Choosing an Axis of Rotation for Equilibrium Analysis

[Taulant Sholla]

Homework Statement

I can get the answer to this problem, but...

Relevant Equations

torque and force equilibrium

If I choose my axis of rotation for torque analysis to be the left-end of the plank, I can get the correct results.

If I instead choose the com point -- I run into a dead end. Is there a way of a priori knowing this would happen? Thank you.

 

[BvU]

I run into a dead end

Can you show ?

 

[Taulant Sholla]

Here's my work based on using the COM as my axis of rotation. It seems I can't solve for x this way?

 

[BvU]

You introduce angles $a$ and $b$ and now have too many unknowns ? Is that what you mean ?

$\$

 

[Taulant Sholla]

I can find angle a and angle b. Despite this it seems I still can't find x from equations 2, 3 and 4.

 

[BvU]

Ok, so you have three equations with three unknowns, so what is going wrong ?

$\$

 

[cj]

I think there are 4 unknowns: Tr, Tl, m and x.

 

[robphy]

I think there are 4 unknowns: Tr, Tl, m and x.

Do you need to know m to find x?

(Tr/m), (Tl/m), and x are the unknowns.

 

[Taulant Sholla]

Ah, yes - I see. Thank you so much for your help!