travelling with vectors basically a lesson where we recap and apply everything we’ve learnt so far

Travelling with vectors

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

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

ContactDistortion,

FrictionBuoyancy

Non contact – Act at a distance

GravityElectricalMagnetic

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

10

72.12

22 710 F

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 => a2 = b2 + c2 – 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

400

40N

200

600

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

25N

40N

200

400

500

160 Abccba cos2222

160cos402524025 222 a

...38.41042 a

1.64aNF 1.64

Example 3

State the magnitude and bearing of the resultant.

N15

N10

25

7525

9015

Example 3


Abccba cos2222

130cos101521015 222 a

...83.5172 a ...75.22aNF 8.22

Example 3


N15

N10

25

75

N8.22

xsin

10

130sin

8.22

10

sin

8.22

130sin x

xsin...3359.0 x6.196.44

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 cos65650

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 Component30N

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

400

Question 2 – Find the vertical component.

25N

400


40N

750


36N

350


60N

1010

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)

travelling with vectors basically a lesson where we recap and apply everything we’ve learnt so far

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