a curve with a radius of 74m is banked for a car traveling 80km/h , what is the static friction for a car not to skid when traveling at 95km/h ?

Question

Can you please help me answer this question?

Answer 1

Greg,

I suggest the following. You need to figure all the forces on the car doing the 95 km hr^-1 loop, but you already know that that will depend on the angle of banking of the road.

So how do you figure the angle of banking? It's the angle that results in NO skidding tendency for the 80 km hr^-1 car; i.e., the car has only a force NORMAL to the surface.

OK, that works out to a = v²/r. Figure the value of a out. You don't in fact need to calculate a FORCE here, since the mass of the car is constant throughout all the geometry! However, the net vector for gravity PLUS the acceleration must be normal to the banked surface; that allow you to calculate the angle of bank (hint tan^-1 function useful!).

Now you're ready to figure the forces on the 95 km hr^-1 car. Again, the lateral a = v²/r; your gravity is acting straight down. When you decompose both the lateral acceleration into tangential and normal components, and sum the respective components, you'll have expressions proportional to the forces in each direction. The coefficient of static friction must be at least the ratio of the two : (Ftang/Fnorm), because that's what will supply that ratio, and hence amount, of force.

By the way, you might want to keep in mind for when you get your driver's license, you should never try to push that limit on public roads! Things like wet roads, oil slicks, ice, gravel, bumps, debris of other sorts, and so on, can really ruin your coefficient of static friction. And once you are skidding, YOU ARE A PROJECTILE -- ABS and 4-wheel drive can't help you at all.