Which of the following is the odd one out?

MassSpeedForce

TemperatureDistanceElephant

DO NOW!

Which of the following is the odd one out?

MassSpeedForce

TemperatureDistanceElephant

DO NOW!

Scalars and vectors

Scalars

Scalar quantities have a magnitude (size) only.

For example:

Temperature, mass, distance, speed, energy.

Vectors

Vector quantities have a magnitude (size) and direction.

For example:

Force, acceleration, displacement, velocity, momentum.

Scalars and Vectors

scalars vectors

Magnitude (size)

No direction

Magnitude and direction

temperature mass

speed

velocity

forceacceleration

Representing vectors

Vectors can be represented by arrows. The length of the arrow indicates the magnitude, and the direction the direction!

Representing velocity

Velocity can also be represented by an arrow. The size of the arrow indicates the magnitude of the velocity, and direction the direction!

When discussing velocity or answering a question, you must always mention the direction of the velocity (otherwise you are just giving the speed).

Adding vectors

When adding vectors (such as force or velocity) , it is important to remember they are vectors and their direction needs to be taken into account.

The result of adding two vectors is called the resultant.

Adding vectors

For example;

6 m/s 4 m/s 2 m/s

4 N

4 N 5.7 N

Resultant force

Resultant force

How did we do that?

How did we do that?

4 N4 N

5.7 N

4 N

4 N

Scale drawing

You can either do a scale drawing

4 cm

4 cm

1 cm = 1N

θ = 45°

θ

Or by using pythagorous and trigonometry

4 N

4 N

Length of hypotenuse = √42 + 42 = √32 = 5.7 N

Tan θ = 4/4 = 1, θ = 45°

Subtracting vectors

For example;

6 m/s 4 m/s 10 m/s

4 N

4 N 5.7 N

Resultant velocity

Resultant force

Subtracting vectors

For example;

4 N

4 N

5.7 N

An interesting example

Think of a dog (dead) orbiting the earth with constant speed (in a circle).

An interesting example

At this point, what is its velocity?

velocity?

An interesting example

velocity

An interesting example

velocity?

What is its velocity here?

An interesting example

velocity

As you can see the velocity has changed as it is now going in another direction.

An interesting example

velocity

In uniform circular motion, we have constant speed but changing velocity.

Of course a changing velocity means it must be accelerating! We’ll come back to this next year!

Resolving vectors into components

Resolving vectors into components

It is sometime useful to split vectors into perpendicular components

Resolving vectors into components

A cable car question

Tension in the cables?

10 000 N

?? 10°

Vertically 10 000 = 2 X ? X sin10°

10 000 N

?? 10°

? X sin10° ? X sin10°

Vertically 10 000/2xsin10° = ?

10 000 N

?? 10°

? X sin10° ? X sin10°

? = 28 800 N

10 000 N

?? 10°

? X sin10° ? X sin10°

What happens as the angle deceases?

10 000 N

?? θ? = 10 000/2xsinθ

Error bars

• X = 0.6 ± 0.1• Y = 0.5 ± 0.1

Gradients

Minimum gradient

Maximum gradient

y = mx + c

y = mx + c

• Ek = ½mv2

y = mx + c

• Ek = ½mv2

Ek (J)

V2 (m2.s-2)

Let’s try some questions!

Resultant of forces (addition of vectors)

Page 13 Questions 1 to 6

Sorry, I nearly forgot!

Resultant force