A question i am having trouble with.

[scguy]

This question is out of my study guide but i am not sure if it can even be answered as it does not say how long the rod is.

 

G= 10ms^2

 

Q: A uniform rod of mass 20kg is hinged at its lower end and supported at 60deg to the verical by a horizontal string attached to its upper end. The upper end of the rod carries a load of 40kg. Find the tension in the string.

 

 

Now, surely if i dont know the length of the rod then it could be 1000m long or 1mm which would give very different moments about the axis at the hinged end and hence different tensions in the string. Either i am completely missing the point here or this has to be a typo.

[swansont]

I think you'll find the length doesn't matter. The two torques (from the tension and from the weight) scale with the length, so it should cancel out in the final result.

[scguy]

I dont know why i didnt just assign an arbitrary value to the length, the further from the horizontal the more leverage the supporting wire gains and also the ratio still remains constant, i feel so stupid now

[ydoaPs]

why would you assign a value?

[swansont]

why would you assign a value?

 

You might assign it an arbitrary length L, which would then cancel out of the equations you set up. But I've noticed some students actually want to assign and calculate numerical values in intermediate steps rather than manipulate the variables. It's a really bad habit to get into.

[ydoaPs]

i would have just used L and let it cancel itself out.

[swansont]

i would have just used L and let it cancel itself out.

 

And that would be the right way to do it.