# Free body diagram problem: Linkage w/ magnets and friction hinge

I am a bit stumped on a IRL problem, which i simplified in the diagram below:

There are left and right beams (gray) linked together by a friction hinge. The bottom beam (black) is connected to the left and right beam by a frictionless pivot point (on the right), and another frictionless pivot point w/ a slider (on the left). There are magnets (green) embedded on the left and right beams that are attracting the magnets embedded on the bottom beam.

Given the following variables:

distances/lengths: A,H,B and C

torque of the friction hinge: T_friciton_hinge

attraction force of magnet: F_magnet1 and F_magnet2

Assume perfectly rigid beams.

Solve the maximum downward force (F_load) possible before the friction hinge rotates

Here what I tried to do to solve for F_load:

Let me know if my thought process is unreasonable.

• Some questions. -Is the black beam flexible? If not, why include it on the diagram? -The slider at the left end should give a vertical reaction (if not, it would not be a slider, just a free end), which makes $F_{load}$ redundant. -Is the hinge a "static friction" kind of thing? i.e. no rotation until a threshold moment is surpassed? Apr 11 at 3:26
• Hi @Zegpi, assume black beam is rigid. If you apply an excessive F_load, this would happen: imgur.com/a/tY9OyqH, where the friction hinge would rotate, and the magnets would separate. Hope this makes sense. Yep, assume static friction for the hinge. Apr 12 at 18:36
• Got it about the hinge and the black bar, but what about the slider? As presented, F_load has no effect on the gray beam, as it will go directly to the black bar. As it's presented, your system looks like it simplifies to this diagram imgur.com/a/R5bKAmc . Apr 19 at 20:01