EQUILIBRIUM!! Aims: To know a variety of strategies to solve equilibrium problems.

Newton’s First Law Definition Every object remains in a state of rest or uniform motion in a straight line unless forces act on it to change that state. Standing still Constant velocity

What do we mean by equilibrium? The resultant of all forces equals ZERO If an object is at rest is stays at rest. If an object is in motion it continues with the same motion.

Triangle method for equilibrium If 3 forces are in equilibrium, they should form a closed triangle when placed end to end. You can think of it as if you followed all three forces separately you would end up back where you started from. P Q R P Q R

Why is this a useful method? Because if the forces form a right angled triangle we can use Pythagoras and trigonometry. If they form a non right angled triangle we can use the sine rule and the cosine rule! Sine RuleCosine Rule

Resolving forces in equilibrium If a number of forces are in equilibrium then in both directions you choose to resolve the resultant force must equal zero. Forces to the Right = Forces to the Left Forces Up = Forces Down

Question 1 The following three forces are in equilibrium find the unknown forces labelled with letters. R 4N S 20 0

Question 2 The following three forces are in equilibrium find the unknown forces labelled with letters. 300N T U

Poster Questions θ0θ0 A B C 100N 20N 30N 80N D E Solve each question to find the values of the missing forces and angles. You can choose to solve using either method. Easy Medium Hard

Extension

Summary You can use either method. Is there a way to tell when one method is preferable? Advice: try to resolve first, if this leaves you with two simultaneous equations you don’t know how to solve, then try a triangle. (but remember you can use the calculator to help solve.)

Independent Study Exercise C p 61 (solutions p 150)