Download AS90183_NBC_1a

22/05/2017
Physics 101
Achievement Standard
AS90183
Demonstrate understanding of
mechanics in one dimension
5 Credits
Significant figures
22/05/2017
Significant figures are important in physics
and we need to understand what role 0
plays in this.
Consider the following:
21000
240
0.00045
all these have the same number of sig
figs: 2
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When zero is not a place holder then it
becomes significant
e.g.
23.00 4 sig figs
0.330 3 sig figs
22045 5 sig figs
Rounding
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When rounding we need to be able to
consider what is important and note when
the zero is important or not:
try these
25.34
round to 2 sf
65.68
round to 3 sf
0.4997 round to 3 sf
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If we have to find a solution based
on some rounded figures, then this
will affect our final answer. Consider:
2 sf
15
 5.7692308
3 sf can
2.60be no more
The answer
accurate than the input data, thus 2
sf is the best we can do, giving 5.8
Motion
22/05/2017
The motion of an object, such as a runner or
a car, is described using quantities like the
distance covered, the time taken, speed
reached and the acceleration required to
achieve such a speed.
To define time and distance we generally
use two well known and universal units.
Motion
22/05/2017
• The Second (s), this is the S.I. unit for
time.Time is given the symbol t in
formulas.
• The Metre (m), this is the S.I. unit for
distance. Distance is given the symbol d
in formulas
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Other units for
distance include
Km, mm, µm
Other units for time
include Min, hours
and days
Motion
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When we look at distance travelled in a
given time we are investigating the speed
of something.
Motion
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We may further qualify speed
Average speed:
This is the speed calculated over a defined distance.
Instantaneous speed:
This is the speed at a particular point during a journey
and can be described as the actual speed at a particular
point in time.
When the speed during a journey does not change then
it can be described as a steady, uniform or constant
speed.
Motion
22/05/2017
By the very definition of speed as distance
covered in a given period of time we
define the formula for speed as:
distance travelled
average speed =
time taken to travel distance
d
v av 
t
Motion
22/05/2017
The units used to measure speed are related to the way
in which the speed value is calculated. For example if
we measure the distance in kilometres (km) and time in
hours (h) then speed will be defined in km per hour.
Often in physics and science since we measure in
metres and seconds, speed is quoted in metres per
second.
We write these units in a particular way:
• km per hour = kmh -1
• metres per second = ms-1
Motion
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Examples:
Determine the average speed of a car traveling 128km
between 2:15 pm and 4:15 pm one day.
Distance = 128 km
Time = 2 h

distance 128km
speed =

 64kmh1
time
2h
Motion
22/05/2017
Example:
Determine the average speed of a bike
wheeling down a slope of length of
525m in 25 s.
Distance = 525 m
Time = 25 s

distance 525m
speed =

 21ms1
time
25s
Vectors
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• In physics we often deal with specific
vector values.
• Vectors have a size and a direction
• We consider initially two vectors:
–
–
Displacement (distance travelled in a
specific direction)
Velocity (speed in a specific direction)
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To calculate displacement we just need to
pay attention to the distance travelled and
the direction. Opposite directions have
negative effects
To calculate velocity we divide the
displacement achieved during a period of
time, by the time taken. The maths is the
same as for speed.
Distance Time (dt) graphs
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Distance time graphs display information
regarding the distance movement of an
object over a period of time. The gradient
(slope) of the line of the graph describes
the speed of the object.
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The slope of any graph is determined as:
change in y - axis
gradient 
change in x - axis
On a distance time graph, this becomes:

change in distance Δd
gradient 

change in time
Δt
Time (s)
Object stationary,
distance does not
change over time
Distance (m)
Distance (m)
Distance (m)
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Time (s)
Object has a
constant speed
Time (s)
Object has
a constant
speed,
faster than previous
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Distance (m)
Distance (m)
When a d-t graph does not have a straight line then the
object concerned is changing speed.
Time (s)
Speeding up
accelerating
Time (s)
Slowing down
decelerating
Speed time graphs
22/05/2017
Speed time graphs are used to give a
more detailed and an accurate picture of
the changing speeds of an object during a
journey
The gradient (or slope) of the line of the
graph gives the acceleration of the object.
Time (s)
Constant speed
Spped (ms-1)
Spped (ms-1)
Spped (ms-1)
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Time (s)
Change speed
Accelerating
Time (s)
Changing speed
Deceleration
Area under S-T Graph
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We can determine the distance travelled
by an object from the area under a speed
time graph.
Divide the area of the graph up into easily
calculated areas (e.g. rectangles and
triangles)
Find the area of each subdivision and then
sum all the areas together
Area under S-T Graph
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Spped (ms-1)
• Example: Find areas of sections A, B and C
A = 12 (5  6)
6
B=56
4
C = 12 (10  6)
2
0
A
0
B
5
Time (s)
A B C
C
10
15

20
 15  30  30
 75m
Acceleration
22/05/2017
• Acceleration is the rate of change of speed
of an object.
• For example if the acceleration of an
object is stated as 2 ms-2, then its speed is
increasing by 2ms-1 every second.
22/05/2017
The formula to determine acceleration is defined
by:
change in speed
V v 2  v1
a


time taken for that change
t
t 2  t1
Where v1 is the starting speed and v2 the finishing speed
t1 is the start time and t2 the finish time

If the value for acceleration is negative then the object is
slowing down or decelerating
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Examples:
1. Find the acceleration of a car starting from rest
at zero seconds and reaching a speed of
15ms-1 after 5 seconds.
V1=0, v2=15, t1=0, t2=5 a 
v 2  v1 v 15  0 15
a


  3ms2
t 2  t
t 5  0
5
1
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•
Examples:
1.
Find the acceleration of a skier going downhill. They
start at 7ms-1 and increase their speed to 13ms-1
between 28s and 31s after starting down the slopes.
V1=7, v2=13, t1=28, t2=31
a
v 2  v1 v 13  7 6
a


  2ms2
t 2  t1 t 31 28 3

Force Diagrams
22/05/2017
We can represent the forces being applied
to an object using what is called a force
diagram. Arrows are used to represent the
direction of a force and a value is written.
Forces in opposing directions subtract
from each other
Force at right angles do not affect each
other.
Force Diagram Example
600
2000
40 NNN
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600
2500
40 NNN
Applied force represented with an arrow pointing in
the direction of the force.
We identify the value with a number of Newtons (N).
Equal forces from opposite directions are said to be
balanced forces.
Illustrations
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Balanced forces
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• When the two forces applying in opposite
directions are equal in size we say that the
forces are balanced.
• If we consider the situation below, what
will be the resulting motion of the object?
400N
400N
5000N
5000N
Newton’s laws
22/05/2017
• We can state that
“an object will remain stationary or move at
a steady speed in a straight line unless
acted on by an unbalanced force”
• This is known as Newton’s 1st law of
motion.
• We have already met his 2nd law, f=ma.
Exploding trolley experiments 22/05/2017
1. Place the trolley so that the plunger is facing
into open space. Trigger the plunger and
observe what happens.
2. Now place the trolley so that the plunger will
strike a solid object, such as a wall. Trigger the
plunger and observe what happens this time
3. Now place two trolleys so that the plunger will
strike one of the trolleys while both trolley are
free to move. Trigger the plunger and observe
what happens this time.
Direction of forces
22/05/2017
• Forces are applied in a direction and can result
in movement of an object.
• The direction of that movement will be in the
direction of the resulting force
• Thus find the resulting force value direction and
associated acceleration for the diagram below.
700N
500N
Mass of car
275Kg
Newton’s laws
Newton’s third law states:
“for every action force there
is an equal and opposite
reaction force”
This means that when we
apply a force against
something, like pushing
against a wall then the wall
pushes back against us.
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Identify the action and reaction forces in the following
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Pressure?
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What is pressure?
The application of a force over a specific area. If
the area is very small then the pressure will be
very large.
The formula to connect these is:
F
P
A
Where P= pressure, F=force (N) and A=area (m2)
22/05/2017
• Consider an elephant weighs a lot, but has a
large foot pad. The force of its weight is spread
out and the animal can stand easily on its feet all
day.
• A lady sometimes wears a stiletto heel shoe.
Her weight will be significantly less than an
elephant, but over the small area of the stiletto
heel the pressure will be enormous.
• Moral your foot will hurt if stood on by an
elephant, but a stiletto will pierce your foot
example
22/05/2017
What is the pressure experienced by a 15
Kg sledgehammer resting on the top of a
tent peg size 2 cm x 1 cm.
P=F/A, F
= 15x 10 = 150 N
A
= 0.02 x 0.01 =0.0002m2
P
= 150/0.0002
= 750000 Nm-2 ( or Pa)
22/05/2017
The pressure of the atmosphere around us
is 100 000 Pa. How many Kg of
atmosphere must be pressing down on
each square metre of Earth?
P=F/A, F=P.A=
100000Pa .1 m2
F= 100 000 N,
F=mg, thus m = F/g = 100 000/10 =
10 000 kg
(10 tonne)
Gravitational force
22/05/2017
Gravity is a non–contact force that exists
between two objects with a mass.
The mass of the Earth is so big we state
that an object is attracted to the Earth.
An object with a big mass is attracted to
the Earth by a bigger force. Thus
weightlifters get a higher score for lifting a
greater mass above their heads, it is more
difficult.
Mass and Weight
22/05/2017
Mass describes the amount of matter in an
object and is measured in Kilograms (kg)
Weight is a measure of the force due to gravity
acting on an object.
We define:
W= m x g
W=weight (N)
m = mass (kg)
g= gravitational pull in N/Kg
Weight on different places
22/05/2017
On Earth the g= 10 N/kg, thus the weight
of any object is 10 times the mass.
Different planets have gravitational pulls.
On Mars, Venus and the Moon it is less,
on Jupiter, Saturn and the Sun it is greater.
Weight on different places
Location
Earth
G
N/kg
10.0
Object
mass (kg)
33.45
Moon
1.6
16
Mars
3.8
22
Saturn
26.0
5
Sun
275
0.02
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Object
weight (N)
Weight on different places
Location
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Earth
G
N/kg
10.0
Object
mass (kg)
33.45
Object
weight (N)
334.5
Moon
1.6
16
25.6
Mars
3.8
22
83.6
Saturn
26.0
5
130
Sun
275
0.02
5.5
Force and distance
22/05/2017
When a force is applied to an item we do work.
Depending on how far the item is push and by
what amount of force will determine the amount
of work done.
We summarise this by the following equation:
W= f d
Where
W = work done in Joules (J)
f = force applied in Newtons (N)
d = distance travelled in metre (m)
W
f
d
Examples
22/05/2017
1. How much work is done when pulling a 25 Kg
bag of scoria stones with 200N 15m.
W=fxd, f= 200N, d=15m
W=200 x 15 =3000J
2. A 100Kg car is pushed by a force of 145N, find:
a) the acceleration of the car
f=ma, f=145N, m=100kg
145=100.a, a=145/100=1.45 ms-2
b) The work done to move the car 0.5 km
W=fd, f =145N, d=500m
W=145 x 500 = 72500J
Watt is Power
22/05/2017
Power is a measure of how much work is done
in a given period of time.
As usual time is measured in seconds and work
in Joules.
Thus power is defined as the number of joules
used per second.
P = W/t
The unit for power is the Watt (W) after James
Watt and his work on the steam engine in
1770’s.
Now do: Page 27 of blue book
Potential energy
•
•
•
•
22/05/2017
There are various types of potential
energy and we have discussed these
previously:
Elastic
Chemical
Nuclear
Gravitational
22/05/2017
Gravitational potential energy is defined by:
• The height (h) of something above the ground in
metres
• The mass (m) of something above the ground in
kg
• The strength of gravity (g) at that point in space
in Nkg-1
This gives the formula
g on Earth is 10 Nkg-1
Epg = mgh
Kinetic energy
22/05/2017
When an object is moving the energy it
has will depend upon:
The mass of the object (m) in kg
The velocity or speed of the object (v) in
ms-1
This give us the formula:
Ek = ½ mv2
Changes in energy
22/05/2017
We find that an object falling from a height
will lose potential energy and gain kinetic.
Ignoring effects of air friction then all PE
will change to KE. The reverse of this will
occur when something is thrown or
projected into the air.
The conservation of energy allows us to
equate Epg =Ek in these situations.
Examples
22/05/2017
A 4.6 kg rock is kicked off a 120m cliff
a)
How much potential energy does the rock lose as it falls?
EPgrav = mgh = 4.6 x 10 x 120 = 5520J
b)
How much kinetic energy does the rock have just before it hits
the ground?
Loss of EPgrav = EK = 5520 J
c)
What is the speed of the rock just before it hits the ground?
EK = ½ mv2 = 5520
 (4.6)/2 *v2 = 5520
 v = (5520/2.3) = 49.0 ms-1
d)
What happens to all the kinetic energy when the rock hits the
ground?
Turns to sound and heat energy
Momentum
22/05/2017
• Momentum is a quantity you may have heard of
and even have a basic understanding of.
• It is related to the velocity and size of an object.
• Small objects will require a lot of velocity to have
a lot of momentum and thus be difficult to stop.
• Large objects even at slow velocities can be
hard to stop.
• Momentum = mv
where m = mass in kg
v = velocity in ms-1
Momentum is measured in kgms-1
Density
22/05/2017
• What do we mean when we describe
something as light ?
• Which is heavier a tonne of feather or a
tonne of coal?
• The real question is which would occupy
the biggest volume, a tonne of feather or a
tonne of coal? We know that a tonne of
feather would occupy a larger volume.
Density
22/05/2017
Density can be described as the amount of
mass of a material per unit volume.
The formula is:
m
ρ
Where
V
m= mass in kg
V= volume in m3
ρ = density in kgm-3
Example
22/05/2017
Find the density of the following:
a) Lump of metal weighing ½ kg with a
volume of 5cm x 5 cm x 5cm
b) 1 tonne of a metal has a volume
of 0.4 m3
c) a lump of wood weighing 25 kg is 1m
square by 0.1 m in length