EXAMPLE 5.0.6: APPLICATION OF MOMENT OF COPLANAR FORCES

The tow truck's front wheels will be lifted off the ground if the moment of the load W about the rear axle exceeds the moment of the 6200-lb weight of the truck. Determine the largest W that may be safely applied.

From the given condition,

                                                      

where



For Mw, we take the components of W as it is inclined. However, the question lies on what angle is W inclined.

We can solve for   using trigonometric laws but we have to start with identifying the triangle sides.




then





The hypotenuse of triangle is computed using Pythagorean theorem


                                 

Now, using sine law (or cosine law), we can determine .

                                

                                

                                

Then we can identify the components of W

                               

                             

Both Wx and Wy rotate clockwise so both are added. By using the original point where W acts

                              

                             

                             

Solve W

                              

                                                                ANSWER


A shorter way to solve is to slide force W to a point 10ft from the rear wheel. By placing the components at this point, Wx will be running through the rear wheel which will make the moment of Wx = 0.

                              

                              

Thus,

                              

                                                                 ANSWER


Discrepancy is due to rounding of numbers.

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