Question

8. I drive a small sedan (a 2009 Toyota Yaris) that is front wheel drive. This means that the engine is linked only to the front wheels, so only the static friction coming from the front wheels can provide traction to help me move forward. 2 However, it has brakes on all four wheels, so static friction from both the front and the back wheels can provide traction to help me stop. Since the engine is the heaviest part of the car, the front wheels bear most of the car’s weight. For this problem, assume that the front wheels supply 2/3 of the normal force and the rear wheels supply the other 1/3. In the summer of 2018, I was driving this car on some steep and dusty mountain roads (µs = 0.7) in the mountains in Colorado. When I was climbing up the mountains, I was confident that I could make it safely back down any slope that I could climb up. However, I knew the reverse wasn’t true, and was very reluctant to drive down a steep slope since I didn’t know if I could make it back up. • What is the steepest slope that my car can drive up (at a constant velocity)? • What is the steepest slope that my car can travel down safely (without sliding down the slope)? • Will four wheel drive help you avoid a car accident on icy roads in Syracuse? Will it help you avoid getting your car stuck?

Answer 1

(a) The following figure is showing the free body diagram when the car is climbing up. mg sine Cosa J2mg mga " The net force acting along the x direction is zero. Therefore, balance the forces acting along the x direction. fi= fa + mg sino uN, = uN, +mg sino "EN )=-N)+mg sino WN = mg sine Here, N, is the reaction force experienced by the front wheels and N, is the normal force experienced by the rear wheels. The net force acting along the y direction is also zero. Therefore, balance the forces acting along the y direction. N=mg cosa = mg sino and solve for angle 0. Substitute mg cos for N in equation" u(mg cos ) V= mg sino tan 6 = = 13.130

(b) The following figure is showing the free body diagram of the car when it is coming down the hill: NX mg sine K 12 mg mere mg cos The net force acting along the x direction is zero. Therefore, balance the forces acting along the x direction mg sin 8 = f2 + fi = uN, +uN - | - + = UN Here, N, is the reaction force experienced by the front wheels and N, is the normal force experienced by the rear wheels. The net force acting along the y direction is also zero. Therefore, balance the forces acting along the y direction. N = mg cose Substitute mg cos e for N in equation mg sin 0 = uN and solve for angle 9. mg sin 0 = u(mg coso) tan θ = μ A=tan (u) = tan-(0.7) = 34.992°

(C) Four-wheel drive helps is travelling on icy roads, but it does not provide that much safety. It helps the car in moving in snow, but it causes loss of traction. Traction is the friction between the wheels and roads. This traction is necessary to avoid slipping of car on the icy roads. Hence, four-wheel drive cannot help is avoiding accident on icy roads, but yes, it helps in avoid getting car stuck.