We consider an automobile of mass m traveling along a curved but level road. To avoid skidding, the road must supply a frictional force F = ma, where a is the car’s acceleration vector. The maximum magnitude of the frictional force is μmg, where μ is the coefficient of friction and g = 9.8 m/s². Let v be the car’s speed in meters per second.

You want to reverse your direction in the shortest possible time by driving around a semicircular bend (Figure 17). If you travel at the maximum possible constant speed v that will not cause skidding, is it faster to hug the inside curve (radius r) or the outside curb (radius R)? Hint: Use Eq. (8) to show that at maximum speed, the time required to drive around the semicircle is proportional to the square root of the radius.

Transcribed Image Text:

R LIE