Torsional springs provide a simple propulsion mechanism for toy cars. When the rear wheels...

Torsional springs provide a simple propulsion mechanism for toy cars. When the rear wheels are rotated as if the car were moving backward, they cause a torsional spring (with one end attached to the axle and the other to the body of the car) to wind up and store energy. Therefore, a simple way to charge the spring is to place the car onto a surface and to pull it backward, making sure that the wheels roll without slipping. Note that the torsional spring can only be wound by pulling the car backward; that is, the forward motion of the car unwinds the spring.

Figure P8.37

Let the weight of the car (body and wheels) be W = 5 oz, the weight of each of the wheels be Ww = 0.15 oz, and the radius of the wheels be r = 0.25 in., where the wheels roll without slip and can be treated as uniform disks. Neglecting friction internal to the car and letting the car’s torsional spring be linear with constant kt = 0.0002 ft·lb/rad, determine the maximum speed achieved by the car if it is released from rest after pulling it back a distance L = 0.75 ft from a position in which the spring is unwound.