An SUV has a height h and a wheelbase of length b. Its center of mass is midway between th...

An SUV has a height h and a wheelbase of length b. Its center of mass is midway between the wheels and at a distance ah above the ground, where 0<α<1. The SUV enters a turn at a dangerously high speed, v. The radius of the turn is  R (R ≫ b), and the road is flat. The coefficient of static friction between the road and the properly inflated tires is μs. After entering the turn, the SUV will either skid out of the turn or begin to tip.

 a) The SUV will skid out of the turn if the friction force reaches its maximum value, F → μsN. Determine the speed, vskid, for which this will occur. Assume no tipping occurs.

b) The torque keeping the SUV from tipping acts on the outside wheel. The highest value this force can have is equal to the entire normal force. Determine the speed, vtip, at which this will occur. Assume no skidding occurs.

c) It is safer if the SUV skids out before it tips. This will occur as long as vskidtip. Apply this condition, and determine the maximum value for a in terms of b, h and μs.