Which of the following is the odd one out?

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DO NOW!
Which of the following is the odd one
out? Mass Speed Force Temperature Distance Elepha
nt
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DO NOW!
Which of the following is the odd one
out? Mass Speed Force Temperature Distance Elepha
nt
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Scalars and vectors
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Scalars

• Scalar quantities have a magnitude (size) only.
• For example
• Temperature, mass, distance, speed, energy.

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Vectors

• Vector quantities have a magnitude (size) and
  direction.
• For example
• Force, acceleration, displacement, velocity,
  momentum.

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Scalars and Vectors
No direction

vectors
scalars
Magnitude (size)
Magnitude and direction
temperature
mass
velocity
force
acceleration
speed
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Representing vectors

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

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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).

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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.

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Adding vectors

• For example

Resultant force
2 m/s
6 m/s
4 m/s
4 N
5.7 N
4 N
Resultant force
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How did we do that?
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How did we do that?

4 N
4 N
4 N
4 N
5.7 N
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Scale drawing

• You can either do a scale drawing

?
1 cm 1N
? 45
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Or by using pythagorous and trigonometry

Length of hypotenuse v42 42 v32 5.7 N Tan
? 4/4 1, ? 45
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Subtracting vectors

• For example

Resultant velocity
10 m/s
6 m/s
4 m/s
4 N
5.7 N
4 N
Resultant force
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Subtracting vectors

• For example

5.7 N
4 N
4 N
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An interesting example

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

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An interesting example

• At this point, what is its velocity?

velocity?
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An interesting example

velocity
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An interesting example
What is its velocity here?

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

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

Of course a changing velocity means it must be
accelerating! Well come back to this next year!
velocity
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Resolving vectors into components
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Resolving vectors into components

• It is sometime useful to split vectors into
  perpendicular components

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Resolving vectors into components
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A cable car question
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Tension in the cables?
?
10
?
10 000 N
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Vertically 10 000 2 X ? X sin10
?
10
?
? X sin10
? X sin10
10 000 N
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Vertically 10 000/2xsin10 ?
?
10
?
? X sin10
? X sin10
10 000 N
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? 28 800 N
?
10
?
? X sin10
? X sin10
10 000 N
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What happens as the angle deceases?
? 10 000/2xsin?
?
?
?
10 000 N
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Error bars

• X 0.6 0.1
• Y 0.5 0.1

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Gradients
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Minimum gradient
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Maximum gradient
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y mx c
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y mx c

• Ek ½mv2

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y mx c

• Ek ½mv2

Ek (J)
V2 (m2.s-2)
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Lets try some questions!

Page 13 Questions 1 to 6
Resultant of forces (addition of vectors)
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Sorry, I nearly forgot!
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(No Transcript)
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Resultant force