Vectors and Scalars

1
Vectors and Scalars

• Scalars have magnitude only e.g. mass, speed,
  distance
• Vectors have magnitude and direction e.g. force
  of 10 N to the left.. Velocity, displacement,
  weight ,acceleration.

2
Adding Vectors

• Vectors are represented by arrows
• 10 N to left or - 10 N
• 20 N to the right or 20 N
• Resultant is 20 - 10 10 N

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Adding Vectors
North

• Add the vectors 6 N north plus 8 N to the East.
• Draw a Vector diagram , add the vectors Head to
  Tail. Use Pythagoreus or scale diagram to
  calculate resultant. Use trig or measure angle ø

10 N on a bearing of 0530
ø
4
Velocity and Displacement

• Displacement ( vector ) Distance as the crow
  flies from start to finish plus the direction

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Velocity and Displacement
North

• A student walks 3 km north then 3 km west.

Distance travelled 3 3 6 km. Displacement
is resultant of vector addition
3150 from north to finishing point
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Acceleration

• Rate of change of velocity Vector

7
Graphs

• Slope of velocity time graph is acceleration
• Area under velocity time graph is displacement
• Slope of displacement time equals velocity
• Velocity / acceleration / displacement downwards
  normally negative

8
Equations of Motion
9
Projectile Motion

• Horizontal and vertical motion
• Ignore spin and friction horizontal velocity
  remains constant
• Vertical velocity subject to gravitational force

10
Projectile Motion

• Consider vertical motion

a
v
Ball falling vertically. Accelerates at - 9.8 ms-2
t
t
11
Projectile Motion

• Consider horizontal motion

v
Ball travels at constant horizontal velocity
t
12
Projectile Motion

• Combine both motions

Horizontal velocity remains constant BUT the
vertical velocity increases at a rate of 9.8 m s-2
13
Forces

• Force is a push or a pull
• Forces change the speed, shape or direction of an
  object
• Unbalanced forces cause vehicle to accelerate (
  velocity changes )
• I N causes a vehicle of mass 1 kg to accelerate
  at 1 m s-2

14
Newtons Second Law of Motion

• Fun m . A

Reaction force of floor on man Fr
Fg gt Fr therefore unbalanced force, Fun acts
downwards
Man in lift !
Weight Fg
15
Newtons Second Law of Motion

• Fun m . A

Reaction force of floor on man Fr
Fr gt Fgtherefore unbalanced force, Fun acts
upwards
Man in lift !
Weight Fg
16
Newtons Second Law of Motion

• Vehicles accelerate to right at 2 m s-2

1000 kg
5000 kg
Force transmitted through towbar accelerates car
at 2 m s-2 m. a 1000 x 2 2 000 N Total
force applied accelerates tractor and car at 2 m
s-2 m. a 6000 x 2 12 000 N
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Conservation of Energy

• Ep to Ek

Work done against friction
18
Momentum

• Product of mass and velocity
• Vector
• units kg ms-1 or N s
• p m.v

19
Momentum

• Momentum is conserved provided NO external forces
  act
• Elastic collision Ek is conserved
• Inelastic collision Ek is lost
• Explosion Ek is gained

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Impulse
This is called the impulse of the force and it
equals the change in momentum
21
Impulse

• In collisions the bigger the collision time the
  smaller the force acting and the less damaged
  caused. Crumple zones on cars increase the
  collision time.

Force
Area under graph change in momentum
time
22
Density

• Mass per unit volume
• 1 g per cm3 1 kg per m3

23
Density

• Densities of solids and liquids are approx 1000
  times greater than gases.
• Particle spacing in a gas is approx 10 times
  greater than in a solid
• If a solid is made up of millions of cubes then
  each cube would contain 1000 particles ( 10 x 10
  x 10 ) but a gas would only contain 1 particle
  per cube hence density of solid is c.a. 1000
  times that of gas

24
Pressure
Pressure Force Area (1 N/m2
1 Pascal )
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Pressure in Liquids
Pressure in liquids acts in all directions
26
Greater the depth the greater the weight of
liquid Greater the density of liquid the greater
the weight acting at the same height Greater g
greater the weight P ?.g.h
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Buoyancy

• Pressure on bottom of sub gt pressure on top
• Pressure force acting per unit area
• Hence force acting on bottom surface gt force
  acting on top
• Unbalanced force acts upwards called Upthrust
  or Buoyancy Force

F upthrust
F gravity
28
Kinetic Theory of Gases

• Matter is made of small particles
• Particles are different sizes for different
  elements
• Particles cannot be compressed
• Particles are always moving
• At same temp ALL particles have the same kinetic
  energy
• ALL collisions are ELASTIC

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Kinetic Theory of Gases

• Gas exerts a pressure because the particles hit
  wall of container ( pressure force per unit
  area )
• Pressure depends on
• number of collisions per second
• force acting per collision ( actually change in
  momentum )

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Kinetic Theory of Gases

• As Temp increases the Ek of particles increases,
  they hit the wall with a bigger force and more
  frequently hence pressure increases
• As volume decreases the number of collisions per
  second increases and the average force acting
  increases pressure increases

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Absolute Zero

• At 0 Kelvin , particles of a gas would have NO
  kinetic energy and would be stationary. This is
  the lowest temperature in the universe.
• 0 K - 2730C 0 0C 273 K
• A temp difference of 1 K equals a temp difference
  of 1 0C

32
Gas Laws
33
Pressure Volume

• At constant Temperature

34
Pressure Temperature

• At Constant Volume

35
Volume Temperature

• At Constant Pressure