Question

What is the max. speed at which a 1500 kg car can round a curve on a flat road if the radius of the curve is 90 m and the coefficient of static friction is 0.50? Is it necessary to know the mass of the car to solve this problem?

MEDAL WILL BE GIVEN TO THE FIRST CORRECT ANSWER!

Answer 1

So here is what I got.

Fc = Fs

mv^2/r = Usmg

multiply by r both sides

mv^2 = rUsmg

divide both sides by m

v^2 = rUsg

v = sqrt(rUsg)

When I plug in the values for g, Us, and r, I get 21 m/s as the answer.

Therefore, the mass is not required to solve this problem.


I really don't understand how I got the answer. Why is the static force equivalent to the centripetal force? I haven't worked with static friction that much so yeah.

Answer 2

When something slides we want the sliding friction factor, when rolls, we can use the static friction factor, as there is no sliding.

Mass cancelled out because both forces, centripetal and friction ere proportional to mass.

Answer 3

Also look at the car - there is only one force acting on it, the force of static friction, that is pushing the car inwards to counteract its tendency to go flying off the track. Since it's undergoing circular motion, then the sum of the forces is equal to some centripetal acceleration, and since the only force acting is the force of friction, when the forces are summed you get

\[\sum F = F_{net}\]
\[F_{net} = F_{cent}\]
\[\sum F = F_{friction}\]
therefore

\[F_{friction} = F_{cent}\]