A door 1.84 m high and 1.11 m wide has a mass of 29.8 kg . A hinge 0.30 m from t

Question

Explanation / Answer

W = width of door = 1.11 m
L = length of door = 1.84 m
m = mass of door = 29.8 kg
g = acceleration due to gravity = 9.8 m/s^2
R = vertical distance between hinges = 1.84 - 2*0.30 = 1.24 m

Let location A be the upper hinge and location B be the lower hinge:
Ax = horizontal force component on hinge A
Ay = vertical force component on hinge A
Bx = horizontal force component on hinge B
Ay = vertical force component on hinge B

Since each hinge is said to support half the weight of the door, a simple vertical force balance on the door shows:

Ay + By = m*g
Ay = By = m*g / 2 =(29.8*9.8)/2 =146.02 N

Now summing the moments on the door about hinge A, we have:
R*Bx - (W/2)*m*g = 0
Bx = W*m*g/(2*R)
Bx = 1.11*29.8*9.8/(2*1.24)
Bx = 200.98 N

Now summing the moments on the door about hinge B, we have:
R*Ax - (W/2)*m*g = 0
Ax = W*m*g/(2*R)
Ax = 1.11*29.8*9.8/(2*1.24)
Ax = 200.98 N

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