The physics associated with statics has considerable applications in engineering. As a mechanical engineer working for a tow-truck manufacturer, you have been asked to evaluate the purchase of a new line of towing cable. The supplier claims that, although its cables are not as strong as its competitors (maximum tension capability of 5120 lb5120 lb), the cost savings make it a good investment.
A schematic of the towing configuration is shown. The car weighs 36513651 lb, which is as large as the company expects their tow trucks to service. The overall length ?L of the car is 10.710.7 ft, and the distance ?d between the midpoints of the front and back tires is 9.639.63 ft. The bottom of the car's frame is a height ℎf=0.370hf=0.370 above the ground, and the car's center of mass is a height ℎCM=1.50hCM=1.50 above the bottom of the car's frame. The angle ?ϕ between the midpoint of the tires and the tow cable is 50.0∘50.0∘. Assume the CM of the car is positioned exactly halfway across its length, the geometry of the wheels and front/rear of the car is symmetrical, and that the coefficient of friction between the road and tires is sufficient to maintain no acceleration in the system.
Calculate the tension in the cable just as the front of the car begins to lift off the ground. Assume that the front end rises at a constant velocity.
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