1
$\begingroup$

A 200×250 mm panel of mass 20 kg is supported by hinges along edge AB. Cable CDE is attached to the panel at C, passes over a small pulley at D, and supports a cylinder of mass m. Neglect the effect of friction.

For those who cannot see the picture. The axis are oriented as follows, x+ is pointing out and to the right, y+ is pointing up and z+ is out and to the left. $A=[0,0,.25]$ $ B=[0,0,0]$ $ C=[.2sin(\Theta),-.2cos(\theta),.125]$ $ D=[.2,.1,0]$

I have $\sum F_x=0=A_x+B_x+\frac {mg}{\lVert CD\rVert}(.2-.2sin(\theta))$

$\sum F_y =0=A_y+B_y-192.2+\frac {mg}{\lVert CD\rVert}(.1+.2cos(\theta))$

$\sum F_z=0=A_z+B_z+\frac {mg}{\lVert CD\rVert}(-.125)$

I am having trouble deciding where I want to make my moment in order to create a system I can solve for m in terms of $\theta$.

Static System in quesiton

$\endgroup$
1
  • 2
    $\begingroup$ You can take moments about anywhere you like, but it's usually a good plan to choose points where some of the force vectors have zero moment, and therefore don't appear in your equations. $\endgroup$
    – alephzero
    Oct 2 '16 at 3:11
0
$\begingroup$

Since you are only interested in the mass $m$, all you have to do is to set the moment about the hinge AB to zero for equilibrium.

This means you have to consider only the two forces $M g$ (panel weight) and $m g$, since only they contribute to the relevant moment.

(If you wish, I can work out the complete answer, but probably this is all you need to arrive at the answer yourself.)

For reference, my calculations give me the result for $m$ as $$ \frac{5 M \sin (\theta )}{\sin (\theta )+2 \cos (\theta )}$$

The plot shows that $m$ increases with $M$ and $\theta$ as expected.

enter image description here

An interesting confirmation is that the current configuration will not work for $\theta \gtrsim 2$.

enter image description here

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.