Travelling with vectors Basically a lesson where we recap and apply everything we’ve learnt so far.

SOHCAHTOA with vectors You can also turn a vector into horizontal and vertical components.

Forces Know how to draw force diagrams Understand how to find the resultant of 2 forces. To be able to find components of forces. & the resultant of more than two forces using components

What is a force? Something that causes an object to change speed OR change direction OR change shape Contact Distortion, Friction Buoyancy Non contact – Act at a distance Gravity Electrical Magnetic Types of forces Units? Newtons (Named after Sir Isaac Newton)

Force Diagrams In groups draw on all the forces for each diagram. Try to name all the forces. Consider carefully where to label them.

Book on a table

Apple on a tree

Ship at sea

Space shuttle launch

Tug of war

Ice hockey puck

Treating forces as vectors We can use all the same ideas we have looked at with vectors for velocity and displacement with forces. The main case is setting up vector triangles again to find the resultant force. Lets have a quick reminder!

The triangle method P P Q Q R To find the resultant of the two forces P and Q we can make them into a triangle. This is done by drawing them tip to tail. The resultant is the direct route from one end to the other

Find the resultant of two forces A and B. When A = 10i and B = 7j Example 1

The triangle method Why is this method useful? Because we can use the sine and cosine rules from Core 2. Sine rule => a=b=c sinA sinB sinC Cosine rule => a 2 = b 2 + c 2 – 2bc cosA Remember you must learn the Sine Rule The Cosine Rule is given in the Formula booklet

Example 2 Find the magnitude of the resultant of the two forces. 25N N

Example 2 Find the magnitude of the resultant of the two forces. 25N 40N

Example 3 State the magnitude and bearing of the resultant.

Example 3 State the magnitude and bearing of the resultant.

Example 3 State the magnitude and bearing of the resultant.

Splitting forces into components Sometimes we may not want to set up forces into a triangle. In these situations we may use an alternative method of finding components. This means splitting up a force into two parts. Usually this will be into their horizontal and vertical components.

30 cos If you know the angle between the force and the component you always use cosine If you do not know the angle between the force and the component you always use sine Horizontal Component Vertical Component 30N 30 sin65

Quiz Time Write down the number 1-8. Write down the calculation to find the desired component. Use your calculator to find the magnitude of the component to 3 significant figures. 2 marks for each question.

Question 1 – Find the horizontal component. 25N 40 0

Question 2 – Find the vertical component. 25N 40 0

Question 3 – Find the horizontal component. 40N 75 0

Question 4 – Find the vertical component. 40N 75 0

Question 5 – Find the horizontal component. 36N 35 0

Question 6 – Find the vertical component. 36N 35 0

Question 7 – Find the horizontal component. 60N 101 0

Question 8 – Find the vertical component. 60N 101 0

Splitting into components A resultant for two or more forces can be found by splitting all forces into their horizontal and vertical components. You can then find the total horizontal and vertical component. This allows you to set up a triangle in the same way as earlier. This will always be a right angled triangle meaning that you can the use: – Pythagoras to find the magnitude. – And trigonometry to find the angle.

Find the magnitude and direction of the resultant force.

Independent Study Equilibrium Example Video Exercise A p56 (solutions p149)