Forces in Two Dimensions - Mission F2D4 Detailed Help

A sign is hung by two cables, each of which makes an angle of theta with the horizontal. As the angle theta is INCREASED (or DECREASED), the weight of the sign ____; the tension force in the cable ____; and the vertical component of the tension force ____.

Definition of Equilibrium:
is the condition in which all the individual forces acting upon an object are balanced.

If the sign remains at equilibrium, then all three individual forces that are acting upon it must remain balanced as the angle Thetais changed. A change in the angle will affect the amount of horizontal pull in the cable that in turn affects the amount of tension in the cable. The more horizontally aligned the cable is, the more it will pull horizontally. Thus, a decrease in the angle Thetawill increase the horizontal component of tension and an increase in the angle Thetawill decrease the horizontal component of tension. These changes in the horizontal components will result in the same change in the overall tension in the cable.

Some students who have difficulty with the concept of weight will have difficulty with this question. The weight of a sign depends upon its mass. Don't be fooled! Changes in the cables that support the sign will not effect the sign's weight.

Other difficulties with this question relate to the vertical component of the tension force. For a sign hung symmetrically by two cables, the weight of the sign is distributed equally to the two cables. Thus, the upward pull (vertical only) of the cables is one-half the weight of the sign. Changes in the angle Thetawill affect the horizontal component of tension; but the vertical component of tension must be of sufficient value to balance one-half the weight of the sign.


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