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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…….
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
North
Adding Vectors
• 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
ø
10 N on a bearing of 0530
Velocity and Displacement
• Displacement ( vector ) : Distance as the
crow flies from start to finish plus the
direction
Velocity
=
Displaceme nt
Time
North
Velocity and Displacement
• A student walks 3 km north then 3 km west.
Distance travelled = 3 + 3 + 6 km.
3150 from
north to
finishing
point
Displacement is resultant of vector
addition =
displaceme nt
velocity =
time
(3 2 + 3 2 )
= 4.24 km bearing of 315 0
4.24
= 4.24 km h
1
_1
bearing of 315 0
Acceleration
• Rate of change of velocity : Vector
final velocity _ initial velocity
Acceleration =
time for change
a =
v_u
t
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
Equations of Motion
v = u + at
2
2
v = u + 2as
1 2
s = ut + at
2
Projectile Motion
• Horizontal and vertical motion
• Ignore spin and friction : horizontal velocity
remains constant
• Vertical velocity subject to gravitational
force
Projectile Motion
• Consider vertical motion
a
v
Ball falling
vertically.
Accelerates
at - 9.8 ms-2
t
t
Projectile Motion
• Consider horizontal motion
v
Ball travels at constant
horizontal velocity
t
Projectile Motion
• Combine both motions :
Horizontal velocity
remains constant BUT the
vertical velocity increases
at a rate of 9.8 m s-2
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
Newton’s Second Law of Motion
• Fun = m . A
Man in lift !
Reaction force
of floor on
man Fr
Weight
Fg
Fg > Fr therefore
unbalanced
force, Fun acts
downwards
Newton’s Second Law of Motion
• Fun = m . A
Man in lift !
Reaction force
of floor on
man Fr
Weight
Fg
Fr > Fgtherefore
unbalanced
force, Fun acts
upwards
Newton’s 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
Conservation of Energy
• Ep to Ek
m . g. h = 0.5 .m. v 2
Work done against
friction
W
= Fav .d
Momentum
•
•
•
•
Product of mass and velocity
Vector
units kg ms-1 or N s
p = m.v
Momentum
• Momentum is conserved provided NO
external forces act
• Elastic collision Ek is conserved
• Inelastic collision Ek is ‘lost’
• Explosion Ek is ‘gained’
Impulse
v_u
F = m . a but a =
t
v_u
therefore F = m
t
multiply both sides by t
F .t
= m(v _ u )
This is called the impulse of the force
and it equals the change in momentum
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
Density
• Mass per unit volume
• 1 g per cm3
1 kg per m3
Density
Mass

Volume
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
Pressure
Pressure = Force
Area
(1 N/m2 = 1 Pascal )
Pressure in Liquids
Pressure in liquids
acts in all directions
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 = ρ.g.h
Buoyancy
F upthrust
F gravity
•Pressure on bottom of sub >
pressure on top
•Pressure = force acting per
unit area
•Hence force acting on
bottom surface > force acting
on top
•Unbalanced force acts
upwards : called Upthrust or
Buoyancy Force
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
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
Δ. m v
in momentum )
F
=
Δt
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
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
Gas Laws
P1 V1
T1
=
P2 V2
T2
Pressure Volume
• At constant Temperature
Pr essure
Volume
1
Volume
Pressure Temperature
• At Constant Volume
Pr essure
Temperature (Kelvin)
Volume Temperature
• At Constant Pressure
Volume
Temperature (Kelvin)