Question

A car rounds a flat circular track with radius 250m . The coefficient of static friction between the tires and track is 0.90. What's the maximum speed for the car if it's to stay on the track?

Answer 1

Alright, remember that the centripetal force is being enacted by the coefficient of static friction that's parallel to the track's radius. We know that the car cannot afford to have any inward acceleration, and therefore the forces we're concerned with sum to zero ∑F=ma=f_{s}-F_{c}=0, where f_{s}=μ_{s}F_{N}=μ_{s}ma_{g}, and F_{c}=m(v^2)/r. We aren't given the mass of the car, however: μ_{s}ma_{g}-m(v^2)/r=0, and dividing by m gives us μ_{s}a_{g}-(v^2)/r=0, and solving for v will have: v=√(rμ_{s}a_{g}).

Answer 2

and what about the kinetic friction