Tension forces in a cable and reaction at the supports

Question

I made this problem to better understand how supports react to tension forces.

Here we have a weight Mg attached to a cable, the left side of the cable is angled at 10 degrees, while the right side is horizontal. The cable is supported by L2 and L1

Now what I am interested in knowing is how the supports L2 and L1 will react. I am assuming there will be no bending moments at either L2 and L1 as this is a cable.

Answer 1

Assuming that the posts are rigid (non deformable) and the rope is weightless, then pole L1 should experience only horizontal forces at the top (which will be converted to shear forces for the pole).

Additionally you are right that :

• there will be no bending moments transferred (because its a rope)
• the force on post L2 from the rope will be forming a 10$^o$ (clockwise) with the horizontal axis, and its vertical component should be equal to $Mg$. i.e. $$F_{L2} \sin(10^o) = Mg $$

therefore: $$F_{L2} = \frac{Mg}{\sin(10^o)} $$

and also for the force on the pole L1 ($F_{L1}$) the magnitude will be:

$$F_{L1} =F_{L2}\cos(10^o) \rightarrow F_{L1} =\frac{Mg}{\sin(10^o)}\cos(10^o) \rightarrow \boxed{F_{L1}= \frac{Mg}{\tan(10^o)}}$$

And the direction will be towards the left.