A curve of radius 138 m is banked at an angle of 11°. An 762-kg car negotiates the curve at 82 km/h without skidding. Neglect the effects of air drag and rolling friction. Find the following.
(a) the normal force exerted by the pavement on the tires
(b) the frictional force exerted by the pavement on the tires
(c) the minimum coefficient of static friction between the pavement and the tires
This problem is more complex than it looks. The centripetal force on the car is horizontal to the ground, but this force does produce a component in the direction normal to the pavement. Gravity of course adds to this normal component.
I set up the solution here, but I do not calculate the values.
(a) Fcen = mv^2/r. Fn = Fcen *sin 11 + mg * cos 11.
(b) The friction force can be found by doing a summation of forces in the direction along the slope. Fnet in this direction is zero since there is no skidding. Gravity and the centripetal force both have components in this direction.
0 = Ffriction + Fcen * cos 11 + m*g sin 11
(c) once we know the Ffriction we can calculate the coeff of friction
u = Ffriction/Fnormal
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