A car skidded off an icy road and became stuck in deep snow at the road shoulder.
Question:
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 masses of the cars, estimate the maximum impact force that can be developed in the cable, and the resulting cable elongation. Assume that the steady state force, acting on the rope, is equal to the weight of the car. Do not use the textbook's canned equations. Instead, start from an energy conservation point of view comparing two states. In state 1, the tension in the cable is zero and the jerking car has velocity, v. In state 2, the tension in the cable is Maximum and the jerking car has a velocity of zero.