Transcript Document

Motion Unit
Grade 10 Science
Chapter 11
Displacement and Acceleration
Introductory Activity
From Here to There (Use GPS Compass and Paces)
Giving directions isn’t always easy – it forces us to think about things we do automatically.
(a) Working in a group, write clear instructions from where you are to some other location in your
school.
(b) Produce a map, drawn to scale, showing the route to the target location
(c) Exchange instructions and/or maps with another group and try to reach their target location by
following their directions
(d) Evaluate the other group’s map and instructions. Suggest a better form of communication?
Suggest some improvements to the instructions. What are some sources of uncertainty? How
confident are you in their set of instructions?
GPS Activity
• Using the GPS’s and longitude and latitude, create a
scavenger hunt
• Choose a word with 6-8 letters and place 1 letter from
the word at each of the points on your map
• Unscramble the word when you complete the
scavenger hunt.
11.1 Vectors : Position and Displacement
Question : If you leave home on a trip, and then end up back at home at the
end of the trip, the total distance travelled is not zero, but something is
zero. What is zero, and , how does this depend on direction?
Question : How can we show direction on a graph?
Question : When providing directions for a visitor, what are some of the
different ways to indicate direction?
All distances and directions are generally stated relative to some reference point, which
is usually the origin or starting point. For example if you go on a trip most people
would say their reference point or origin is their home.
Your position is the separation and direction from a reference point. For example you
may be at a position of 152 m [W] – one hundred and fifty two meters west of the
reference point.
152 m [W]
0
A change in position (  d ) is known as displacement.  means “the change in” and
d means “ change in position”.
d = d 2 - d 1
A change in position from one point to another is calculated using the above
formula.
d = d 2 - d 1
d = (152 m) - (0)
 d = 152 m [W]
Symbol Format
When communicating a vector quantity, the value is accompanied
by a direction
Direction is best communicated with a direction from a compass
needle not forwards or backwards
Example :  d = 38 km [W]
Drawing Vectors
An alternative way of communicating a vector quantity is to draw a vector. A vector is a
line segment that represents the size and direction of a vector quantity. Example :
1 cm = 25 km
A quantity that involves a direction, such as position, is called a vector quantity.
A vector quantity has both size (152m) and direction [W].
A quantity that involves only a size, such as distance, (250 km) is called a scalar
quantity.
A scalar quantity has no direction.
Assignment:Q1-8 pg 417
CBL Velocity Lab #1
11.3 Adding Vectors Along a Straight Line
Two vectors can be added together to determine the result
(or resultant displacement).
Vector Diagrams
When you add vector quantities such as displacement
you need to consider both the size and direction of each
quantity being added.
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
Anne 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.
Vector Scale Diagram Method
1)State the direction (e.g. with a compass symbol)
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 Anne and Zack
Is 35 m [W].
Adding Vectors Algebraically
This time Anne’s brother, Carl, 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 Carl and Zak is 75 m[W]
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
Combined Method for representing vectors
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
50m
60m
30m
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 zak is 20 m [W]
Assignment
• Questions 1-7 pg 423
11.7 Describing Motion in Words
This lesson introduces you to the terms associated with kinematics,
the study of motion. The key ideas are position, distance, and
displacement which were all studied in previous lessons.
The new terms are speed and velocity, which are closely related.
Velocity is a vector: it is just speed with direction.
Speed is a scalar: it is just speed
Objects with constant velocity have uniform motion.
Velocity:the distance traveled by a moving object per unit of time.
11.7
Describing Motion in Words
A speed along with a direction is a vector, which means that the
direction and the size (speed) stay the same.
On a plane trip from Toronto to Winnipeg the pilot will usually
announce an air speed such as 425 km/h. However, both the pilot
and passengers know that the direction is west, so the velocity is
425 km/h [W]
Average velocity
Average velocity is defined as the rate of change in position from start to
finish. It is calculated by dividing the resultant displacement ( which is the
change in position ) by the change in time.
Vav =

dR
t
Comparing average speed with average velocity
Average Speed
Average Velocity
From Chapter 10
Kilometers (km) or
Meters (m)
d
Speed/Velocity (km/h) or
(m/s)
V
t
Velocity only gives distance and time.
Hours (h) or
Seconds (s)
From Chapter 10
Average Velocity: the speed of moving objects is not always constant:
Average Velocity = total distance / total time
d tot
Vav
t tot
d tot= d2 – d1
t tot= t2 – t1
Since speed is distance/time, we can write:
Speed = distance (10m) = 5 m/s
time (2s)
No direction but …
Velocity is… speed in a given direction.
e.g. Sydney walks 3 kilometers north for 2 hours .
This is because…
Velocity = Displacement 3km[N] = 1.5 m/s[N]
Time(2h)
Velocity must have the same units as speed
-normally in physics we use m/s or km/h.
Velocity includes both
 d = change in displacement with a direction
 t = change in time
0m
5m
A
B
5s
d
V
t
N
5m[E] / 5s = 1m/s [E]
Average Velocity is…
change in resultant displacement (dR)
change in time(t)
A
3m
5m resultant
1s
B
1s
C
dR
Vav
t
4m
5m [SE] / 2s = 2.5 m/s [SE]
Leon walks quickly around the outside of a basketball court.
She walks 50 m north, 25 m east and 50 m south. This takes 50
seconds.
1.What is the distance she has walked?
(50+25+50)m =125m
2.What is her final displacement?
50m[N] + 25m [E] + 50m[S] = 25m[E]
50m
3.What is her velocity?
125m / 50 s = 2.5m/s
4.What is her average velocity?
25m[E] / 50s = 5m/s [E]
Work these out, then check your answers
25m
50m
dR
Assignment
• Questions 1-7 pg 436