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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?