8. Centripetal Forces & Gravitation

A truck can go around a flat curve of radius 150m with a maximum speed of 32m/s before slipping. Calculate the maximum speed it can go around a tighter curve of radius 75m.

A flat (unbanked) curve on a highway has a radius of $170.0$ m. A car rounds the curve at a speed of $25.0$ m/s. What is the minimum coefficient of static friction that will prevent sliding?

(II) A car drives in a spiral path of gradually decreasing radius in a large empty parking lot. The speed is held constant at 10.0 m/s, and the car starts at a distance of 50.0 m from the center of the spiral. If the coefficient of static friction is 0.80, how far is the car from the center when it first starts to skid?

A car is heading along a flat slippery road at a speed of 95 km/h. The minimum distance within which it can stop (because of ABS) is 66 m. Estimate the radius of the sharpest curve the car can negotiate on an icy flat surface at the same speed without skidding out.

A car can just barely turn a corner on an unbanked road at 45 km/h on a dry sunny day. What is the car's maximum cornering speed on a rainy day when the coefficient of static friction has been reduced by 50%?