How Do You Calculate Tension in a Cable and Force on a Hinge?

[confused111]

Homework Statement

A 20 kg uniform beam 10m long is attached to a wall with a cable.
The cable is attached to the middle of the beam at 90º
to the beam. A box of mass 50 kg is suspended from the beam as shown.
Determine the tension in the cable.
Determine the force acting on the hinge at the bottom.

Homework Equations

The Attempt at a Solution

I tried to do the first part like this:
(((20/sin50)x5)+50sin40x10x9.8)/5=656N

 

[SteamKing]

Working a problem like this 'by the seat of your pants' rarely gives the correct result.

You should draw a proper free body diagram and show all the forces acting on the beam

Once you have done that, then you should be able to write the equations of static equilibrium and solve for the unknown tension.

BTW, we are all big boys and girls here at PF, so writing 'x' every time you want to indicate multiplication is very confusing, especially since 'x' often is used to indicate an unknown quantity.

 

[Rellek]

Hey there!

I think we are assuming that the system is in equilibrium.

If this is the case, you can use the equilibrium equations to solve this:

$\sum F_{x} = 0$
$\sum F_{y} = 0$
$\sum M_{p} = 0$