Question

Marc drives like a maniac. His defense is always "It’s OK, I know the physics of driving so I do it safely". Marc is coming up to a horizontal turn of radius r = 150 m. Since Marc is a physicist, he just knows the coefficient of static friction between the tires and the road is µ = 0.45. If the center of mass of Marc’s car is xcm = 60 cm above the ground and his car’s wheel base is ` = 1.3 m, determine the following:

(a) a formula for the maximum speed Marc can complete the turn without flipping the car.

(b) a formula for the maximum speed Marc can complete the turn while remaining on the road (hint, you will have to compare the value from two formulas).

(c) whether Marc can safely complete the turn if his speed is 100 km/h? What about at 80 km/h?

(d) Show that if µs < ` 2xcm , then it is impossible to flip your vehicle.

(e) The above ratio is something that vehicle engineers must be aware of (as it is a safety thing). Moving vans, obviously, have a much higher center of gravity, however, due to width constraints (width of lanes on the road, parking spots, etc), they are not able to make the wheelbase that much wider. If the wheelbase of a moving van is 2 m and it’s center of mass (when modestly loaded) is 5 ft, is it able to flip (using the same µs as above)?

Answer 1