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Part (a) Choose the correct free-body diagram for the door. F, Mg Mg F. F. F Mg F Mg F Part (b) Calculate the force, in newtons with its sign, that the upper hinge exerts on the door in the x-direction. Part (c) Calculate the force, in newtons with its sign, that the lower hinge exerts on the door in the x-direction.

Part (a) Choose the correct free-body diagram for the door. F, Mg Mg F. F. F Mg F Mg F Part (b) Calculate the force, in newtons with its sign, that the upper hinge exerts on the door in the x-direction. Part (c) Calculate the force, in newtons with its sign, that the lower hinge exerts on the door in the x-direction.

International Edition---engineering Mechanics: Statics, 4th Edition
International Edition---engineering Mechanics: Statics, 4th Edition
4th Edition
ISBN:9781305501607
Author:Andrew Pytel And Jaan Kiusalaas
Publisher:Andrew Pytel And Jaan Kiusalaas
Chapter1: Introduction To Statics
Section: Chapter Questions
Problem 1.20P: Find the elevation h (km) where the weight of an object is one-tenth its weight on the surface of...
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It is common to hang objects on doorknobs and over-the-door hooks. There is a (а) limit to the amount of weight that a door can hold because of the forces exerted on the hinges. A door of height h= 2.2 m and width h/2 has a mass of M= 33 kg. The mass is distributed uniformly, so the center of mass is located at the geometric center of the door. One hinge is located a distance h/4 from the top of the door. The second hinge is a distance h/4 from the bottom of the door. Refer to (a) in the figure. The door's weight is supported entirely by the two hinges and each hinge supports half of the weight. In other words, the vertical force exerted by each hinge is exactly one half of the total weight, including any additional load. For this problem, take the positive y-direction to be directly upward and the positive x-direction pointing from the hinge side of the door to the knob side. -h/2 h14 H Hinge 1 |Hinge 2 h/4 (b) (c) |-h/4--h/4- mg F. =? Lx F. Mg mg Mg h/2
Transcribed Image Text:It is common to hang objects on doorknobs and over-the-door hooks. There is a (а) limit to the amount of weight that a door can hold because of the forces exerted on the hinges. A door of height h= 2.2 m and width h/2 has a mass of M= 33 kg. The mass is distributed uniformly, so the center of mass is located at the geometric center of the door. One hinge is located a distance h/4 from the top of the door. The second hinge is a distance h/4 from the bottom of the door. Refer to (a) in the figure. The door's weight is supported entirely by the two hinges and each hinge supports half of the weight. In other words, the vertical force exerted by each hinge is exactly one half of the total weight, including any additional load. For this problem, take the positive y-direction to be directly upward and the positive x-direction pointing from the hinge side of the door to the knob side. -h/2 h14 H Hinge 1 |Hinge 2 h/4 (b) (c) |-h/4--h/4- mg F. =? Lx F. Mg mg Mg h/2
Part (a) Choose the correct free-body diagram for the door. F, Me 2y F. F, F Mg F. 2x 2x Part (b) Calculate the force, in newtons with its sign, that the upper hinge exerts on the door in the x-direction. Part (c) Calculate the force, in newtons with its sign, that the lower hinge exerts on the door in the x-direction. Part (d) A bag of mass m = 14 kg is hung on the doorknob, which is located a distance h/2 from the bottom of the door. To make the math easier, you may assume that the load is exerted on the right edge of the door. Refer to (b) in the figure. Calculate the force, in newtons with its sign, that the upper hinge exerts on the door in the x-direction. Part (e) The same bag of mass m = 14 kg is now hung on a hook in the middle of the top of the door. Refer to (c) in the figure. Calculate the force, in newtons with its sign, that the upper hinge exerts on the door in the x-direction.
Transcribed Image Text:Part (a) Choose the correct free-body diagram for the door. F, Me 2y F. F, F Mg F. 2x 2x Part (b) Calculate the force, in newtons with its sign, that the upper hinge exerts on the door in the x-direction. Part (c) Calculate the force, in newtons with its sign, that the lower hinge exerts on the door in the x-direction. Part (d) A bag of mass m = 14 kg is hung on the doorknob, which is located a distance h/2 from the bottom of the door. To make the math easier, you may assume that the load is exerted on the right edge of the door. Refer to (b) in the figure. Calculate the force, in newtons with its sign, that the upper hinge exerts on the door in the x-direction. Part (e) The same bag of mass m = 14 kg is now hung on a hook in the middle of the top of the door. Refer to (c) in the figure. Calculate the force, in newtons with its sign, that the upper hinge exerts on the door in the x-direction.
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