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 toevaluate 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 of8170 lb), the cost savings make it a good investment.

A schematic of the towing configuration is shown below. The car weighs 5.570 × 103 lb, which is as large as the company expects their tow trucks to service. Calculatethe 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 itslength, 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 maintainno acceleration in the system.

Answer 1

As car is just lifted from ground that means normal reaction of
front tire will decrease to zero.

and all normal force will shift to rear tire.

and normal force and friction force will on rear tire.

hence balancing moment about ground touching point of rear tire.

Horizontal distance of cable point from rear tire = 10.9 - ( (10.9-9.81)/2) = 10.355 ft

Net torque/moment = (9.81/2 * 5671) - ( 10.355 * Tsin48) + (0.3 *Tcos48)   = 0

27816.255 = 7.695 T - 0.2T

T = 3711.67 lb