A door 2.30 m high and 1.30 m wide has a mass of 13.8 kg. A hinge 0.40 m from th

Question

A door 2.30 m high and 1.30 m wide has a mass of 13.8 kg. A hinge 0.40 m from the top and another hinge 0.40 m from the bottom each support half the door's weight. Assume that the center of gravity is at the geometrical center of the door, and determine the magnitude of the horizontal force component exerted by each hinge on the door. Enter your answers numerically separated by a comma. Determine the vertical force component exerted by each hinge on the door. Enter your answers numerically separated by a comma.

Explanation / Answer

You need to use torques (moments)
The CoG is 1.3/2 = 0.65m away from the hinges horizontally.
The hinge separation is 2.3 - 0.4 - 0.4 = 1.5m.
Suppose the top hinge exerts a force with components FTx and FTy.
Taking moments about the lower hinge:
(13.8x9.81) x (0.65) = FTx * 1.5
FTx = 58.6N
The only other horizontal force is the horizontal component of force ar the bottom hinge, FBx; so this must be FBx = -58.6N (i,e, direction 'into' door)

(B)To get the vertical force (FTy and FBy both acting upwards) we note
FTy + FBy = 13.8x9.81 = 135.37N
By symmetry FTy = FBy = 135.37/2 = 67.69N

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