The rescue attempt in Problem 7.5 resulted in only slight movement of the stuck car because the cable force decayed so quickly to zero. Besides, concern was felt about possible damage to the car attachment points because of the high "instantaneous" force developed. One witness to the proceedings brought a 12-m elastic cable of overall stiffness only 2.4 N/mm and suggested that it be tried. Because of the longer length of the elastic cable, its use enabled the rescue car to reach 12 km/h at the point of becoming taut. Estimate the impact force developed and the resulting cable elongation. If the stuck vehicle does not move significantly until the rescue car has just come to a stop, how much energy is stored in the cable? (Think of this in terms of the height from which a 100-kg mass would have to be dropped to represent an equivalent amount of energy, and consider the potential hazard if the cable should break or come loose from either car.) What warnings would you suggest be provided with elastic cables sold for this purpose?

Problem 7.5

A car skidded off an icy road and became stuck in deep snow at the road shoulder. Another car, of 1400-kg mass, attempted to jerk the stuck vehicle back onto the road using a 5-m steel tow cable of stiffness k = 5000 N/mm. The traction available to the rescue car prevented it from exerting any significant force on the cable. With the aid of a push from bystanders, the rescue car was able to back against the stuck car and then go forward and reach a speed of 4 km/h at the instant the cable became taut. If the cable is attached rigidly to the center of mass of each car, estimate the maximum impact force that can be developed in the cable, and the resulting cable elongation (see Figure P7.5)