A schematic of the towing configuration is shown below. The car weighs 3651 lb,

Question

A schematic of the towing configuration is shown below. The car weighs 3651 lb, which is as large as the company expects their tow trucks to service. Calculate the tension in the cable just as the front of the car begins to lift off the ground. Assume the center of mass (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. Based on your results, what would you advise your company? The cable they are offering is too weak to use. I would decline the purchase. The cable they are offering is more than adequate. The cost savings make this a worthwhile investment

Explanation / Answer

Here,

let the tensionn in the string is T

Balancing the moment of forces about the rear wheels

T * sin(theta) * (10.9 - (10.9 - 9.81)/2) + T * cos(theta) * 0.350 - 3651 * (9.81/2) = 0

T * sin(42) * (10.9 - (10.9 - 9.81)/2) + T * cos(42) * 0.350 - 3651 * (9.81/2) = 0

solving for T

T = 2491.1 lb

the tension in the string will be 2491.1 lb

hence

the cable they are offering is more than adequate.The cost savings make this a worthwhile investment

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