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Science 10 – Unit 2 – Physics Notes – Mrs. Horne
Lesson 1:
Significant digits & scientific notation
Uncertainty of measurements
All measurements are subject to uncertainties. All instruments used are influenced by external
circumstances, and the accuracy of a measurement may be affected by the person making the
reading.
Recording measurements:
When you read any measuring device, you always record the measurement by . . . reading the
smallest division on the scale and then “guessing at” or estimating, the tenth of the smallest
division.
These estimates create uncertainty!
Record the correct readings of the ruler
a.
b.
c.
d.
e.
Record the correct reading on the thermometer:
Significant digits.
Significant digits are all those digits obtained from a properly taken measurements: all of the
certain digits plus one estimated digit. The number of significant digits indicates the precision
of the measurement. More sig digs means a more precise measurement.
Rules:
 1. All digits 1-9 are significant
◦ Ex. 123 ( 3 sig digs)
 2. leading zero’s are not significant
◦ Ex. 0.12 & 027 (2 sig digs)
 3. Zero’s to the right are only significant if:
a. it is after a decimal
◦ Ex: 0.12700 & 20.000 (5 sig digs)
 b. units are attached to the number
◦ Ex. 100 g (3 sig digs)
c. In scientific notation
Examples:
1.
2.
3.
4.
5.
Manipulation of data:
When adding, subtracting, multiplying & dividing:
Ensure that your final answer has the same amount of significant digits as the least amount of
sig digs in the question
 Ex. 12.3 + 10 = 22
(3) (2) (2)
When doing a series of calculations to arrive at an answer, never round off your sub-steps.
Only round your final answer. If possible, keep the significant digits in your calculator. A good
rule of thumb is to write three more significant digits than you’ll need to round to at the end.
Rounding:
1. if the number to the right is 4 or less, the last digit should not be changed
2. if the number to the right is 5 or greater, the last digit should be increased by one.
Scientific notation:
Put the decimal after the first digit
Ex. 123 000 000 = 1.23 000 000
To find the exponent count the number of places from the decimal to the end of the number
8
Ex. 1.23 000 000 = 10
Drop any zeros that are to the right
◦
8
Ex. 1.23 x 10
0
2
1 = 1 x 10
-2
100 = 1 x 10
1
0.01 = 1 x 10
-1
10 = 1 x 10
0.1 = 1 x 10
Kilo hecto deca base unit deci centi mili
3
10
2
10
1
10
0
10
-1
10
-2
10
-3
10
Evaluating powers of 10
 When multiplying : add powers of ten
4
3
3
2
4+3
7
◦ Ex. 10 x 10 = ( 10 ) 10
 When dividing : subtract powers of ten
◦
3-2
Ex. 10 / 10 = (10
1
) 10
Complete: Scientific notation and significant digits worksheet
Lesson 2: Algebra Review, Units & Unit conversions:
SI (system international) Units: are an internationally decided upon set of base units for which
most calculations are to be recorded/ reported as.
Some area of science choose to use different SI units because it is easier
EX: Astrophysics: uses light years (distance light travels in one year) instead of 9.454259555 x 10
15
m
There are 7 fundamental SI units. You will only work with the following 5.





*Length
*Mass
*Time
Electrical current
Temperature
meter
kilogram
second
Ampere
Kelvin
m
kg
s
A
k
Prefixes are used to give names to powers of 10. They are found in your data book and range
12
-12
from tera (10 ) to pico (10 )
Base units are the units which you will multiply by the power of ten. They are:
meter (m), gram (g), liter (L), and mole (mol).
What is their power of 10?
Metric conversions:
Converting between Km/h and m/s
m/s = (km/h) x (1000m/1km) x (1h/3600s)
Km/h = (m/s) x (1km/1000m) x (3600s/1h)
*** remember there are 60 seconds in a minutes, 60 minutes in an hour, therefore 60s x 60
min = 3600s/h
Algebra (isolating a variable):
Lesson 3: graphing:
Scatter plot graphs
 Scatterplot graphs are useful for analyzing the relationship between quantitative data in
which both the manipulated and responding variables continually change during an
experiment.
 Shows the relationship between 2 variables
Independent variable:
 The independent variable is also called the manipulated variable. It is the one that the
experimenter changes, or has control over.
 It is always plotted on the horizontal axis, or x-axis
 When looking at the data table, the independent variable will be seen to increase by
regular intervals
Dependent variable:
 The independent variable is also called the manipulated variable. It is the one that the
experimenter changes, or has control over.
 It is always plotted on the horizontal axis, or x-axis
 When looking at the data table, the independent variable will be seen to increase by
regular intervals
For Example:
 To determine the density of a liquid, a student measures the mass of various volumes of
the liquid.
 Volume is the independent variable because the experimenter set it, and it increases at
regular intervals.
 Mass is the dependent variable because the experimenter measured it and it does not
increase by regular intervals
Graphing rules:
Your title should be short, but still clearly tell what you have graphed
2. Labeled Axis
Make sure to write out the full name of what you have graphed on each axis, along with the
units you used.
 X-axis : manipulated variable
 Y-Axis: responding variable
3. A well chosen scale
The information you plot should cover at least 75% of the area on your graph
You should have an even scale
4. The correct data plotted
You should always put little circles around each dot, since they might be hard to see on the
graph paper.
5. A best Fit Line (curve, straight line, no relationship)
Usually you do not want to play “connect the dots” with your plots on your graph
Instead you should try to draw a completely straight line that best fits your data
Try to get half of the points above the line and half below the line
Line of best fit
 If there is a clear pattern among the points, draw a best fit line that comes as close to
most of the points. Best fit line may be straight or curved.
Slope:
SLOPE(M) MEASURES THE AMOUNT OF STEEPNESS OF A GIVEN LINE SEGMENT
SLOPE MAY BE DEFINED AS THE VERTICAL CHANGE (RISE) DIVIDED BY THE HORIZONTAL CHANGE (RUN)
rise
Y –Y
2
1
Slope = ------------- = -------------run
X –X
2
1
Pick 2 points on the straight line graph and it will give you the slope.
Lesson 4:
Displacement vs. Distance
Scalar– magnitude (amount or size) only, but no direction
examples: time, mass, distance and speed
Vector – magnitude & direction
examples: displacement, velocity, force
**vector quantities are written with an arrow above the symbol
Distance (∆d)- length of a path between 2 points (scalar)
Displacement(∆đ) – length of a path & direction (N,S,E,W)
Displacement
∆d = d 2 - d 1
Where
∆ d is displacement
d 2 is the final or ending position
d 1 is the initial or starting position
The SI unit for position and displacement in metres, m.
 The displacement of an object is defined as its change in position, relative to where it
started
 Calculated by using the initial & final positions of an object
Vector signs
 When using vector quantities in formulas, we do not write the direction using words.
Instead we use negative (-) and positive (+) signs
Negative directions
positive directions
Backward
forward
Down
up
Left
right
West
east
South
north
Find the displacement vector from position A to B if:
dA = -4.0cm & dB = +11.0cm
Bart drives 6 m and then turns around and walks 8 m. w
what is his total displacement? Distance?
If Bart ran 2 km [E], then turned around and ran 5 km[W]. What is his displacement? Distance?
Draw a vector diagram.
Lesson 5: speed and velocity
Speed: the distance travelled by an object during a given time interval divided by the time interval
•
Scalar quantity!
Speed
v ave =
d
t
Where v ave is average speed in metres per second,m/s.
d is distance in meters, m
t is the time interval in seconds, s.
Velocity is the displacement of an object during a time interval divided by the time interval
•
Vector quantity
Velocity
v ave 
d d
d
or v ave  2 1
t2  t1
t
where v ave is average velocity in meters per second,m/s.
∆ d is the displacement in meters,m.
d 2 is the final position in metres, m.
d 1 is the initial position in metres,m.
∆t is the time interval in seconds,s.
t2 is the final time in seconds, s.
t1is the initial time in seconds,s.
Speed example:
•
A car travelled a distance of 550 m in a time of 35 s. What is the speed of the car?
Velocity example:
•
•
•
•
2 trainers with stop watches
Timer 1: is at 12 m[S]
Timer 2: is at 65 m[S]
from the start line
Each stop their watches once the runner passes them.
Timer 1: 1.6s
•
Timer 2: 8.7s
What is the runners velocity while running between trainers?
Graphing velocity
Ex 1. Sprinter at rest, no change in position
Ex 2. Sprinter steadily changing position
Ex 3. Sprinter changes position in opposite direction
Each of the 3 previous graphs shows a constant velocity
(speed and direction not changing!)
This is called uniform motion
(no change in velocity)
Position time graphs
Calculating slope:
•
•
When calculating slope of a line DO NOT use any of the actual points because they may
not lie directly on the line.
Choose 2 points of the line that are near the opposite ends of the line. Calculate the
slope from these points
Lesson 6: acceleration
Acceleration
a ave 
d
t
or
a ave 
Unit Analysis
v 2  v1
t2  t1
Where a ave is average acceleration in
a ave 
d
t
m
m
 s
s2
s
Meters par second squared, m/s2
m m s
 
s2 s 1
∆ v is the change in velocity in meters per
second, m/s.

v1 is the initial velocity in meters per second, m/s
m 1

s s
v2 is the final velocity in meters per second, m/s
t2 is the final time in seconds, s

m
s2
t1 is the initial time in seconds, s.
Acceleration: Any change in the velocity of an object during a time interval
When solving problems, the sign ‘+’ or ‘-’ will tell you the direction of the acceleration
Ex: a person observed a cheetah reach a speed of 19 m/s from a standing start in a period of 2.0
seconds.
What was the acceleration?
Graphing Accelerated motion!
Position vs time graphs
How to find acceleration of an abject in a curved graph
Take the first two points, and the last two points
Velocity time graphs!
Ex 1. Velocity time graphs!
Ex 2. Velocity is decreasing uniformly
Ex 3. Velocity is increasing uniformly
Lesson 7: Quiz up to this point thus far
Lesson 8: Uniform motion lab/Acceleration lab
Lesson 9: Force (Newton’s laws)
There are many kinds of energy:
Kinetic energy (energy of motion)
Gravitational potential energy (energy at a height)
Light energy
Electrical energy
Sound energy
Thermal energy (heat)
Chemical energy
Nuclear energy
The energy transformation involved to produce all motion is due to a force, whether provided
by gravity or by applied force.
A force is a push or a pull. Force is in Newtons (N).
F = ma
Where
F = force (N)
m = mass (kg)
a= acceleration (m/s2)
Newton’s First Law
An object at rest will remain at rest or an object in moving with constant velocity will remain
in motion, unless an external non-zero net force acts upon the object.
-Inertia: property of an object the resists acceleration.
Newton’s Second Law
Fnet = m x a
When non-zero net force acts on an object, the object accelerates in the direction of the net
force. Acceleration is directly proportional to force and inversely proportional to mass.
Newton’s Third Law
When an object exerts a force on a second object, the second object exerts an equal and
opposite force on the first.
“For every action (force) there is an equal, but opposite reaction (force).”
FAonB = -FBonA
Example:
1. While standing on a horizontal, frictionless surface, two students push against each
other. One student has a mass of 35 kg, and the other 45 kg. If the acceleration of the 35
kg student is 0.75 m/s2 south, what is the acceleration of the 45 kg student?
F1 = F 2
m1a1 = -m2a2
(35 kg) (0.75m/s2) = - (45kg) a2
a2 = 0.58 m/s2 north
Calculating Work From Force vs Displacement Graphs
Lesson 10:
- Energy is the ability to do work. Energy is measured with the unit of JOULES
Work is when a force causes motion.
If there is no force, there is no work being done.
If there is nothing moving (no distance travelled) there is no work being done.
- Work can be calculated using the following formula:
W  F d  Ek
Where W = work joules (J)
F = force (N)
d = distance (m)
Work is also equal to the CHANGE in Kinetic Energy.
Ex. You exert a force of 25 N on your textbook while lifting it a height of 1.4 m to put it on a
shelf. How much work did you do on your textbook?
W = ? F = 25 N d = 1.4 m W = 25 x 1.4 = 35 J
Ex. You push on a wall with a force of 40 N. The wall does not move. How much work did you
do on the wall?
0 J! If there is no distance moved, then work is not being done!
Energy of Motion = Kinetic Energy
Calculating Kinetic Energy
Ek 
1 2
mv
2
where Ek is the kinetic energy in Joules (J)
m is the mass of the object in kilograms (kg)
v is the speed in meters par second (m/s)

m
m
m2
Joule = (kg) ( )( ) = Kg ● 2
s
s
s
Ex. A car with a mass of 1500 kg is moving at a speed of 14 m/. What is the kinetic energy of
the car?
Ek = ?
m = 1500 kg
v = 14 m/s
Ek = 1.5 x 105 J
Work and Kinetic Energy
-The relationship between kinetic energy and work is often studied using the first law of
thermodynamics (energy cannot be created or destroyed). It suggests that work done (joules)
to make an object move from rest is equal to its kinetic energy (joule) once it is in motion.
-Some work must always be done against friction. Thus some energy goes into heat.
Lesson 11:
Potential energy is often described as the energy stored in a substance or object due to its
position or condition.
An example of condition is the compression of a spring.
Form of Potential Energy
1. Elastic Potential Energy
An object is elastic if it always returns to its original form.
2. Chemical Potential Energy
Chemical potential energy: energy stored in the bonds of chemical compounds which is
released when bonds in a molecule break or are rearranged.
Chemical potential energy is the difference in the potential energy of reactants and
products.


Some chemical reactions release energy when they
Proceed (exothermic)
Some chemical reactions require an input of energy in order to proceed. (endothermic)
3. Nuclear Potential Energy
The energy stored in the bonds between protons and neutrons in the nuclei of atoms.
Fission : When the nucleus of an atom splits into smaller nuclei.
The nuclear potential energy that is released when the large nuclei fissioned is transformed into
thermal energy. This thermal energy in nuclear reactors converts water into the steam that
drives an electric generator.
4.
Gravitational Potential Energy
Gravitational potential energy is stored as a result of an object’s position (height above surface)
Explaining Gravity
Gravity is a property of anything that has mass.
Gravitational potential energy depends only how far an objects is lifted vertically.
Acceleration due to gravity: the acceleration with which all objects near Earth’s surface would
fall if there were no air friction; approximate value is 9.81 m/s2.
Calculating Gravitational Potential Energy




Mass and weight are not the same.
Mass affects the weight
Mass never change.
Weight is the force of gravity acting on a mass
Weight
Fg = mg
Where Fg is used to represent weight and the units are newtons (N)
m is the mass in kilograms (kg)
Gravitational Potential Energy
g is the acceleration due to gravity in meters per
Eg = mg∆h
second squared (kg ●m/s2)
Where Eg is the gravitational potential energy in joules (J)
m is mass in kilograms (kg)
g is the acceleration due to gravity in meters per second squared
(m/s2)
∆h is the height in meters (m)


See Model problem 5 page 210
Do Practice Problems page 212
Ex: A 1.2 kg book sits on a shelf 1.8 m above the floor. What is the potential energy of the
book?
Ep = ?
m = 1.2 kg
g = 9.81 m/s2 h = 1.8 m
Ep = 21 J
Assignment:
Practice problems pg 212 #41-49 OR Ep worksheet
Lesson 11: Efficiency of Energy Conversions
Heat is a by-product of most energy transformation.
Efficiency and the Second Law of Thermodynamics
Second Law of Thermodynamics
“No process can be 100 percent efficient. Some energy will
always remain in the form of thermal energy.
All machines convert one form of energy into another form in order to accomplish a specific
task.
Useful energy: Energy that performs a task.
During any process, some energy is always converted into a form that is not useful. This energy
is often said to be “wasted”.
Calculating Efficiency
Efficiency = useful output energy × 100%
total input energy
If for example, a system is 30 percent efficient (i.e., has a useful energy output of 30 percent),
this means that 70 percent of the energy going into the system is wasted.
Lesson 12: Mechanical Energy and the Pendulum (pendulum lab)
Mechanical Energy

Mechanical energy is the energy of an object because of its position, or because of
its motion.

If you throw a ball into the air, the ball has kinetic energy as it leaves your hand;
however, eventually the ball will reach its highest point where it will come to a stop.
At this point, the ball as potential energy. Kinetic energy was converted to potential
energy, then back to kinetic energy as the ball falls back towards your hand.

The sum of the kinetic and potential energies is constant throughout the motion. The
mechanical energy remains constant.

The law of conservation of mechanical energy states:
In a frictionless system mechanical energy is conserved.
∆Ek + ∆Ep = 0
And therefore, ∆Ek = - ∆Ep
½ mv2 = - mgh
**Since “m” is on BOTH sides of this equation, we can cancel them out.
½ v2 = -gh

If there is friction, then some of mechanical energy is converted to thermal energy.
Pendulum :
Examples
1.
A heavy object is dropped from a vertical distance of 12.0 m above the ground.
What is the speed of the object as it hits the ground?
∆Ek = - ∆Ep
½ mv2 = - mgh
½v2 = - gh
V = 15 m/s
2.
A pendulum is dropped from a position of 0.25 m above the equilibrium position.
What is the speed of the bob as it passes through the equilibrium position?
Ek = - Ep
1/2v2 = -gh
½ v2 = -(-9.81m/s2)(0.25m)
V = 2.2 m/s
Assignment
Mechanical Energy Practice Problems.doc Worksheet