Ms g or .6 g. Change 100 kph into mps and solve for the stopping distance d = vt + v^2/1.2g where g is g = 9.81 m/sec^2. If d < D, then the deer and your car are saved.



Note, the deceleration a = kg when the slope theta = 0 in general, k = Ms or Mk as appropriate. This is why it takes longer to stop with sliding friction, the sliding k value is less than for static friction, so the deceleration is slower. This is why you need to leave more space between you and the car in front on icy or snowy roads. The icy or snowy k is smaller than the dry road k; so a is less and it takes longer to come to a halt.
tomsing98
2009-10-04 15:35:39 UTC
Those appear to be the static coefficient of friction (Ms) and the kinetic coefficient of friction (Mk). Normally, those are written with the Greek letter mu, but since that's a bit of work to get on a keyboard, whoever wrote the problem you're looking at just used a capital M.



If you want to know more about static and kinetic coefficients of friction, try here: http://en.wikipedia.org/wiki/Coefficient_of_friction#Coefficient_of_friction



I hope that helps you out!


This content was originally posted on Y! Answers, a Q&A website that shut down in 2021.
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