A banking angle (r=60m) is designed for a speed of 90 km/hour. When the coefficient of static friction is 0.3, what are the min and max speeds a car can go without skidding?

I determined that the angle is about 46.7 degrees, but when I tried calculating the min and max speeds I got different answers than my textbook's solution. I'm using the assumption that the normal force = mg/cos(46.7deg), which has an inward component of mg*tan(46.7deg).

I then added the max and min force provided by friction and came up with: v=sqrt(r*g*(sin plus-minus 0.3)/cos)

Where did I go wrong?

Question

A banking angle (r=60m) is designed for a speed of 90 km/hour. When the coefficient of static friction is 0.3, what are the min and max speeds a car can go without skidding?

I determined that the angle is about 46.7 degrees, but when I tried calculating the min and max speeds I got different answers than my textbook's solution. I'm using the assumption that the normal force = mg/cos(46.7deg), which has an inward component of mg*tan(46.7deg).

I then added the max and min force provided by friction and came up with: v=sqrt(r*g*(sin plus-minus 0.3)/cos)

Where did I go wrong?

vincent-lyon.fr · Answer

normal force = mg/cos46.7° would be ok if acceleration was purely parallel to the surface. But in your case, acceleration is centripetal.

Have you made a sketch of this situation?