Sunday

February 1, 2015

February 1, 2015

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)

**Answer this Question**

**Related Questions**

physics - A door, essentially a uniform rectangle of height 2.00 m, width 0.78 ...

physics - A door, essentially a uniform rectangle of height 2.00 m, width 0.78 m...

Physics - A uniform 22 kg door that is 2.5 m high by 0.80 m wide is hung from ...

physiC - A uniform door (0.81 m wide and 2.1 m high) weighs 150 N and is hung on...

physics - A student opens a 12.0 kg door If the door is 2.00 m in height and 1....

PHYSICS! - A horizontal force of 10 N is applied to the outer edge of a door at...

Physics - uniform door (0.81 m wide and 2.1 m high) weighs 122 N and is hung on...

Physics - A uniform door (0.81 m wide and 2.1 m high) weighs 122 N and is hung ...

Physics - A uniform door (0.81 m wide and 2.1 m high) weighs 122 N and is hung ...

Math - A door frame that appears rectangular has height 80 in., width 32 in., ...