1. Forces & Equilibrium

2. Equilibrant Forces Equilibrant – A single, additional force that is exerted on an object to produce equilibrium, which is the same magnitude as the resultant force but opposite in direction Equilibrant – A single, additional force that is exerted on an object to produce equilibrium, which is the same magnitude as the resultant force but opposite in direction

3. Creating Equilibrium Hanging Sign A 168-N sign is supported in a motionless position by two ropes that each make 22.5  angles with the horizontal. What is the tension in the rope? A 168-N sign is supported in a motionless position by two ropes that each make 22.5  angles with the horizontal. What is the tension in the rope? sign ΘΘ

4. Creating Equilibrium FAFA Given  = 22.5  Fg = 168-N FBFB FgFg Unknown FA = ? FB = ?

5. Creating Equilibrium FAFA Given  = 22.5  Fg = 168-N FBFB FgFg Unknown FA = ? FB = ? ΘΘ

6. Creating Equilibrium Notice that each tension force (F T ) can be broken down into its x and y components. Notice that each tension force (F T ) can be broken down into its x and y components.

7. Creating Equilibrium Each string holds half of the weight b/c the angles are the same Each string holds half of the weight b/c the angles are the same Therefore the y component for each string is half of F g (168N / 2 = 84N) Therefore the y component for each string is half of F g (168N / 2 = 84N) Simple trig  sinΘ = Opp/Hyp Simple trig  sinΘ = Opp/Hyp Solve for Hyp (aka F T ) Solve for Hyp (aka F T )

8. Creating Equilibrium FAFA Given  = 22.5  Fg = 168-N FBFB FgFg Unknown FA = ? FB = ? ΘΘ 84N

9. Creating Equilibrium sin 22.5° = 84N / Hyp sin 22.5° = 84N / Hyp Hyp = 84N /(sin 22.5) Hyp = 84N /(sin 22.5) F T = Hyp = 220N F T = Hyp = 220N

10. Hanging Sign Practice Problem A 150-N sign is suspended by two wires that make an angle of 130  with each other. The tension in the wires are equal. A 150-N sign is suspended by two wires that make an angle of 130  with each other. The tension in the wires are equal. Draw a pictorial diagram Draw a pictorial diagram Draw a free-body diagram Draw a free-body diagram What is the tension in the wires What is the tension in the wires