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.

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.

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

Step 2 Resolve Forces to X and Y components

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

Apply equilibrium equation to light

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

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= 74.74 N

FT1 = 74.73 N FT2 = 1.12FT1 FT2 = 1.12(74.73 N) FT2 = 83.71 N FT3 = W = 100N