Transcript Grade 10 Science - Killarney School

Grade 10 Science
Motion Unit
Significant Digits
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The correct way to record measurements is:
Record all those digits that are certain plus one and no
more
These “certain digits plus one” are called significant digits
ALL DIGITS INCLUDED IN A STATED VALUE (EXCEPT
LEADING ZEROES) ARE SIGNIFCANT DIGITS
Measurements
Examples
Table 1 Certainty of Measurements
307.0 cm
Certainty
(#of Significant Digits)
4
61 m/s
2
0.03 m
1
0.5060 km
4
3.00 x 10 8 m/s
3
Measurement
2340.00
0.1240
2005
Decimal
Present
A Red Arrow pops the 0’s
like balloons until it sticks in
a digit between 1 and 9.
Then you count the rest of
the digits that are left.
0.003450
2500
Decimal
Absent
Counted and Exact Values
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When you count the number of something (example –
students in the class), this is an exact value and has an
infinite number of significant digits.
When you use a defined value such as 100 cm/m or 60
s/min, you also have an infinite number of significant
digits.
Note the calculation rules on BLM 9.2B
Converting Units
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When you want to change
units we use a conversion
factor (or equality)
100cm/m
1000m/km
Some
Equalities
60 s/min
60 min/h
Assignment : Significant Digits
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BLM 9.2a, 9.2b
Complete the Significant Digits Worksheet See
answer key
Questions 1-6, 9 pg 349 in your text
Relating Speed to Distance and Time
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Average Speed Vav is:
The total distance divided by the total time for a trip
Vav =
d
t
See BLM 9.5a for examples
Instantaneous speed – the speed an object is travelling at a
particular instant. Ie. Radar trap
Constant Speed (uniform motion) – if the instantaneous speed
remains the same for a period of time. Ie. Cruise control on your car
A car travels 45 km at a speed of 90 km/h.
How long did the trip take?
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What do you know in the Question
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d= 45 km
Vav = 90 km/h
t=?
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Decide on a formula
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t=
d
Vav
d
Vav
t
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Substitute the knowns into the formula and solve
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t
= 45 km
90 km/h
t = 0.5 h
•Write a concluding statement:
It takes 0.5 h for the car to travel 45 km at a speed of 90 km/h
Problem Solving Summary
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List the variables you know
Decide on a formula
Substitute what you know into the formula
Solve and write a concluding statement
Speed- Click Me
Assignment : Relating Speed to
Distance and time
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BLM 9.5 a,b, d
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Answer Key
Questions 1,2,3,6,7,8 pg 358
Answer Key
Distance – Time Graphs
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Independent variable - X axis is always time
Dependent Variable - Y axis is always distance
Speed is determined from the slope of the best fit
strait line of a distance – time graph
SmartBoard Slope of a Line
See BLM 9.7a
In the following diagram:
a = constant speed
b = not moving
c = accelerating
Assignment : Distance – Time Graphs
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Lab 9.5 Graphing Distances During Acceleration
Questions 3,4,5,6 pg 365
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Activity 9.9 Simulation : Average Speed on an Air Table
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Answer Key
BLM 9.9a
Worksheet – Determining Speed from a d/t Graph
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Q 1-6
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Lab9.6 Balloon Cars Lab
Lab 9.10 Determining an Average Speed
Review Questions 1,3,4,7,9,11 pg 376
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Answer Key
Answer Key
Test Chapter 9
Introduction to Vectors
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Reference Point – origin or starting point of a journey. Ie. “YOU ARE
HERE” on a mall map
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Position – separation and direction from a reference point. ie. “150 m
[N] of “YOU ARE HERE”
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Vector Quantity – includes a direction such as position. A vector
quantity has both size and direction ie. 150m [N] of Sport Chek
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Scalar quantity – includes size but no direction. ie. 150 m away from
Sport Chek
Find Your Friend – You receive a text from a close friend asking for a
money loan, that they desperately need. Your task is to find your friend
in the Uptown Mall (Map Scale is 1mm = 10m)
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Enter the mall at the Silver Entrance and walk to the * You Are Here
Map at K7 Use Vectors (arrows drawn to scale on a map) to show
your journey – be very accurate in your line length!!!
Walk 300 m [SE]
Walk 850 m [NE]
Walk 500 m [SE]
Walk 356m [E]
Where is your Friend? Use a Position and Reference Point
Where is the nearest Exit? Describe it as both a vector and a scalar
quantity
Could your friend have got his money any other way?
Chapter 11 Displacement and Velocity
Quantity Symbol
Symbol
Example
Scalar Quantity
Distance
d
Time
t
292 m
3.0 h
Vector quantity
Position
Displacement
200 m [E]
(from Michael’s)
d
d
30 m [S]
of *You Are Here
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Displacement
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Symbol Format
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– a change in position. See BLM 11.1a
– used when communicating a vector. See BLM 11.1b
Drawing Vectors –
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Draw a compass rose (N,E,S,W)
and the scale i.e. 1 cm = 10m
Draw the arrow to the stated scale or write the size of
the vector next to the line
20 m
The direction of the arrow represents the direction of
the vector and the length of the line represents the size
of the vector
Assignment : Introduction to Vectors
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Questions 1,5,6,7,8 pg 417
Walk the Graph Activity pg 418 & BLM 11.2
Adding Vectors on a Straight Line
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Vector Diagrams – Join each vector by connecting
the “head” end of one vector to the “tail end of the
next vector.
vector.
Find the resultant vector by drawing an arrow from
the tail of the first vector to the head of the last
vector
 Resultant
d
R
displacement is a single displacement that has the same
effect as all of the individual displacements
combined.
Adding vectors can be done by one of
the following methods
using
scale diagrams
adding vectors algebraically
combined method
 See
BLM 11.3
11.3 Adding Vectors Along a Straight Line
Two vectors can be added together to determine the
result
(or resultant displacement).
Use the “head to tail” rule
Join each vector by connecting the “head” and of a
vector to the
“tail” end of the next vector
d1
d2
dR
Resultant vector
Scale Diagram Method
Leah takes her dog, Zak, for a walk. They walk 250 m
[W] and then back 215 m [E] before stopping to talk to a
neighbor. Draw a vector diagram to find their resultant
displacement at this point.
Scale Diagram Method
1)State the direction (e.g. with a compass symbol)
N
2)List the givens and indicate the variable being solved
d1 = 250m [W], d2 = 215m [E], dR = ?
3)State the scale to be used
1 cm = 50 m
4)Draw one of the initial vectors to scale
5)Join the second and additional vectors head to tail and
to scale
6)Draw and label the resultant vector
dR
7)Measure the resultant vector and convert the length
using your scale
0.70 cm x 50m / 1 cm = 35m [W]
8)Write a statement including both size and direction of
the resultant vector
The resultant displacement for Leah and Zak
Is 35 m [W].
Adding Vectors Algebraically
This time Leah’s brother, Aubrey, takes Zak for a walk
They leave home and walk 250 m [W] and then back
175 m [E] before stopping to talk to a friend. What is the
resultant displacement at this position.
Adding Vectors Algebraically
When you add vectors, assign + or – direction to the value
of the quantity.
(+) will be the initial direction
(-) will be the reverse direction
1.Indicate which direction is + or –
250 m [W] will be positive
2.List the givens and indicate which variable is being
solved
d1 = 250 m [W], d2 = 175 m [E], dR = ?
3.Write the equation for adding vectors
dR =
d1
+
d2
4.Substitute numbers (with correct signs) into the
equation and solve
dR = (+ 250 m) + (-175 m)
dR = + 75 m or 75 m[W]
5.Write a statement with your answer ( include
size and direction)
The resultant displacement for Aubrey and Zak is 75 m [W]
Combined Method
Zak decides to take himself
for a walk.
He heads 30 m [W] stops,
then goes a farther 50 m [W]
before returning 60 m[E].
What is Zak’s resultant
displacement?
Combined Method
1)State which direction is positive and which is negative
West is positive, East is negative
2)Sketch a labeled vector diagram – not to scale but
using relative sizes
30m
50m
60m
dR
3)Write the equation for adding the vectors
dR = d1 +d2 +d3
4)Substitute numbers( with correct signs) into the equation and
solve
dR = (+ 30 m) + (+50m) + (-60m)
dR = + 20m or 20m [W]
5)Write a statement with your answer (including size and
direction)
The resultant displacement for Zack is 20 m [W]
Assignment : Adding Vectors in a Straight
Line
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Questions 1-3,5-7 pg 423 Answer Key
Activity “Bug Race”
Adding Vectors at an Angle
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If we know the path an object takes we can draw an
accurate to scale vector diagram of the journey. We can
then determine the following;
compare the final position to the reference point
determine the resultant displacement
Certain rules must be followed add vectors at an angle.
See BLM 11.5a
Adding Vectors at an Angle
Scale 1 cm = 5 Km
d R = 5cm
d 1 = 3 cm
dR = 5 cm x 5 Km/1cm
dR = 25 Km [SE]
d 2 = 4 cm
N
Assignment : Adding Vectors at an Angle
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BLM 11.5b
Activity “Hide a Penny Treasure Hunt”
Velocity
Velocity –
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v
a vector quantity that includes a direction and a speed
ie. 100 km/h [E]
Constant Velocity – means that both the size
(speed) and direction stay the same
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Average Velocity – v
av
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is the overall change of position from the start to finish.
It is calculated by dividing the resultant displacement
(which is the change of position) by the total time
V av
=
dR
t
See BLM 11.7a,b
Assignment : Velocity
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BLM 11.7c
Questions 3,5,7, pg 436
Activity Tracking and Position pg 438 & BLM 11.9
Review Questions 4,8,9,10 pg 442
Test Chapter 11
Chapter 12 Displacement, Velocity,
and Acceleration
Position – Time Graphs
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Position and displacement are vectors and
include direction. It is possible to represent vector
motion on a graph. Very much like a distance –
time graph. Can you see the differences?
Can you see the differences?
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The slope of a position-time graph is equal to the
velocity of the motion
The slope of the tangent at a point on a positiontime graph yields the instantaneous velocity.
Instantaneous velocity is the change of position
over an extremely short period of time.
Instantaneous velocity is like instantaneous speed
plus a direction
Assignment : Position-Time Graphs
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Activity : Describing Position-Time Graphs “Walk
the Dog”
Activity : The Helicopter Challenge
Exercise : BLM 12.1 a,b,c
Velocity Time Graphs
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A velocity – time graph can show travel in opposite
directions over a period of time.
The slope of the line on a velocity –time graph
indicates the acceleration of an object
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Acceleration – a
is calculated by dividing the change in velocity by
the time. Because there is a direction associated
with the velocity, the acceleration is also a vector
quantity.
Constant acceleration is uniformly changing
velocity.
Formula
a
=
v
t
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Average Velocity of an object in motion can be
determined from the ratio of total distance divided
by total elapsed time.
V av
=
dR
t
See BLM 12.2 a,b
Assignment : Velocity – Time Graphs
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BLM 12.2 c
Acceleration and Displacement
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Acceleration is the change of velocity over time
Questions 5,7,8 pg 465
Test Chapter 12