Marc drives like a maniac. His defense is always \"It’s OK, Iknow the physics of driving so I do it safely\". Marc is coming upto a horizontal turn of radius r = 150 m. Since Marc is aphysicist, he just knows the coefficient of static friction betweenthe tires and the road is µ = 0.45. If the center of mass of Marc’scar 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 turnwithout flipping the car.
(b) a formula for the maximum speed Marc can complete the turnwhile remaining on the road (hint, you will have to compare thevalue from two formulas).
(c) whether Marc can safely complete the turn if his speed is100 km/h? What about at 80 km/h?
(d) Show that if µs < ` 2xcm , then it is impossible to flipyour vehicle.
(e) The above ratio is something that vehicle engineers must beaware of (as it is a safety thing). Moving vans, obviously, have amuch higher center of gravity, however, due to width constraints(width of lanes on the road, parking spots, etc), they are not ableto make the wheelbase that much wider. If the wheelbase of a movingvan 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)?
