A car of mass M travels on a circular loop of radius R. The coefficient of static friction for the track is s and the coefficient of kinetic friction is k. What is the maximal velocity the car can travel without skidding? (gravity=g)
A (Rgs)1/2
B (Rgk)1/2
C (Rgk/M)1/2
D (Rgs/M)1/2
I thought the answer was B because the car is moving (kinetic friction) but the answer says it's A (static friction) (I know how to get the answer, i'm just having trouble understanding why they used static instead of kinetic friction
here is the explanation they give
Explanation: The car will skid if its centripetal force is greater than the force of kinetic friction. Therefore, the maximal velocity is achieved when the two quantities are equal, i.e. when Mv2/R=Mgs, therefore the maximal velocity is (Rgs)1/2. (Remember that you have to use the coefficient of static friction because the car is not actually moving up the track)
What do they mean not actually moving up? does it mean the velocity at that instant toward the skidding direction is 0 so we have to use static friction? (please explain why)
thanks
A (Rgs)1/2
B (Rgk)1/2
C (Rgk/M)1/2
D (Rgs/M)1/2
I thought the answer was B because the car is moving (kinetic friction) but the answer says it's A (static friction) (I know how to get the answer, i'm just having trouble understanding why they used static instead of kinetic friction
here is the explanation they give
Explanation: The car will skid if its centripetal force is greater than the force of kinetic friction. Therefore, the maximal velocity is achieved when the two quantities are equal, i.e. when Mv2/R=Mgs, therefore the maximal velocity is (Rgs)1/2. (Remember that you have to use the coefficient of static friction because the car is not actually moving up the track)
What do they mean not actually moving up? does it mean the velocity at that instant toward the skidding direction is 0 so we have to use static friction? (please explain why)
thanks
-
They phrased it badly. Of course the car is moving. The wheels are spinning, but the rubber is not SLIDING along the surface. Just as when you are walking, you shoe soles are not SLIDING across the surface, You push back on the ground(which gives you a push forward) but your shoes don't slip(unless you are on ice) so it is STATIC friction not kinetic. Same with tyres. They push back without slipping, otherwise they would spin (which can happen if you floor it). If they spin it is kinetic friction. Which is less than static, so not useful for accelerating or stopping fast (hence anti-lock brakes)So why do racers spin wheels?? To melt the rubber and increase friction !! Isn't Physics wonderful ??