A door of width 1.07 m and height 2.29 m weighs 286 N and is supported by two hi

Question

A door of width 1.07 m and height 2.29 m weighs 286 N and is supported by two hinges, one 0.40 m from the top and the other 0.40 m from the bottom. Each hinge supports half the total weight of the door.

Question: Assuming that the door's center of gravity is at its center, find the horizontal components of force exerted on the door by each hinge.

Answer is NOT:

87.4 N

99.9 N

100 N

Problem 11.44 Part A A door of width 1.07 m and height 2.29 m weighs Assuming that the door's center of gravity is at its center, find the horizontal components of force exerted on the door by each hinge. N and is supported by twoh from the top and the other 0.40 m from the bottom. Each hinge supports half the total weight of the door. Submit My Answers Give Up Incorrect; Try Again; 3 attempts remaining Not quite. Check through your calculations; you may have made a rounding error or used the wrong number of significant figures. Provide Feedback Continue

Explanation / Answer

W = width of door = 1.07 m
L = length of door = 2.2.9 m
R = vertical distance between hinges = 2.29 - 2*0.40 = 1.49 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 = 286 / 2 = 143 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) = 1.07*286 / 2*1.49 = 102.7 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) = 1.07*286 / 2*1.49 = 102.7 N

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