Embed Size (px)
Citation preview
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
force
acceleration
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
