The physics associated with statics has considerable applications in engineering. As a mechanical engineer working for a towtruck 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 $6280$ lb $),$ the cost savings make it a good investment.

A schematic of the towing configuration is shown.

The car weighs $4358$ lb $,$ which is as large as the company expects their tow trucks to service. The overall length $L$ of the car is $10\mathrm{.}7$ ft $,$ and the distance $d$ between the midpoints of the front and back tires is $9\mathrm{.}63$ 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 $$ between the midpoint of the tires and the tow cable is $48\mathrm{.}0.$

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.

$T=$

lb