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Science 10
Motion
Numbers vs. Measurement
• There is a difference in between numbers
used in math and measurement used in
science.
• In math, every number carries importance
• In science, not every number in a
measurement carries the same
importance.
– More important numbers are called significant figures.
– Less important numbers are called place holders.
Measurement
• Every measurement contains an exact
amount of significant figures.
– It includes all numbers that were measured
from the scale used.
– Plus 1 extra ‘guessed number’ that is not on
the scale.
• Always include one more number than
your scale tells you!
Our scale
Scale
The
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ustens
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tens
and the
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those
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We
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a guessed
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and is
47.0
50
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not significant.
and
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100cm
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47isare
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5
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and
it is significant
are
Rules for Significant Figures
•
There are 2 rules for determining the
number of significant figures.
1. Decimal rule- (use this rule when the
measurement contains a decimal)
– Count the numbers from left to right
beginning at the first non-zero number.
0.001234- 4 sig. figs.
12340.0- 6 sig. figs.
1.234- 4 sig. figs.
12340.- 5 sig. figs.
0.123400- 6 sig. figs.
1.2340 x 10-35 sig. figs.
Rules for Significant Figures
2. Non-decimal rule- (use this rule when the
measurement does not contain a decimal)
– Count the numbers from right to left
beginning at the first non-zero number.
1234- 4 sig. figs.
12340- 4 sig. figs.
102340- 5 sig. figs.
12340.- 5 sig. figs.
0.123400- 6 sig. figs.
100002- 6 sig. figs.
Scientific Notation
• Scientific notation is a method of writing
numbers that:
– Can make large numbers more easy to read.
– Indicate the proper number of significant
figures.
Rules for Writing in Scientific
Notation
1. Write down all the significant numbers
2. Put a decimal after the first number. (the
number will now be between 1-10)
3. Write “x 10”
4. Write the power corresponding to the number
of places the decimal was (would have) been
moved. (Moving right is negative, moving left is
positive)
•
Count the number of digits between where the
decimal was before and where it is now
25 000 000 000 000
4.Write
1.Write
2.Put
a the
down
decimal
power
all after
the
corresponding
significant
the first number.
to the
3.Write
“x
10”
numbers
(the
number
number
of places
will now
the be
decimal
between
was110)
(would
have) been moved. (Moving right
is negative, moving left is positive)
13
25
. x 10
0.000 000 000 030 0
4.Write
1.Write
2.Put
a the
down
decimal
power
all after
the
corresponding
significant
the first number.
to the
3.Write
“x
10”
numbers
(the
number
number
of places
will now
the be
decimal
between
was110)
(would
have) been moved. (Moving right
is negative, moving left is positive)
-11
300
. x 10
How do you write the number
10 000 with 3 significant
figures?
4
100
. x 10
-3
10
Change 0.00123 x
into
proper scientific notation.
123
. x 10
-3 -3= -6
-6
Calculating using Significant
Figures
•
There are 2 rules for calculating with
significant figures.
1. Precision rule- (used for addition and
subtraction)
– The answer will have the same precision as
the least precise measurement from the
question.
10 cm
Least precise
10. cm
10.0 cm
10.00 cm
Most precise
1.234
+0.05678
1.29078
=1.291
This value is the
least precise value.
The answer will
end at the same
spot.
Round the
value after the
last sig. fig.
12340
+5678000
5690340
=5690000
6
=5.690 x 10
This value is the
least precise value.
The answer will
end at the same
spot.
Round the
value after the
last sig. fig.
Calculating using Significant
Figures
2. Certainty rule- (used for multiplication and
division)
– The answer will have the same number of
significant figures as the least number of
significant figures from the question.
123
X 45
5535
1
2
5500
Place holders
3 significant figures
2 significant figures
The answer will have
2 significant figures
Round the value after
the last significant
figure
450
X 0.0123
5.535
1
5.5
2
2 significant figures
3 significant figures
The answer will have
2 significant figures
Round the value after
the last significant
figure
Units
• A unit is added to every measurement to
describe the measurement.
Ex.
– 100 cm describes a measured length.
– 65 L describes a measured volume.
– 12.4 hours describes a measured time.
– 0.011 kg describes a measured mass.
Units
• In Canada we use the metric (SI) system.
• The metric (SI) is a system designed to
keep numbers small by converting to
similar units by factors of 10.
• Prefixes are added in front of a base unit
to describe how many factors of 10 the
unit has changed.
Units
• Base units of measurement are generally
described by one lettre.
– m- metre (length)
– s- second (time)
– g- gram (mass) *The base unit for mass is
actually the kg (kilogram)
– L- litre (volume)
Units
• Prefixes
Kilo
(k)
hecto
(h)
deca
(da)
base
deci
(d)
centi
(c)
milli
(m)
• Prefixes are added to the front of any base
unit.
Ex. mm, cm, dm, m, dam, hm, km
Converting units
• There are 2 methods to convert units
1. Step Method- count the number of places to
move the decimal.
2. Dimensional Analysis- multiplication by
equivalent fractions of 1.
Converting Units
• Step method– Move the decimal the same number of spaces
and direction as the distance in between
prefixes.
Convert 34.56 cm into m
Kilo
(k)
hecto
(h)
deca
(da)
base
deci
(d)
centi
(c)
We
It
starts
move
at 2centi
spaces
(for to
centimetre)
the left to
get from centimetre to metre
So we move the decimal 2
places to the left in our number
0 3456
. cm
m
milli
(m)
Convert 21.0 kg into g
Kilo
(k)
hecto
(h)
deca
(da)
base
deci
(d)
centi
(c)
milli
(m)
We
It
starts
move
at 3kilo
spaces
(for kilogram)
to the right to
get from kilogram to gram
So we move the decimal 3
places to the right in our number
210
. 00
kgg =2.10 x
4
10 g
Converting Units
• Dimensional Analysis– Multiply the measurement by a fraction that
equals 1
– The fraction will contain the old unit and the
new unit.
– The fraction must cancel out the old unit.
(follow the rule that tops and bottoms cancel
out)
Convert 34.56 cm into m
Kilo
(k)
hecto
(h)
34.56 cm
deca
(da)
base
1 m
100 cm
deci
(d)
centi
(c)
milli
(m)
Move 2 places so we
need 2 0’s
= 0.3456 m
We need to make the fraction equal 1.
Counted and exact values do not
Put
the larger
asthe
1 and
count
forMultiply
significant
figures
themeasurement
tops and divide
addbottoms
0’s
tofraction
theby
smaller
measurement.
The
contain
Multiply
amust
fraction
(# of the
zeroes
number
newequals
and oldthe
unit.
Tops of
places
thebottoms
prefixescancel
are moved.
and
out
Convert 21.0 kg into g
21.0 kg 1000 g = 2.10
4
21000g
x10 g
1 kg
Convert 15.0 m/s into km/h
15.0 m 1 km
s 1000m
60 s
1 min
60 min
1 h
WeWe
multiply
= 54.0
km/h
followthe
the same rules,
but we
tops,
and divide
convert
1 unit the
at a time.
bottoms.
Convert 80.0 km/h into m/s
1 h
80.0 km 1000 m
h 1 km 3600s
WeWe
multiply
= 22.2
m/s
followthe
the same rules,
but we
tops,
and divide
convert
1 unit the
at a time.
bottoms.
Defined Equations
• Relationships between variables can be
expressed using words, pictures, graphs
or mathematical equations.
– A defined equations is a mathematical
expression of the relationship between
variables
Ex. Mass and Energy are related by the speed
of light
E = mc2
Defined Equations
• Defined equations can be manipulated to
solve for any of the variables.
– We use the same principles from math.
• There are 2 rules that must be followed to
isolate a variable.
1.It must be alone
2.It must be on top (numerator)
Solve E = mc2 for m
m must be isolated
2
m
mc
E=
2
2
c
c
Divide both sides
by c2
m is already on top so we will not
touch m. We have to isolate m by
moving c2 to the other side.
Solve d = m/v for v
v d =m v
d
vd
Divide bybyd von
Multiply
onboth
both
sides
v is on the bottom so we need
to move v first and then isolate.
Speed
• The distance travelled by the amount of
time.
– How fast something is moving.
v = Δd
Δt
• Speed is measured in m
s
Speed
• You can look at speed in 3 different ways
– Average- the speed over the whole trip.
• Total distance divided by total time.
– Instantaneous- the speed at one point in the
trip.
• Looking at the speedometer.
– Constant- the speed remains the same over a
period of time.(uniform motion)
• Cruise control.
Calculations for speed
• Using the formula, v = d/t, we can make
some mathematical calculations about
speed.
– Follow the same 3 steps to solve every
problem.
1. Identify your givens and unknowns.
2. Identify the defined equation and isolate for the
unknown variable.
3. Solve the equation using proper significant
figures and units.
A trip to Calgary is 758 km. If you were to
complete the trip in 7.25 h, what was you speed?
Givens
Formula
Solve
d= 758 km
t= 7.25 h
v= ?
v=d
t
v = 758km
7.25 h
v = 105km
h
What type of speed did we calculate in
the previous problem?
Average speed
If someone is travelling at a constant speed of 40.0
km/h, how far would they travel in 32.4 min.
Givens
Formula
Solve
d= ?
t= 32.4 min
v=d
t
d = 40.0km (0.54 h)
h
d=vt
d = 21.6 km
v= 40.0 km
h
32.4 min
1 h
60 min
= 0.540 h
Representing Speed Graphically
• We can represent speed with words (fast,
slow), numbers (32 km/h) and we can also
represent it visually with a graph.
– Speed is represented on a distance vs. time
graph.
• The slope of the graph is the speed.
Distance (m)
Travelled the greatest
distance in the same
time. (fastest speed)
The slope of theThe steeper the slope,
line is equal to the
the greater the speed.
speed
A straight line indicates
a constant speed.
Travelled the least
distance in the same
time. (slowest speed)
A curved line indicates non-constant
speed. (speeding up or slowing down.)
Time (s)
Describe the motion in the following
graph? 1.Moving slowly at a constant speed
2.Moving faster at a constant speed
Distance (m)
Where is the person
3.Not moving
going in this graph?
4.Moving back to the start at a constant speed
5.Speeding up
Back to the original
starting position.
What is the speed of this graph?
0 m/s
Time (s)
Identify the 3 types of speed on the graph?
Instantaneous
Constant
Distance (m)
Average
the speed remains
the same over a
period of time
the speed over the whole trip
the speed at one point in the trip
Time (s)
Acceleration
• The change in speed by the amount of
time.
– How quickly something is speeding up (or
slowing down)
a = Δv
Δt
• Acceleration is measured in m
s2
Acceleration
• You can look at 2 types of acceleration.
– Average- the acceleration over the whole
time period.
•
The change in speed over time.
– Constant- the acceleration remains the same
over a long period of time.
Calculations for acceleration
• Using the formula, a = Δv/Δt, we can make
some mathematical calculations about
acceleration.
– ‘Δ’ means change, Δv means change in
speed
– Δv = vfinal – vinitial
Or
– Δ v = v2 – v 1
A person on their bike changes their speed from
10.0 m/s to 15.0 m/s in 15.2 s. What is the
acceleration of the bike?
Givens
Δ v=15.0m/s –10.0m/s
= 5.0 m/s
Δ t= 15.2 s
a= ?
Formula
a = Δv
Δt
Solve
a = 5.0m/s
15.2 s
a = 0.33m
s2
A car is traveling down the road when they see an
obstruction. The person accelerates at -3.2 m/s2
for 5.0 s until they stop. How fast was the car
moving?
Givens
v 1= ?
v2= 0 m/s
Δ t= 5.0 s
a= -3.2 m/s2
Formula
Solve
a = v 2- v 1
Δt
v1=0 m/s –(-3.2m/s2)5.0s
v1 = v2- aΔt
v1 = 16 m/s
Representing Acceleration
Graphically
• We can represent acceleration with words
(speeding up, slowing down), numbers
(9.8 m/s2) and we can also represent it
visually with a graph.
– Acceleration is represented on a speed vs.
time graph.
• The slope of the graph is the acceleration.
• The area under the graph represents the distance
travelled
Speed (m/s)
Increased the speed
the most in the same
time. (fastest
acceleration)
The slope of theThe steeper the slope,
line is equal to the
the greater the
acceleration
acceleration.
A straight line indicates a
constant acceleration.
Increased the speed
the least in the same
time. (slowest
acceleration)
A curved line indicates non-constant
acceleration. (speeding up or slowing
down at a changing rate.)
Time (s)
Describe the motion in the following
graph? 1.Constantly speeding up slowly
speed (m/s)
2.Constantly speeding up faster
What is the
3.Moving at a constant speed
acceleration of this
4. Slowing down to a stop
graph?
A negative acceleration,
they are slowing down.
What is the acceleration of this
graph? 0 m/s2, but it is a constant speed.
Time (s)
Identify the 3 types of acceleration on the graph?
Non-uniform
Constant(uniform)
speed (m/s)
Average
the change in
speed remains the
same over a
period of time
the change in speed over the
whole trip
the speed is increasing at a changing rate
Time (s)
Answer the questions using the following graph.
18
How long did it take
for the turtle to
reach 14m?
16
distance (m)
14
12
10
What is the average
speed of the turtle
over the entire trip?
v=d/t
8
v = 16.5m
78s
6
v = 0.21m
s
It would make it
about 1m
4
2
10
20
How far did the
turtle get in 25s?
It would take 70 sec.
30
Time (s)50
60
70
80
90
Answer the questions using the following graph.
18
16
speed (m/s)
14
12
10
How
did the
it take
Howlong
far did
for
the travel?
hare to reach
hare
10m/s?
Distance is calculated
using the area under
It would
travelling
thebegraph
about 14.5 m/s
What is the average
acceleration of the
hare over the entire
trip? a = v / t
8
a = 16.5m/s
78s
6
a = 0.21m
s2
4
A = ½ bh
b = 80 s
H = 16 m/s
A = ½ (80s)(16m/s)
A = 640m
How fast was the
going at the
It would takehare
58 sec.
72s mark?
2
10
20
30
Time (s)50
60
70
80
90