Question

determining the net force
consider a sign suspended on a boom that is supported by a cable, as shown. what is the proper equation to use for finding the net force in the y direction?
$f_{nety}=(f_{t})(\sin 32^{\circ})+f_{g}$
$f_{nety}=(f_{t})(\sin 32^{\circ})-f_{g}$
$f_{nety}=(f_{t})(\cos 32^{\circ})+f_{g}$
$f_{nety}=(f_{t})(\cos 32^{\circ})-f_{g}$

Explanation:

Step1: Analyze Force Components

The tension force \( F_T \) has a vertical component. To find the vertical (y - direction) component of \( F_T \), we use the sine function because the angle is measured with respect to the horizontal. The vertical component of \( F_T \) is \( F_T\sin(32^{\circ}) \) (upward), and the gravitational force \( F_g \) is downward.

Step2: Determine Net Force in y - direction

Net force in the y - direction is the sum of the upward forces minus the downward forces. The upward force is the vertical component of \( F_T \) (\( F_T\sin(32^{\circ}) \)) and the downward force is \( F_g \). So the net force in the y - direction \( F_{nety}=(F_T)\sin(32^{\circ})-F_g \) (since upward is positive and downward is negative, we subtract the downward force \( F_g \) from the upward component of \( F_T \)).

Answer:

\( F_{nety} = (F_T)(\sin 32^{\circ}) - F_g \) (the second option)