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Grade 10 Science. Motion Unit. Significant Digits. 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

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grade 10 science

Grade 10 Science

Motion Unit

significant digits
Significant Digits
  • 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

slide4

2340.00

0.1240

2005

Decimal

Absent

0.003450

Decimal

Present

2500

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.

counted and exact values
Counted and Exact Values
  • 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
Converting Units
  • When you want to change units we use a conversion factor (or equality)
assignment significant digits
Assignment : Significant Digits
  • 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
Relating Speed to Distance and Time
  • 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
A car travels 45 km at a speed of 90 km/h. How long did the trip take?
  • What do you know in the Question
    • d= 45 km
    • Vav = 90 km/h
    • t = ?
slide10
Decide on a formula
    • t = d

Vav

d

Vav

t

slide11
Substitute the knowns into the formula and solve
    • 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
Problem Solving Summary
  • 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
Assignment : Relating Speed to Distance and time
  • BLM 9.5 a,b, d
    • Answer Key
  • Questions 1,2,3,6,7,8 pg 358
  • Answer Key
distance time graphs
Distance – Time Graphs
  • 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
slide15

In the following diagram:

A = constant speed

B = not moving

C = accelerating

See BLM 9.7a

Distance-Time Graphs

assignment distance time graphs
Assignment : Distance – Time Graphs
  • Lab 9.5 Graphing Distances During Acceleration
  • Questions 3,4,5,6 pg 365
    • Answer Key
  • Activity 9.9 Simulation : Average Speed on an Air Table
    • BLM 9.9a
  • Worksheet – Determining Speed from a d/t Graph
    • Q 1-6
      • Answer Key
  • Lab9.6 Balloon Cars Lab
  • Lab 9.10 Determining an Average Speed
  • Review Questions 1,3,4,7,9,11 pg 376
    • Answer Key
  • Test Chapter 9
introduction to vectors
Introduction to Vectors
  • Reference Point – origin or starting point of a journey. Ie. “YOU ARE HERE” on a mall map
  • Position – separation and direction from a reference point. ie. “150 m [N] of “YOU ARE HERE”
  • Vector Quantity – includes a direction such as position. A vector quantity has both size and direction ie. 150m [N]
  • Scalar quantity – includes size but no direction. ie. 150 m
slide20
Displacement – a change in position.
  • See BLM 11.1a
  • Symbol Format – used when communicating a vector.
  • See BLM 11.1b
  • Drawing Vectors –
    • state the direction (N,E,S,W)
    • Draw the line to the stated scale or write the size of the vector next to the line
    • The direction of the line represents the direction of the vector and the length of the line represents the size of the vector
assignment introduction to vectors
Assignment : Introduction to Vectors
  • Questions 1,5,6,7,8 pg 417
  • Walk the Graph Activity pg 418 & BLM 11.2
adding vectors on a straight line
Adding Vectors on a Straight Line
  • Vector Diagrams – Join each vector by connecting the “head” end of one vector to the “tail end of the next vector.
  • Find the resultant vector by drawing an arrow from the tail of the first vector to the head of the last vector
  • Resultant displacement -

is a single displacement that has the same effect as all of the individual displacements combined.

  • Vector Diagrams – Join each vector by connecting the “head” end of one vector to the “tail end of the next vector.
  • Find the resultant vector by drawing an arrow from the tail of the first vector to the head of the last vector
  • Resultant displacement - d R

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
Adding vectors can be done by one of the following methods
  • using scale diagrams
  • adding vectors algebraically
  • combined method
  • See BLM 11.3
slide24

11.3 Adding Vectors Along a Straight LineTwo vectors can be added together to determine the result (or resultantdisplacement).Use the “head to tail” ruleJoin each vector by connecting the “head” and of a vector to the“tail” end of the next vector

slide26

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.

slide27

N

Scale Diagram Method

1)State the direction (e.g. with a compass symbol)

2)List the givens and indicate the variable being solved

3)State the scale to be used

4)Draw one of the initial vectors to scale

d1 = 250m [W], d2 = 215m [E], dR = ?

1 cm = 50 m

slide28

5)Join the second and additional vectors head to tail and to scale

6)Draw and label the resultant vector

7)Measure the resultant vector and convert the length using your scale

8)Write a statement including both size and direction of the resultant vector

dR

0.70 cm x 50m / 1 cm = 35m [W]

slide30

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.

slide31

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 –

2.List the givens and indicate which variable is being solved

250 m [W] will be positive

d1 = 250 m [W], d2 = 175 m [E], dR = ?

slide32

d1 +

dR =

d2

3.Write the equation for adding vectors

4.Substitute numbers (with correct signs) into the equation and solve

5.Write a statement with your answer ( include size and direction)

dR = (+ 250 m) + (-175 m)

dR = + 75 m or 75 m[W]

The resultant displacement for Aubrey and Zak is 75 m [W]

slide33

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?

slide34

Combined Method

1)State which direction is positive and which is negative

2)Sketch a labeled vector diagram – not to scale but using relative sizes

West is positive, East is negative

30m

50m

60m

dR

slide35

3)Write the equation for adding the vectors

4)Substitute numbers( with correct signs) into the equation and solve

5)Write a statement with your answer (including size and direction)

dR = d1 +d2 +d3

dR = (+ 30 m) + (+50m) + (-60m)

dR = + 20m or 20m [W]

The resultant displacement for Zack is 20 m [W]

assignment adding vectors in a straight line
Assignment : Adding Vectors in a Straight Line
  • Questions 1-3,5-7 pg 423 Answer Key
  • Activity “Bug Race”
adding vectors at an angle
Adding Vectors at an Angle
  • 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 angle1
Adding Vectors at an Angle

Scale 1 cm = 5 Km

dR = 5 cm x 5 Km/1cm

dR = 25 Km [NW]

d R = 5cm

d 1 = 3 cm

N

d 2 = 4 cm

assignment adding vectors at an angle
Assignment : Adding Vectors at an Angle
  • BLM 11.5b
  • Activity “Hide a Penny Treasure Hunt”
velocity
Velocity
  • Velocity – 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
slide41
Average Velocity – v av
    • 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 = d R

t

  • See BLM 11.7a,b
assignment velocity
Assignment : Velocity
  • 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
position time graphs
Position – Time Graphs
  • 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?
slide46
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 position-time 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
Assignment : Position-Time Graphs
  • Activity : Describing Position-Time Graphs “Walk the Dog”
  • Activity : The Helicopter Challenge
  • Exercise : BLM 12.1 a,b,c
slide49
Avelocity – 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
slide50
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
Formula

a = v

t

slide52
Average Velocity of an object in motion can be determined from the ratio of total distance divided by total elapsed time.

V av = d R

t

See BLM 12.2 a,b

acceleration and displacement
Acceleration and Displacement
  • Acceleration is the change of velocity over time
  • Questions 5,7,8 pg 465
  • Test Chapter 12