When we solve problems using forces, we are usually careful to split the forces

Question

When we solve problems using forces, we are usually careful to split the forces into, for example, horizontal and vertical components, and then consider the horizontal forces separately from the vertical forces. We actually don't do this for torques - both horizontal and vertical forces can be considered in the same torque equation. This situation is an example.

The picture above shows one of your kitchen cabinet doors. The lower hinge on the door has broken, and the upper hinge is represented by the black circle with the red center near the top left. If the upper hinge was the only support point, the force of gravity acting on the door would cause the door to move clockwise, finding a new equilibrium with the door askew, and the center of gravity located directly under the hinge. To prevent this from happening (to keep the door in equilibrium in the position shown in the picture above, that is), you have tied a horizontal string to the bottom right corner of the door - the tension in the string is shown on the diagram. Also shown are some relevant distances. The relative magnitudes of the two forces are not necessarily represented correctly on the diagram.

The force of gravity acting on the door has a magnitude of mg = 1.20 N.

(a) Which has a larger magnitude, the force of gravity acting on the door or the force of tension in the string?

(b) Determine the magnitude of the tension in the string. (N)

FBD1 FBD2 FBD3

(c) Which of the free-body diagrams above represents the full free-body diagram of the door (not worrying about the relative sizes of the forces, just about the forces and their directions)? Additional forces shown on FBD 2 and 3, compared to FBD 1, represent the horizontal and vertical components of the force applied by the hinge on the door.

Explanation / Answer

a) weight is clockwise moment, tension is anticlockwise moment, hinge is pivot clockwise moment = anticlockwise moment mgd = 3Fd Since mg = 1.2, F = 0.4, so the weight is larger b) already done above c)FBD3 is correct, since it shows how the hinge has a vertical component equal to the vertical component of weight, as well as the horizontal component equal to the horizontal component of tension required to keep the door in equilibrium.

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