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October 22, 2014

October 22, 2014

Posted by **anonymous** on Thursday, March 29, 2012 at 10:54pm.

- physics -
**Elena**, Friday, March 30, 2012 at 2:01pmImagine the points: A and B are the bottom and top hinges, respectively, O is the center of the door.

Use Lami’s Theorem(If three forces acting on a particle keep it in equilibrium, each is proportional to the sine of the angle between the other two, and the lines of forces are intersected in the same point).

Examine two similar triangles: OAB and the force triangle with following sides: gravity force (directed downwards), and reactions of bottom and top hinges,R(A) and R(B) (along the lines AO and BO, respectively):

mg/AB =R(A)/OA= R(B)/OB

OA = OB (as the hinges are located symmetrically)

AB = 2H/3

OA = sqrt ((H/3)^2 +(W/2)^2).

Then R(A) = R(B) = OA• mg/AB = sqrt ((H/3)^2 +(W/2)^2)• mg/(2H/3)

R(A) directed along AO (from A)

R(B) directed along AO (to B)

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