Problem

Let the mass of the car (body and wheels) be m = 120 g, the mass of each of the wheels be...

Let the mass of the car (body and wheels) be m = 120 g, the mass of each of the wheels be mw = 5 g, and the radius of the wheels be r = 6 mm, where the wheels roll without slip and can be treated as uniform disks. In addition, let the car’s torsional spring be linear with constant kt = 0.00025 N·m/rad. Neglecting any friction internal to the car, if the angle of the incline is ϕ = 25° and the car is released from rest after pulling it back a distance L = 25 cm from a position in which the spring is unwound, determine the maximum distance dmax that the car will travel up the incline (from its release point), the maximum speed υmax achieved by the car, and the distance dvmax (from the release point) at which υmax is achieved.