SCIENCE 10
UNIT B: ENERGY FLOW IN TECHNOLOGICAL SYSTEMS
Unit Focus Questions
- Which came first: science or technology, and is it possible for technological development to take place without help from “pure” science
- How did effort to improve the efficiency of heat engines result in the formation of the first and second laws of thermodynamics?
- How can the analysis of moving objects help in the understanding of changes in kinetic energy, force, and work?
- Why are efficiency and sustainability important considerations in designing energy conversion technologies?
Chapter B1.0 Investigating the energy flow in technological systems requires and understanding of motion, work, and energy
Key Concepts
- One-dimensional Motion
- Work
Learning Outcomes
- Define, compare and contrast scalar and vector quantities
- Describe displacement and velocity quantitatively
- Define acceleration quantitatively as a change in velocity during a time interval
- Explain that, in the absence of resistive forces, motion at constant speed requires no energy input.
- Recall from previous studies the operational definition for force as a push or pull, and work as energy expended when the speed of an object is increased or when an object is moved against the influence of an opposing force.
- Investigate and analyze one-dimensional scalar motion and work done on an object or system using algebraic and graphical techniques.
.
B1.1 Motion
Uniform MotionReference point – where you measure things from.
Motion – the changing in position of an object relative to a reference point; an imaginary line joining the object to the reference point changes in length and direction or both.
How fast are you moving right now?
Most would answer you are stationary.
Some would say the world is spinning.
Some would say you are orbiting around the Sun.
Some would say the solar system is orbiting the centre of the galaxy.
All are correct, depending on where you measure zero from.
Most would answer you are stationary.
Some would say the world is spinning.
Some would say you are orbiting around the Sun.
Some would say the solar system is orbiting the centre of the galaxy.
All are correct, depending on where you measure zero from.
Uniform Motion – movement in a straight line at a constant speed. Does not speed up or slow down.
Non-uniform motion – movement that changes direction and/or changes speed.
Average Speed – the total distance traveled divided by the total time required to travel the distance
v = d/t
- v - speed , m/s
- d - distance, m
- t - time, s
Ex. A person walks 500 m in 5 min. What was the person’s average speed?
v = d/t
v = 500 m / (5 min x 60 s/min)
v = 1.67 m/s
Ex. A horse runs at 15 m/s for 200 s. How far did the horse go? v = 500 m / (5 min x 60 s/min)
v = 1.67 m/s
d = vt
d = 15 m/s x 200 s
d = 3000 m
d = 3.0 x 103 m
d = 15 m/s x 200 s
d = 3000 m
d = 3.0 x 103 m
How to convert km/h to m/s
Ex. Convert 100 km/h into m/s.
Practice Problems
Try practice problems 1 to 3 on page 128
Using Graphs to Analyze Average Speed
Graphs are often used to represent the motion of a moving object.
Graphs make it easy to interpret the motion.
The time is the manipulated variable.
The distance is the responding variable.
Slope is a mathematical measure of the steepness of the line on a graph.
It is a ratio of the rise (up) to the run (right).
On an graph the slope is the y-axis divided by the x-axis.
Ex. What is the slope of the graph?
You will see linear regression and slope in math 10 common.
Which is moving faster?
Which is moving faster?
Practice Questions
Try practice problem 4 on page 130
Plotting a Speed-Time Graph
Time is the manipulated variable, X-axis
Speed is the responding variable, Y-axis
We have used d = vt.
On a speed vs time graph the v is the y axis and t is the x axis. If we multiple the v by t we get the area under the line.
Practice Questions
Try practice problem 5 on page 133
Ex. Convert 100 km/h into m/s.
100 km/h x 1000 m/ km x 1 h / 60 min x 1 min / 60 s = 27.8 m/s
To change km/h into m/s divide by 3.6
To change m/s into km/h multiply by 3.6
To change km/h into m/s divide by 3.6
To change m/s into km/h multiply by 3.6
Speed Examples
- 0.3 ×10-9 m/s Continental drift
- 0.013 m/s garden snail
- 1.0 m/s average walking speed
- Usain Bolt in the 2009 Berlin World Championships 43 km/h or 11.95 m/s
- 25 m/s peak speed of a galloping horse
- 30 m/s cheetah (fastest land animal) or sailfish (fastest fish)
- 36 m/s fastest human powered vehicle Canadian Sam Whittingham
- 90 m/s high speed train or diving peregrine Falcon (fastest bird)
- 113.3 m/s Bugatti Veyron SS (fastest production car)
- 343 m/s speed of sound
- 347 m/s Thrust SSC (fastest car)
- 981 m/s SR-71 Blackbird (fastest jet plane)
- 1815 m/s X-15 (fastest manned rocket plane)
- 3111 m/s X-43 scramjet (fastest plane)
- 9 604 m/s Space Shuttle
- 70 220 m/s speed of Helio 2 solar probe (fastest man mad object)
- 30 000 000 m/s speed of an electron in a cathode ray tube
- 299 792 458 m/s speed of light (3.00×108 m/s) speed limit of the universe (as far as we know)
Practice Problems
Try practice problems 1 to 3 on page 128
Using Graphs to Analyze Average Speed
Graphs are often used to represent the motion of a moving object.
Graphs make it easy to interpret the motion.
The time is the manipulated variable.
The distance is the responding variable.
Slope is a mathematical measure of the steepness of the line on a graph.
It is a ratio of the rise (up) to the run (right).
On an graph the slope is the y-axis divided by the x-axis.
Ex. What is the slope of the graph?
Use points (1.0 s, 0.5 m) and (4.0, 1.25m)
v = Δd / Δt
v = (d2 - d1) / (t2 - t1)
v = (1.25 - 0.5 m) / (4.0 - 1.0 s)
v = 0.25 m/s
The velocity is 0.3 m/s. (rounded to one significant digit)
The slope is easy to calculate for a perfect straight line graph. However, most experiments do not give a straight line graph. Linear regression gives the best possible slope. v = Δd / Δt
v = (d2 - d1) / (t2 - t1)
v = (1.25 - 0.5 m) / (4.0 - 1.0 s)
v = 0.25 m/s
The velocity is 0.3 m/s. (rounded to one significant digit)
You will see linear regression and slope in math 10 common.
Which is moving faster?
Which is moving faster?
Practice Questions
Try practice problem 4 on page 130
Plotting a Speed-Time Graph
Time is the manipulated variable, X-axis
Speed is the responding variable, Y-axis
We have used d = vt.
On a speed vs time graph the v is the y axis and t is the x axis. If we multiple the v by t we get the area under the line.
Practice Questions
Try practice problem 5 on page 133
Review Questions
What is the equation for velocity?What is the difference between uniform and non uniform motion?
What is the manipulated variable on a distance vs time graph?
What is the responding variable on a distance vs time graph?
What is the manipulated variable on a speed vs time graph?
What is the responding variable on a speed vs time graph?
Practice Questions
B1.1 Check and Reflect page 135
.
Slope is a mathematical measure of the steepness of the line on a graph.
It is a ratio of the rise (up) to the run (right).
On an graph the slope is the y-axis divided by the x-axis.
Ex. What is the slope of the graph?
The slope is easy to calculate for a perfect straight line graph. However, most experiments do not give a straight line graph. Linear regression gives the best possible slope.
You will see linear regression and slope in math 10 common.
Which is moving faster?
Which is moving faster?
Speed is the responding variable, Y-axis
We have used d = vt .
On a speed vs time graph the v is the y axis and t is the x axis. If we multiple the v by t we get the area under the line.
What is the difference between uniform and non uniform motion?
What is the manipulated variable on a distance vs time graph?
What is the responding variable on a distance vs time graph?
What is the manipulated variable on a speed vs time graph?
What is the responding variable on a speed vs time graph?
Ex. I walked 5.0 km
Vector – quantity that indicates magnitude and direction
Ex. I walked 5.0 km [North].
Displacement – vector quantity that measures the change in distance and the change in direction or position of an object
It is a ratio of the rise (up) to the run (right).
On an graph the slope is the y-axis divided by the x-axis.
Ex. What is the slope of the graph?
Use points (1.0 s, 0.5 m) and (4.0, 1.25m)
v = Δd / Δt
v = (d2 - d1) / (t2 - t1)
v = (1.25 - 0.5 m) / (4.0 - 1.0 s)
v = 0.25 m/s
The velocity is 0.3 m/s. (rounded to one significant digit)
v = Δd / Δt
v = (d2 - d1) / (t2 - t1)
v = (1.25 - 0.5 m) / (4.0 - 1.0 s)
v = 0.25 m/s
The velocity is 0.3 m/s. (rounded to one significant digit)
The slope is easy to calculate for a perfect straight line graph. However, most experiments do not give a straight line graph. Linear regression gives the best possible slope.
You will see linear regression and slope in math 10 common.
Which is moving faster?
Which is moving faster?
Practice Questions
Try practice problem 4 on page 130Plotting a Speed-Time Graph
Time is the manipulated variable, X-axisSpeed is the responding variable, Y-axis
We have used d = vt .
On a speed vs time graph the v is the y axis and t is the x axis. If we multiple the v by t we get the area under the line.
Practice Questions
Try practice problem 5 on page 133B1.1 Motion Review
Review Questions
What is the equation for velocity?What is the difference between uniform and non uniform motion?
What is the manipulated variable on a distance vs time graph?
What is the responding variable on a distance vs time graph?
What is the manipulated variable on a speed vs time graph?
What is the responding variable on a speed vs time graph?
Practice Questions
B1.1 Check and Reflect page 135.
B1.2 Velocity
Scalar - quantity that indicates magnitude onlyEx. I walked 5.0 km
Vector – quantity that indicates magnitude and direction
Ex. I walked 5.0 km [North].
Distance Traveled and Displacement
Distance traveled – scalar quantity that measures how far an object has traveledDisplacement – vector quantity that measures the change in distance and the change in direction or position of an object
The navigator method
Used by navigators using a compass (boats, planes, orienteering). They used the north star as their reference point. Ex. Draw the following vectors using the navigator method:
A. 60o
B. 200o
A. 60o
B. 200o
The X-axis, polar method
Used by mathematicians who started on the X-axis as zero degrees and rotated counter clockwise. Ex. Draw the following vectors using the X-axis method:
A. 40o
B. 160o
Ex. A dog runs 50 m [N] and then runs 25 m [S] in 75 seconds.
A. What is the dog’s average speed?
B. What is the dog’s average velocity?
A. 40o
B. 160o
Practice Questions
Do practice problem 7 on page 140Practice Questions
Do practice Problem 6 on page 139.Ex. A dog runs 50 m [N] and then runs 25 m [S] in 75 seconds.
A. What is the dog’s average speed?
B. What is the dog’s average velocity?
Average Speed
Average Velocity
Where is the zero angle for the X-axis method?
What is the direction of rotation for the navigator method?
What is the direction of rotation for the X-axis method?
How can you identify a vector variable?
What does Δ mean?
Acceleration - change in velocity during a specific time interval
Positive acceleration is forward acceleration
Negative acceleration is backwards acceleration
Think of a car with no brakes, only forward and reverse gears.
What happens if you are driving forward and accelerate backwards?
What happens if you are driving backwards and accelerate forwards?
Need graph of acceleration over time
Acceleration Questions What acceleration can people survive?
What is a high acceleration?
What is a car’s acceleration?
What is the direction of negative acceleration?
What is the manipulated variable on a speed vs. time graph?
What is the responding variable on a speed vs time graph?
Force – any push or pull
Ex. A hare with a mass of 2.0 kg pushes with a force of 9.4 N. What is the hare's acceleration?
Ex. A Porsche 997 Turbo can accelerate from 0 to 28 m/s [forward] in 3.2 seconds and masses 1443 kg. How much force is required to accelerate it?
A Newton is not a base SI unit, it is made up of kg, m and seconds.
1 N = 1 kg x m / s2
We use the Newton because it is easier and more convenient.
Force Questions
Ex. A gardener pushes a wheelbarrow with 800 N [west] as distance of 20 m [west]. How much work did the gardener do?
Ex. An airplane with a mass of 50 tonnes uses 6.0 x 108 J accelerate over a distance 1.5 km. What is the plane's acceleration?
Note that the definition of work uses energy and the definition of energy uses work. The definitions are circular. It is almost impossible to describe work and energy without examples.
Work Questions
What is work?
What are the units for force?
What are the units for work?
Linear Regression Example
average speed = distance travelled / elapsed time
v = Δd / Δt
v = (50 m + 25 m) / 75 s
v = 75 m / 75 s
v = 1.0 m/s
The average speed is 4.0 m/s.
v = Δd / Δt
v = (50 m + 25 m) / 75 s
v = 75 m / 75 s
v = 1.0 m/s
The average speed is 4.0 m/s.
average velocity = displacement / elapsed time
v = d / Δt
v = (50 m [N] + 25 m [S]) / 75 s
v = 25 m [N] / 75 s
v = 0.33 m/s [N] The average speed is 0.33 m/s [N].
The dog runs north and then south for 75 seconds or the owner can walk north at 0.33 m/s to meet the dog 25 m [N] 75 seconds later.
v = d / Δt
v = (50 m [N] + 25 m [S]) / 75 s
v = 25 m [N] / 75 s
v = 0.33 m/s [N] The average speed is 0.33 m/s [N].
The dog runs north and then south for 75 seconds or the owner can walk north at 0.33 m/s to meet the dog 25 m [N] 75 seconds later.
B1.2 Velocity Review
Review Questions
Where is the zero angle for the navigator method?Where is the zero angle for the X-axis method?
What is the direction of rotation for the navigator method?
What is the direction of rotation for the X-axis method?
How can you identify a vector variable?
What does Δ mean?
Practice Questions
Do check and reflect on page 145.
B1.3 Acceleration
Types of AccelerationAcceleration - change in velocity during a specific time interval
a = v/t
a = (vf - vi)/ t
a = (vf - vi)/ t
- a - acceleration, m/s2
- v - velocity, m/s
- t - time, s
Positive acceleration is forward acceleration
Negative acceleration is backwards acceleration
Think of a car with no brakes, only forward and reverse gears.
What happens if you are driving forward and accelerate backwards?
What happens if you are driving backwards and accelerate forwards?
Practice Questions
Do practice problems 12-15 page 147Need graph of acceleration over time
Practice Questions
Do Practice Problem 16 page 149Acceleration Questions What acceleration can people survive?
What is a high acceleration?
What is a car’s acceleration?
B1.3 Acceleration Review
Review Questions
What is the direction of positive acceleration?What is the direction of negative acceleration?
What is the manipulated variable on a speed vs. time graph?
What is the responding variable on a speed vs time graph?
.
B1.4 Work and Energy
ForceForce – any push or pull
F = ma
- F - force, N
- m - mass, kg
- a - acceleration, m/s2
Ex. A hare with a mass of 2.0 kg pushes with a force of 9.4 N. What is the hare's acceleration?
a = F / m
a = 9.4 N / 2.0 kg
a = 4.7 m/2
a = 9.4 N / 2.0 kg
a = 4.7 m/2
Ex. A Porsche 997 Turbo can accelerate from 0 to 28 m/s [forward] in 3.2 seconds and masses 1443 kg. How much force is required to accelerate it?
a = v / t
a = (28 - 0) m/s / 3.2 s
a = 8.75 m/s2
F = m a
F = 1443 kg x 8.75 m/s2
F = 1.26 x 104 N
a = (28 - 0) m/s / 3.2 s
a = 8.75 m/s2
F = m a
F = 1443 kg x 8.75 m/s2
F = 1.26 x 104 N
A Newton is not a base SI unit, it is made up of kg, m and seconds.
1 N = 1 kg x m / s2
We use the Newton because it is easier and more convenient.
Force Questions
Work
Work – the energy transferred from one object to another. W = Fd
- W - work, J
- F - Force, N
- d - distance, m
- There must be movement
- There must be a force
- The force and the displacement must be in the same direction
Ex. A gardener pushes a wheelbarrow with 800 N [west] as distance of 20 m [west]. How much work did the gardener do?
W = F x d
W = 800 m [west] x 20 m [west]
W = 16 000 J
W = 1.6 x 104 J
W = 800 m [west] x 20 m [west]
W = 16 000 J
W = 1.6 x 104 J
Ex. An airplane with a mass of 50 tonnes uses 6.0 x 108 J accelerate over a distance 1.5 km. What is the plane's acceleration?
F = W /d
F = 6.6 x 108 J / 1.5 x 103 m
F = 440 000 N
a = F/m
a = 440 000 N / 50 x 103 kg
a = 8.8 m/s2
F = 6.6 x 108 J / 1.5 x 103 m
F = 440 000 N
a = F/m
a = 440 000 N / 50 x 103 kg
a = 8.8 m/s2
Practice Questions
Do Practice Problems 18 to 20 page 160Energy
Energy – the ability to do workNote that the definition of work uses energy and the definition of energy uses work. The definitions are circular. It is almost impossible to describe work and energy without examples.
Work Questions
B1.4 Work and Energy Review
Review Questions
What is a force?What is work?
What are the units for force?
What are the units for work?
Practice Questions
Unit B1.0 Section ReviewLinear Regression Example