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 Rule Cosine 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 1The following three forces are in equilibrium find

the unknown forces labelled with letters.

R

4NS

200

Question 2The following three forces are in equilibrium find

the unknown forces labelled with letters.

300N

T

U

400

300

200

Poster Questions

θ0

A

B

C

100N

20N

30N

80N

450

200

600D

E

250

750

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)