The physics associated with statics has considerable applications in engineering

Question

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 7510 lb), the cost savings make it a good investment.

A schematic of the towing configuration is shown below. The car weighs 4964 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?

Explanation / Answer

T = mg sin x

T= tension in the tow string,
M= mass of the car,
x= angle made by the tow string with horizontal.

For the tow string to be worthy,
T bearable must be <= 7510 lb.
mgsinx < = 7510 lb.

if this is true, then the supplier is right.

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