Question

The crane truck has a weight of 11750 lb and a center of gravity at point CG. The parking brake only locks the rear wheels of the truck, so the front wheels are free to rotate. Determine the maximum force F applied at the angle = 32.5° that can be exerted on the crane without it slipping or tipping for each of the following cases: Case 1: The static friction coefficient between the rear tires and the ground is pe = 0.16. Case 2: The static friction coefficient between the rear tires and the ground is po = 0.42. 2013 Michael Swanbom BY NC V kak b * c - Values for dimensions on the figure are given in the following table. Note the figure may not be to scale. Variable Value 7 ft b 9 ft C 6 ft d 4.5 ft h 10.5 ft For Case 1, the constraint is Select an answer and Fmax = For Case 2, the constraint is Select an answer and Fmax =

Answer 1

For case 1:

To not slip:

$\small F\times\sin\theta<\mu(W+F\times\cos\theta)$

$\small F\times\sin(32.5\degree)<0.16(11750+F\times\cos(32.5\degree))$

$\small F<4672.47\hspace{2mm}lb$

To not tip about rear wheel,

$\small F\cos\theta\times c+F\sin\theta\times h<W\times b$

$\small F\cos(32.5\degree)\times6+F\sin(32.5\degree)\times10.5<11750\times9$

$\small F<9881.33\hspace{2mm}lb$

Therefore,

$\small F_{max}\approx4672.47\hspace{2mm}lb$

For case 2:

To not slip:

$\small F\times\sin\theta<\mu(W+F\times\cos\theta)$

$\small F\times\sin(32.5\degree)<0.42(11750+F\times\cos(32.5\degree))$

$\small F<26956.13\hspace{2mm}lb$

To not tip about rear wheels:

$\small F\cos\theta\times c+F\sin\theta\times h<W\times b$

$\small F\cos(32.5\degree)\times6+F\sin(32.5\degree)\times10.5<11750\times9$

$\small F<9881.33\hspace{2mm}lb$

Therefore,

$\small F_{max}\approx26956.13\hspace{2mm}lb$