FACULTY OF SCIENCE Physics Bridging Course Chapter 3 VECTORS AND MOTION IN 2 3 DIMENSIONS School of...

FACULTY OF SCIENCE

Physics Bridging Course Chapter 3VECTORS AND MOTION IN 2 & 3 DIMENSIONS

School of Physics

Questions from last lecture/tutorial?

Welcome to the 2nd dimension!

› So far one dimension only - Straight lines!

› The real world has 3 dimensions.

› This slide has 2 :

- up/down

- left/right

2 Dimensions

To describe something in 2 dimensions

You need 2 quantities

Vectors and Scalars

Vectors have

› Magnitude

› Direction

Examples: Vectors & Scalars

Vectors› Displacement

› Velocity

› Acceleration

› Force

› Electric field

› Magnetic fields

› Gravity

Scalars› Distance

› Speed

› Energy

› Temperature

› Mass

› time

Q: What do you get when you cross a mosquito with a climber?

Working with Vectors

Vectors are tricky to add up:

Sydney Uni

Central

Fish & Chips

Pub

A: Nothing, you can’t cross a vector with a scalar

Working with Vectors

“Resolve them into their components”:

33 + = 6

HorizontalComponent

Working with Vectors

“Resolve them into their components”:

24 - = 2

VerticalComponent

TRIG is your friend!

a

x

y

ay

ax

Horizontal

cos = ax/a

ax = a cos

TRIG is your friend!

a

x

y

ay

ax

Vertical

sin = ay/a

ay = a sin

Unit vectors

a

x

y

ay

ax

a + b = easy!

a

b

a + b

a

b

a - b = ?!

a

b

a - b

a

b

-b

Working backwards…

a

x

y

ay

ax

Magnitude a2 = ax

2 + ay2

Directiontan = ay/ax

Vectors are everywhere

Vector addition works well for displacement and:

› Velocity

› Acceleration

› Forces

Or any other vector quantity…

Worked Example

› I drive to Newcastle, (200 km north and 15 km east of Sydney).

› Then I drive to Mudgee, (130km west and 50 km north of Newcastle).

How far am I from Sydney?

Questions?

Chapter 3 continued: Projectiles

Questions from last lecture/tutorial?

Projectiles

Any object travelling in free-fall is called a projectile.

The physics is quite simple (if you neglect air resistance etc)

“Free fall” does NOT mean falling downwards

Free fall means accelerating downwards with a = g, i.e. at the acceleration due to gravity i.e. under the influence of gravity only

Path of a projectile

› The path of a projectile is parabolic- Or rather, the path of its centre of mass is parabolic

› The projectile moves in two dimensions, horizontally and vertically- That’s why we learnt all about vectors…

Question

One egg is thrown off a cliff. Another egg is dropped at the same time.

Which hits the ground first ?

Bullet fired vs droppedhttp://www.youtube.com/watch?v=D9wQVIEdKh8

Hint

Horizontal and Vertical components are independent.

› What is the vertical acceleration in each case?

› What is the horizontal acceleration in each case?

Let’s do an experiment!

Answer

› The two objects take exactly the same time to fall.

› The vertical and horizontal components of the motion are independent.

Horiz motion: a = 0 Vert motion: a = -9.8 m/s2

Bullet fired vs droppedhttp://www.youtube.com/watch?v=D9wQVIEdKh8

Velocity of a projectile

v

x

y

vy

vx

Vy is affected by gravity

Vx is not

Q: Dropping a package

› A rescue plane flying at 1200 m elevation at 430 km/h approaches a person struggling in the water. At what distance should the pilot release a rescue capsule if it is to strike the water close to the person?

Conditions Apply

› Air resistance

› Spin/slice/swing

› These apply additional forces which we don’t take into account at this stage (too complicated).

Ski Jump on Moon

› Worked example

Questions?