How Do You Calculate Tension in a Cantilever Cable System?

[slain4ever]

Homework Statement

A mass of 50kg is hung from the end of a cantilever 3m long. The cantilever weighs 6kg and is supported by a cable from the wall that is attached 0.5m from the end of the cantilever forming a 30 degree angle with the cantilever.
What is the tension in the wire?
What is the vertical and horizontal components of the force exerted by the wall on the shelf?

heres a picture i drew http://screencast.com/t/YjM4MmQ4M2Yt
it says 30 degrees, 2.5m, 0.5m and 50kg in case u can't read it
not pictured is the weight of the cantilever 0.6kg.

Homework Equations

torque = force * radius

The Attempt at a Solution

i'm very lost on this one.

my guess that clockwise torque would be = 60 * 1.5 + 500* 3 = 1590 (what is the units for torque?)

So this would mean that the ropes vertical component is 1590 right?
this gives a tension of 3180 ( =1590/sin(30) )

however the answers say the answer is 1300

which i have no idea how

 

[PhanthomJay]

Homework Statement

A mass of 50kg is hung from the end of a cantilever 3m long. The cantilever weighs 6kg and is supported by a cable from the wall that is attached 0.5m from the end of the cantilever forming a 30 degree angle with the cantilever.
What is the tension in the wire?
What is the vertical and horizontal components of the force exerted by the wall on the shelf?

my guess that clockwise torque would be = 60 * 1.5 + 500* 3 = 1590 (what is the units for torque?)

Torques are taken about a point..which point did you take? You are missing the torque from another force. Units for torque = force times length = Newton-meters

So this would mean that the ropes vertical component is 1590 right?

wrong.

this gives a tension of 3180 ( =1590/sin(30) )

however the answers say the answer is 1300

which i have no idea how

Why did you equate the vertical force to the torque? This is not correct. You might want to draw a free body diagram of the shelf and calculate the tension force by summing torques about the left support of the shelf (assuming a pinned support at that location capable of providing vertical and horizontal forces only). Note that the x and y components of the rope tension force are related by trig.