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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 $7840$ lb $),$ the cost savings make it a

good investment.

A schematic of the towing configuration is shown.

The car weighs $5065$ lb $,$ which is as large as the

company expects their tow trucks to service. The

overall length L of the car is $10\mathrm{.}5$ ft $,$ and the

distance d between the midpoints of the front and

back tires is $9\mathrm{.}45$ ft $.$ The bottom of the car's frame

is a height h$\_($f$)=0\mathrm{.}300$ above the ground, and the

car's center of mass is a height h$\_($CM$)=1\mathrm{.}50$ above

the bottom of the car's frame. The angle phi

between the midpoint of the tires and the tow cable is $44\mathrm{.}0^($@$).$

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 T 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.