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Basic Physics
PH1.1
S.I. (System Internationale) Units
All units can be divided into two groups …
base units
derived units
kg m s K
A mol cd
J Ω V W N
Hz Bq C Pa
Wb T …….
• only 7 units
• each has a detailed
definition
For example: the kilogram…
any object that has a mass of
1kg has exactly the same
mass as that of the
international prototype of the
kilogram
atmospheric pressure inside
three layers of glass
platinum-iridium alloy at a
constant temperature 19±1C
Why choose platinum-iridium? It is a very dense alloy, so a 1kg sample
has a small volume and hence a small surface area. As a result, very little
surface contamination takes place, so the mass of the sample stays
constant.
For example:
the metre …
1m is the distance between two lines scratched ona
particular bar of platinum-iridium alloy (that is stored
at the Bureau International des Poids et Mesures in
Sèvres, France) at the melting point of ice
Recently, the definition has been altered …
1m is the distance travelled by light through a vacuum in
1/
299792458s!
For example: the mole …
one mole is the amount of
substance that contains the same
number of parts as there are atoms
in 12g of the carbon-12 isotope
this is number is the
Avogadro number
= 6.022 x 1023 ….. an enormous number!!
An Avogadro number of soft drink cans would cover the entire
surface of the Earth to a depth of 200 miles!
If counting atoms at a rate of 10 million per second, it would take 2
billion years to count the atoms in one mole of substance!
Scalar and vector
Every quantity that is measured in Physics is either …
(1)
scalar – magnitude (i.e. a figure) only
eg. distance, time, mass, temperature, speed, density, ….
(2)
vector – magnitude and direction
eg. force, displacement, velocity, magnetic field strength, ….
We use arrows to represent vectors in diagrams …
12N to right
the length of the arrow
represents the size of 4N upwards
the vector
Combining the effect of more than
one vector …
displacement
distance =
+
The effect of more than one vector …
Any two vectors
combine like this to
give a single vector
that has exactly the
same effect, eg. two
forces, two velocities ..
aeroplane’s
velocity
wind
velocity
velocity relative to
the ground
resultant force
The Paralelogram Law – adding vectors A and B
C
A
B
B
A
C
C
=
A
+B
vector C can
be obtained by
a drawing
scale diagram
or by using the
cosine and
sine rules to
calculate it
Pythagoras’s Law – adding perpendicular
vectors
C
A
C
=
A
+B
θ
B
To calculate the magnitude of C …
and its direction …
C2 = A2 + B2
tanθ =
A
B
Resolving vectors – splitting a vector into two
components
… the number of
combinations is
infinite!
Resolving a vector – splitting a vector into two
components
concentrate on two perpendicular vectors
y
y = F·sinθ
F
θ
x
x = F·cosθ
Newton’s First Law
in the absence of a force, an object either
stays at rest or continues to move with
constant velocity
in other words …
all objects have inertia
(an inbuilt reluctance to
change their motion)
it also defines a force …
that which is needed to accelerate an object
Newton’s First Law
a force stops
the van / motor
cycle / car …
but the
stepladder /
cyclist / driver
continue to
move at
constant
velocity!!
Newton’s First Law
Without a force to
change its direction , the
ball moves at constant
speed in a straight line
What is a centrifugal force?
an imaginary force that ‘appears’ as a result of
Newton’s First Law
eg. when a car corners …..
there is no friction
between the tape and
the car’s dashboard, so
there is no force to
change its direction,
until the side of the car
is in contact with it
What is a centrifugal force?
…. the passenger ( ) is under the impression
that he is being pushed towards the driver ( ),
but this is an imaginary force
(note that the car is a left-hand drive!)
Newton’s Second Law
the rate of change of momentum is directly
proportional to the applied force and takes
place in the direction of the force
i.e. it relates the size
of the acceleration
with the force that
causes it
acceleration
smaller mass
larger
mass
force
From the • the acceleration is directly proportional
graph …
to the force that gives rise to it
• the acceleration is inversely
proportional to the applied force
i.e.
force  mass × acceleration
force = k · mass × acceleration k - constant
1N is the force that gives a 1kg mass an
acceleration of 1ms-2
resultant force
when there is more
than one force acting
k=1
force = mass × acceleration
ΣF = ma
acceleration
driving force
drag
G
D
force = mass × acceleration
G-D=m×a
acceleration a =
G-D
m
the acceleration is
directly proportional
to the magnitude of
the resultant force
Newton’s Third Law
In contrast to the first two laws, we are looking at the
forces that are acting on two interacting objects …
to every action there is an equal but opposite reaction
or
if A exerts a force (FAB) on B, then B exerts
an equal but opposite force (FBA ) on A
B
A
5N
5N
action: A pulls B to the left with a force 5N
reaction: B pulls A to the right with a force 5N
Examples:
action: the boy pulls the girl to the left
reaction: the girl pulls the boy to the right
action: the gun pushes the
bullet forwards
reaction: the bullet pushes the
gun backwards (recoil)
action: the man pushes the
boat backwards
reaction: the boat pushes the
man forwards
action: the man pushes the
ground downwards and
backwards
reaction: the ground pushes the
man upwards and
forwards
action: the man pushes the
ground downwards
reaction: the ground pushes the
man upwards
Some peculiar examples …
action: the balloon pushes
the air to the left
reaction: the air pushes the
balloon to the right
action: the rocket pushes the
gases backwards
reaction: the gases push the
rocket forwards
Some peculiar examples …
action: the Earth pulls the
parachutist downwards
reaction: the parachutist pulls the
Earth upwards!!
action: the girl pulls the wall
to the right
reaction: the wall pulls the girl
to the left!!
In any situation, there are many forces acting.
In order to analyse the effects of these forces,
we draw free body diagrams
In a FBD, there is only one object shown,
along with all of the forces that are acting
on it
How many forces are there
acting in this situation?
FBD for the boy:
B
C
A
A – the Earth pulling the boy downwards (i.e. gravity)
B – the chair pushing the boy upwards
C – the book pushing the boy downwards
FBD for the chair:
E
D B′
D – the Earth pulling the chair downwards (i.e. gravity)
B′ – the boy pushing the chair downwards (force B’s partner)
E – the ground pushing the chair upwards (a contact force)
Even though they exist, we ignore the gravitational
forces that act between small masses e.g. the boy
and the chair
FBD for the book:
C′
F
F – the Earth pulling the book downwards (i.e. gravity)
C′ – the boy pushing the book upwards (force C’s partner)
FBD for the Earth:
D′ F′ A
′
E′
A′ – the boy pulling the Earth upwards (force A’s partner)
F′ – the book pulling the Earth upwards (force F’s partner)
D′ - the chair pulling the Earth upwards (force D’s partner)
E′ – the chair pushing the ground downwards
(force E’s partner)
12 forces identified in total (always an even number)
Another example … a car accelerating
• we use a double arrow to show acceleration
• we don not distinguish between the friction and air
resistance that try to prevent the motion
FBD for the car:
B
D
C
E
A
A – the Earth pulling the car downwards (i.e. gravity)
B – the ground pushing the car upwards (contact force)
C – the ground pushing the car forwards (driving force)
D – the ground pushing the car backwards (friction)
E – the carvan pulling the car backwards
• the car accelerates if force C > forces (D+E)
• acceleration a = (C-D-E)/m
(m – mass of car only)
G
FBD for the caravan:
H
E′
F
E′ - the car pulling the caravan forward (force E’s partner)
F – the Earth pulling the caravan downwards (gravity)
G – the ground pushing the caravan upwards (contact force)
H – the ground pushing the caravan backwards (friction)
• the caravan accelerates if force E′ > force H
•acceleration a = (E′-H)/m
(m – mass of caravan only)
FBD for the Earth:
A′ - car pulling the Earth
upwards (A’s partner)
A′ F′
H′
D′
B′ – car pushing the ground
downwards (force B’s partner)
C′
B′
G′
C′ – car pushing the ground backwards (force C’s partner)
D′ – car pushing the ground forwards (force D’s partner)
F′ - caravan pulling the Earth upwards (force F’s partner)
G′ - caravan pushing the ground downwards (force G’s partner)
H′ - caravan pushing the ground forwards (force H’s partner)
We ignore any resultant forces that act on the Earth. Their
effects would be negligible since the mass of the Earth is
enormous.
The moment of a force (or torque) is the turning
effect that a force has bout a pivot
moment = force × distance from the pivot
distance
force
to be exact …
moment = force × distance of the line of action of the force
from the pivot
The Principle of Moments
an object is in equilibrium provided the total
clockwise moments about any point is equal
to the total anticlockwise moments about
that point
or
∑(Fd)clockwise = ∑(Fd)anticlockwise
In its simplest form …
clockwise moment about the pivot
= 201 = 20Nm
anticlockwise moment about the pivot = 102 = 20Nm
clockwise moment = anticlockwise moment
about the pivot
therefore the beam balances
When there is more
than one clockwise
and anticlockwise
moment …
∑clockwise moments
about the pivot
= (201) + (121.8)
= 20 + 21.6 = 41.6Nm
∑anticlockwise moments about the pivot
= (102) + (300.7) = 20 + 21 = 41Nm
total clockwise moments > total anticlockwise moments
therefore it does not balance – the beam tilts in the
clockwise direction
When considering the free body diagram for
the beam …
G
G - force of pivot pushing
beam upwards
If the beam is not accelerating
upwards or downwards …
upward force = G = total of forces acting downwards
= 10 + 30 + 20 + 12 = 72N
Therefore for any object to be truly in equilibrium …
(1) there is no resultant force acting on it
(2) there is no unbalanced moment about any point
The centre of gravity
the centre of gravity is that point from which
all of an object’s weight can be considered to
act
Rather than considering the
weight (w) of each individual
particle, we combine all of
the weights…
W = ∑w
and consider W acting from one point
(the centre of gravity)
W
An object is stable provided its weight does not
produce a moment that causes it to topple …
upright cone
inverted cone
cone on its side
W
W
stable
equilibrium
unstable
equilibrium
W
neutral
equilibrium
What is the effect of the position of the centre of
gravity on an object’s stability?
low C of G
unstable equilibrium at a smaller angle
higher C of G
lower centre of gravity – more stable
What is the effect of the width of the base on stability?
wider base – greater stability
When designing for
stability …
low centre of gravity
wide base
large mass
(greater inertia)
 The density of a
substance is the
mass of 1cm3 of the
material,
 it can also defined as
the mass of 1m3 of a
substance,
the reading will be
the density in gcm-3
 density is a scalar quantity – its unit is
either gcm-3 or kgm-3
The density of some common substances:
density (gcm-3)
0.0013
0.003
density (kgm-3)
1.3
3.0
wood
ice
water
~ 0.7
0.9
1.0
~ 700
900
1000
bricks
aluminum
steel
silver
1.8
2.7
7.8
10.5
1800
2700
7800
10500
mercury
13.6
13600
substance
air
feathers
The density of a material can be measured
using the equation …
mass
density = ─────
volume
the units of density are g/cm3 and kg/m3
Measuring the volumes of regular shapes
Measuring the volume of irregular shapes