Statics: Equilibrant The condition of equilibrium How to solve Example Whiteboards (Demo: Force scales, masses)

Statics – acceleration = 0 Force Equilibrium - = 0 F1F1 F2F2 F3F3 Adding the three forces tip to tail: They add to zero

The Equilibrant is the opposite of the sum. 1.Add the given vectors 2.Negate the sum 3.Find its magnitude 4.Find some angle 5.Draw and label it

Find F, and  such that the system will be in equilibrium (This force is called the equilibrant) W A = 23 N B = 14 N F 29 o 56 o y x  Example: x y A B F Sum0 0

W A = 23 N B = 14 N F 29 o 56 o y x  Example: x y A B F Sum0 0 Find F, and  such that the system will be in equilibrium (This force is called the equilibrant)

W A = 23 N B = 14 N F 29 o 56 o y x  Example: x y A B F Sum0 0 Find F, and  such that the system will be in equilibrium (This force is called the equilibrant)

W A = 23 N B = 14 N F 29 o 56 o y x  Example: x y A B F Sum Mag = √( ) ≈ 26 N  = Atan(22.76/12.29) ≈ 62 o Trig angle = = 242 o 

Whiteboards: Equilibrant 1 | 2 TOC

Find the equilibrant for the forces indicated. Express as a magnitude and a trig angle 22.3 N at 64.5 o W A = 15.0 N B = 35.0 N 23.0 o 42.0 o y x x y A B Equil Sum0 0 Mag = √( ) ≈ N  = Atan(20.15/9.61) ≈ o 

Find the equilibrant for the forces indicated. Express as a magnitude and a trig angle 19.6 N at 24.5 o W A = 18.0 N B = 29.0 N 17.0 o 28.0 o y x x y A B C Equil Sum0 0 Mag = √( ) ≈ 19.6 N  = Atan(8.14/17.85) ≈ 24.5 o C = 12.0 N 12.0 o 