crane truck 01

This crane truck has a weight of 11250 lb and a center of gravity at CG. The parking brake only locks the rear wheels of the truck; the front wheels may roll freely. Therefore, the force exerted on the rear wheels by the ground consists of both a normal component and a tangential component, while the force exerted on the front wheels consists of a normal force only. If a = 6 ft, b = 8 ft, c = 5.5 ft, d = 5 ft, and h = 10 ft, determine the maximum force $F$ that can be exerted on the crane at an angle of $\theta$ = 27 degrees for the following two cases:

Case 1:
The tangential force on the rear wheel cannot exceed 0.8 times the normal force on the rear wheel.
(i.e. there is fairly good grip between the tires and ground)

Case 2:
The tangential force on the rear wheel cannot exceed 0.3 times the normal force on the rear wheel.
(i.e. the ground is more slippery)

Hint: There are two ways that the truck can fail to support the force. The rear wheels can slip backwards, or the truck can tip over backwards. You need to think about how each of these scenarios would be represented on a free-body diagram.

Case 1:
$F_{max}$ =

Case 2:
$F_{max}$ =

be sure to include units with your answers