Question

Consider the static equilibrium diagram here. What is the angle must make with the horizontal?F2 = 20 NF3 = 57 NW = 60 N

Answer 1

If the system is in equilibrium, then, it is necessary that the horizontal component of F1 equals F3. Then, you have:

`\begin{gathered} F_1\cos \theta=F_3 \\ F_1\cos \theta=57 \end{gathered}`

In order to find the angle, consider the vertical components of the forces:

`\begin{gathered} 20+F_1\sin \theta=60 \\ F_1\sin \theta=40 \end{gathered}`

Next, divide first and second equation to get tangent of the angle:

`\begin{gathered} (F_1\sin \theta)/(F_1\cos \theta)=(40)/(57) \\ \tan \theta=(40)/(57) \\ \theta\tan ^(-1)((40)/(57))\approx35 \end{gathered}`

Hence, the angle must be approximately 35 degrees.