A car rounds a banked curve where the radius of curvature of the road is R=100m., the banking angle 10 degrees and the coefficient of static friction is .10 (slippery conditions). A) Determine the range of speeds the car can gave without slipping up or down the road.

Answer 1

down slip problem:

forces along slope pointed down slope:
m g sin 10 - .1 m g cos 10 = m (v^2/r)cos 10

up slip problem, reverse direction of friction
m g sin 10 +.1 m g cos 10 = m (v^2/r) cos 10

note m cancels everywhere

Answer 2

4.5M/S