1. Steps to Solving a Force Problem
1. Draw a Free Body Diagram
2. Resolve the forces to their X and Y components (aka use trigonometry)
3. Create a table of the forces in the X and Y direction.
4. Determine if the object is in equilibrium or accelerating.
5. Create an equation in the x direction and another in the y direction.
6. Solve equations for unknowns.

2. OBJECTS IN EQUILIBRIUM EXAMPLE
A traffic light weighing 100 N hangs from a vertical cable tied to two other cables that are fastened to a support. The upper cables make angles of 35°and 43° with the horizontal. Find the tension in each of the three cables.

4. Step 1
Draw any free body diagrams that may be useful to answer this question.
43o
35o

5. Step 2 Resolve Forces to X and Y components

6. Categorize as an equilibrium problem
The knot is a convenient place to draw an FBD because all forces in question act at this point.
Categorize as an equilibrium problem
No movement, so acceleration is zero
Model as an object in equilibrium

7. Apply equilibrium equation to light

8. Step 2 Resolve forces into x and y components. Force X Component
FT1
-FT1 cos 35
FT1 sin 35
FT2
FT2 cos 43
FT2 sin 43
FT3
-100 N

9. Step 3 Apply Equilibrium Equations In this case, to the knot
ΣFx = 0 = FT2cos43° + -FT1cos35°
FT2cos43° = FT1cos35°
FT2 = FT1(cos35°/cos43°)
FT2 = 1.12FT1
ΣFy = 0 =F T1sin35°+FT2sin43°+ -100
100 = FT1sin35°+1.12FT1sin43°
100 = FT1(.574)+1.12FT1(0.682)
100 = FT1(.574)+FT1(0.764)
100 = 1.338FT1
FT1= N

10. FT1 = N
FT2 = 1.12FT1
FT2 = 1.12(74.73 N)
FT2 = N
FT3 = W = 100N