Chapter 12, Problem 79CP

In order to lift a shovelful of dirt, a gardener pushes downward on the end of the shovel and pulls upward at distance $l_2$ from the end, as shown below. The weight of the shovel is $m\stackrel{\to }{g}$ and acts at the point os application of ${\text{<mover accent="true"> <mi> F </mi> <mo> → </mo> </mover>}}_2$ . Calculate the magnitudes of the forces ${\text{<mover accent="true"> <mi> F </mi> <mo> → </mo> </mover>}}_1$ and ${\text{<mover accent="true"> <mi> F </mi> <mo> → </mo> </mover>}}_2$ as functions of $l_1$ , $l_2$ , mg, and the weight W of the load. Why do your answers not depend on the angle $\theta$ that shovel makes with the horizontal?