Science 10 Physics Notes
I Significant Digits and Scientific Notation 1.
Introduction
Measurements can vary with respect to precision and accuracy.
Precise: how closely measurements agree with one another.
Accurate: how closely measurements agree with the “correct” value.
In general, the more precise a measurement is the more accurate unless the tool is poorly calibrated.
Precision relates to the uncertainty of tools. Significant digits are used to
communicate the uncertainty of the tool. Accuracy refers to how close you are to the true value.
Measurements can only be recorded based on the number of significant digits the tool provides. Ex: 31.26
That is, measured quantities are generally reported in such a way that only the last digit is uncertain. All digits, including the uncertain one, are
called significant digits.
The number 2.2405 has five significant digits. The number of significant digits indicates the exactness of a measurement.
ex: 5.2 cm (ruler) x 1.55 cm (precise ruler) = 8.06 cm2 = 8.1 cm2
2.
Sigdig Rules
i) #'s 1-9 are significant: 4.231 = 4 sigdigs
ii) Leading zeros are not significant: 0.00015 = 2 sigdigs iii) Trailing zeros are significant: 500.00 = 5 sigdigs
iv) Adding rule: answer has same sigdigs as least precise value used = least number of decimal places.
ex: 12.6 + 2.07 + 0.142 = 14.812 = 14.8 (1 dec) (2) (3)
v) Multiplying rule: answer has same sigdigs as least precise value used.
ex: 0.02489 x 6.94 = 0.1727366 = 0.173 (4 sigdigs) (3 sigdigs) (3 sigdigs) vi) Counted values are not significant (5 cows) vii) Constants are not significant (pi)
3.
Scientific Notation
Use to indicate very large or small numbers but keeping the correct number of sigdigs.
Example 1: Write 3 000 000 to 2 sigdigs:
i) move decimal so it rests just after the first non zero number 3. 000 000 (6 places left)
ii) drop all non significant zeros 3.0
iii) multiply the remaining number by 10n where n=the number of times the decimal place was moved.
3.0 x 106
Example 2: Write 0.000521745 to 3 sigdigs i) 5.22 x 10-4
**if decimal moves left n=positive
**if decimal moves right n=negative 4.
Calculator Use
i) 6.2 x 106 ii) 5.11 x 10-3
II
Energy and Motion 1.
Newton’s First Law: Inertia
An object at rest or in motion tends to stay at rest or in motion unless an outside force acts upon it.
The tendency to resist change is called inertia; the more mass, the more inertia.
Lab Assignment
What is the effect of time on distance for a rolling ball?
Materials: stopwatch, ball, graph paper, rulers i) make a table (time (s), distance (tiles)) 1 tile = ? m
ii) record distance ball rolls for 0 - 10 seconds (2 second intervals). Keep speed as uniform as possible.
iii) graph results ( time = mv)
iv) calculate slope = (y2 - y1)/(x2 = x1) Slope Instruction
Pick two points (X-value, Y-value) that are on the line. The easiest points to pick are points where the line crosses the grid of the graph paper so you don't have to extrapolate the x and y values of the points. In this example, Point 1 could be (5,10), i.e., X1 = 5 and Y1 = 10, and Point 2 could be (10,20), i.e., X2 = 10 and Y2 = 20.
Plug these two points into the following formula to calculate the slope:
v) What does slope represent?
2.
The Slope of a Distance -Time Graph (Uniform Motion)
This slope represents the change in distance corresponding to a change in time = SPEED!!
speed (v) = change in distance (∆d) change in time (∆t) v = ∆d
∆t
**Units Distance Time Speed
m s m/s
km h km/h
cm min cm/min
i) If a train traveled 100 km in 0.50 hr, what was its speed?
d = 100 km v = d/t
t = 0.500 hr v = 100 km / 0.50 hr
v = ? v = 200 km/hr = 2.0 x 102 km/hr
ii) What was the train's speed in m/s?
200 km x 1 hr x 1000 m = 56 m hr 3600 s 1 km s
iii) If a car travels at 30 m/s for 10 s, how far does it go?
v = 30 m/s d = vt
t = 10 s d = 30 m/s x 10 s
d = ? d = 300 m = 3.0 x 102 m
iv) If a bus travels at 80 km/h, what is its speed in m/s?
80 km x 1 hr x 1000 m = 22 m **
hr 3600 s 1 km s
v) If a bus traveled at 40 m/s, and went 4.000 km, how long did it take in seconds, minutes and hours?
v = 40 m/s t = d/v
d = 4.000 km = 4000 m t = 4000 m / 40 m/s
t = ? t = 1.0 x 102 s = 1.7 min = 0.028 hr
**km/h --> m/s : /3.6
**m/s ---> km/h: x3.6 3.
Speed
Speed can have 2 meanings:
i) average speed = total distance ÷ total time
ii) instantaneous speed = speed at a particular instant Lab Assignment
What is the effect of time on distance and instantaneous speed for a cart moving on an inclined plane?
Materials: ticker tape, ticker timer, power source, cart, inclined plane, tape, string.
i) Set up materials
ii) Collect data
d1 d2
iii) Make table
Total Time(s) Interval dist. Total dist. Ins. speed (cm/s) (8 spaces = 0.1 s) (cm) (cm) (int. dist ÷ 0.1 s)
1 1.5 1.5 15
2 3.0 4.5 30
3. 8.0 12.5 80
4 15.0 27.5 150
iv) Graph total distance vs. time and speed vs. time.
v) Answer questions:
a) What is the shape of a d-t graph for non-uniform motion?
b) What is the shape of a s-t graph for non-uniform motion?
c) Calculate slope of s-t graph d) What does the slope represent?
4.
The Slope of a Speed-Time Graph (Non-uniform motion) The slope represents the uniform change in speed corresponding to a change in time = acceleration.
When doing calculations: if an object is falling, a = 9.81 m/s2 if an object is going up, a = 9.81 m/s2
acceleration (a) = change in speed (∆v) change in time (∆t) a = (vf-vi) / (tf-ti)
a) A train starts from rest and reaches a speed of 54 km/h in 10 s. What is its acceleration?
v = 54 km/s = 15 m/s a = v/t a = 15 m/s
t = 10 s 10 s
a = ? a = 1.5 m/s2
**change km/h to m/s
**positive acceleration = speeding up
**negative acceleration = slowing down
b) Jack is running at 2.2 m/s and sees a bear. He accelerates at 0.5 m/s2 for 5.0 s. What was his final speed?
vf = vi + at
= 2.2 m/s + 0.5 m/s2 (5.0 m/s) = 4.7 m/s
Analzye this graph:
5. Vector Quantities: Velocity and Displacement
scalar quantities involve only magnitude (amount) eg) time, distance, and speed
vector quantities involve both magnitude and direction eg) displacement, velocity, acceleration
vectors are drawn using arrows which show magnitude in the length as well as direction
when describing a vector, we have two systems for indicating the direction:
o degrees from the x or y axis o degrees using compass directions
vector A: 10 km, 80 E of the y axix OR 10 km, 80 E of S vector B: 1.0 m/s, 65 S of the x axis OR 1.0 m/s, 65 S of W
N
E
S W
+ y axis
y axis
+ x axis
x axis
A
B
10 km 1.0 m/s
80
65
6.
Vector Addition
the resultant is the sum of two or more vectors
to add vectors, arrange them head to tail then draw the resultant from the tail of the first vector to the head of the last vector
+ + = or
***Note that the resultant is the same regardless of the order of the vectors
Vectors in the Same Direction
to add vector quantities that are in the same direction RESULTANT = SUM
Example 1
A person runs 25 m south and then another 15 m south.
a) What is the distance travelled?
d = 25 m + 15 m = 40 m b) What is the displacement?
d = 25 m [S] + 15 m [S]
= 40 m [S]
Vectors in Opposite Directions
to add vector quantities that are in the opposite direction RESULTANT = DIFFERENCE
Example 1
A plane flies 200 km north and then turns around and comes back 150 km.
a) What is the distance travelled?
d = 200 km + 150 km = 350 km b) What is the displacement?
d = 200 km [N] 150 km [S]
= 50 km [N]
Example 2 25 m 15 m
200 km 150 km
A student walks 15.0 m down the hall to the east before turning around and walking 10.0 m back in the opposite direction (west). Determine the following:
a) distance = 15.0 m + 10.0 m = 25.0 m
b) displacement = 15.0 m [E] 10.0 m [W] = 5.0 m [E]
III
Force and Work 1.
Force: Newton's 2nd Law of motion
There is a relationship between force, mass and acceleration. The acceleration of an object is directly proportional to the net force acting on it and is inversely proportional to its mass. The direction of acceleration is in the direction of the force. So:
i) as mass increases, acceleration decreases ii) as force increase, acceleration increases
F = ma, where m = mass in kg
a = acceleration in m/s2
F = force in Kgm/s2 = Newtons (N)
i) If you skateboarded and accelerated at 2.75 m/s2 and your mass is 66.4 kg. What force is needed to push you?
a = 2.75 m/s2 F=ma F=66.4 Kg x 2.75 m/s2
m = 66.4 Kg = 149 N
F = ?
Lab:
What is the effect of increased distance on the force required to stretch an elastic band?
Materials: elastic, meter stick, spring scale (set up on page 378) i) collect data
Distance (m) Force (N)
0 0
0.05 0.10 0.15 0.20 ii) Graph force vs. distance
iii) Create a triangle representing the area under the line of best fit.
Determine the area under line
iv) What are the units for the area under the line.
v) What do you think the area represents?
2.
Work: The Area under a Force - Distance Graph
The area represents the force applied to an object over the distance its was applied = Work
W = Fd, where F = force in N
d = distance in m
W = work in Nm = Joules (kgm/s2 x m = kgm2/s2 = Joules) (no distance = no work)
**A car (1200 kg) is at rest, stuck in snow, and is pushed to 0.30 m/s for 10 seconds for 2.0 m. What work is done on the car? (72J)
IV
Energy 1.
Definitions
There are two main forms of energy:
i) kinetic energy (Ek): energy due to the motion of an object.
ii) potential energy (Ep): stored energy due to:
a) position – gravitational Ep, elastic Ep
b) condition – chemical - bonds between atoms
electrical - electrical attraction between charged objects.
nuclear – bonds between subatomic particles
2.
Potential Energy Forms i) Gravitational Ep.
Stored energy dependent on the mass and height of an object Ep = mgh, where
m = mass in Kg h = height in m
g = acceleration due to gravity = 9.81 m/s2 (constant) Ep = energy in Joules
Example:
**How much Ep does a basketball (1.5kg) have at a height of 3.0 m? (44 KJ)
**If the ball rose in height as 25 J of energy is added, how high did it go?
(4.7 m)
ii) Chemical Ep where energy is stored in chemical bonds.
iv) Ep can be elastic Ep where energy is stored in a wound spring or a stretched rubber band.
v) Ep can be nuclear Ep where energy is stored in atoms and released during nuclear fusion (joining) and fission (splitting)
3.
Kinetic Energy
When Ep is released and the object moves, the Ep is converted to Kinetic energy or Ek which is useful energy. Ek can be:
i) mechanical Ek : movement (unison) ii) thermal Ek: heat (random)
iii) sound Ek: vibrational movement
Kinetic energy depends on the mass and speed of the object:
Ek = 1/2 mv2, where m = mass in Kg
v = speed in m/s2 Ek = energy in Joules
iv) electrical Ek: energy from electricity
Electrical Ep can be converted to Ek by providing a conductor for the charges to move through. When this occurs, you have power.
Power is the rate at which energy is used.
V
Energy Conversions
1. Pendulum: Ep to Ek to Ep
Total Mechanical Energy = Ep + Ek
(assume all energy is transferred)
All Ep
1/2 Ep 1/2 Ek
All Ek
1/2 Ep 1/2 Ek
All Ep
VI
Energy Laws and Efficiency 1.
First Law of Thermodynamics
Energy cannot be created nor destroyed; it is conserved in all energy conversions.
Input Energy ----> CONVERTER ----> Output Energy changes form
Small scale example:
electrical energy ----> hairdryer ----> thermal energy Large scale example:
radiant solar energy ----> chloroplast ----> chemical Ep --->
mitochondria ----> chemical Ek ----> muscles ----> mechanical Ek
These examples show how energy is not created or destroyed but just changes form.
2.
Second Law of Thermodynamics
In every type of energy conversion some energy is converted to thermal energy which is no longer useful (and therefore cannot do work). Another
way to say this is that heat naturally flows from higher temperature to lower temperature.
Electrical Energy ----> Burner ----> thermal energy 92% lost as heat
3.
Efficiency
Energy efficiency is a relative measure that compares the input energy and output energy of conversions.
% efficiency = useful energy output x100 total energy input
4.
Evidence of Energy Conversions
motion – energy from one source causes something to move
change in position – whenever something is raised above the surface of the Earth, there is gravitational EP
change in shape – like the stretching of an elastic band or bend in an archer’s bow
change in temperature – heat is the transfer of EK
Energy conversions take place in many systems:
a. Natural Systems
the fusion of hydrogen atoms on the sun releases solar energy which then travels to the Earth as electromagnetic radiation
chlorophyll in plants converts the solar energy into chemical energy in the chemical bonds of glucose during photosynthesis
plants and animals release this chemical energy during cellular respiration
b. Technological Systems
a hydroelectric power station converts the gravitational potential energy of water into electrical energy through a series of energy conversions
EP(grav) water → EK water → EK turbines → Eelec
a coal burning power station converts chemical potential energy into electrical energy through a series of energy conversions EP(chem) coal → heat water to steam → EK turbines → Eelec
c. Nuclear Systems
after WWII nuclear energy was used to generate electricity
CANDU (Canadian Deuterium Uranium) reactors cause uranium to disintegrate during nuclear fission releasing energy as radiation EP(nuclear) uranium → heat water to steam → EK turbines → Eelec
***Note: Coal, natural gas and nuclear power stations are all called
THERMAL POWER STATIONS since they use heat to produce steam which drives the turbines
d. Solar Cells
solar cells convert solar energy directly into electricity
usually composed of two layers of silicon, one with phosphorus added and one with boron added
when sunlight hits the layers, electrons are released and the two layers become charged
electrons move between the two layers, carrying electric current
the electricity can be used directly or stored in batteries for later use
e. Fuel Cells
a hydrogen fuel cell operates like a battery
it converts chemical energy in hydrogen into electrical energy
it does not required recharging
products of the process are water and heat
used in spacecraft, buses in Vancouver 5.
The Development of Engine Technology
engines turn thermal energy into mechanical energy…allowing work to be done
use second law of thermodynamics which says heat always flows from hot to cold
heat engine turns heat into mechanical energy
heat is always lost
heat pumps use mechanical energy to pump heat from a cooler space into a warmer space
eg) refrigerator
there are several types of engines:
1. Gunpowder Engine 2. Papin’s Heat Engine 3. Savery’s Water Pump 4. Newcomen Engine 5. Watt Engine
6. Internal Combustion Engine 6.
Energy Applications
a. Solar Energy Sources
those derived either directly or indirectly from energy from the
solar radiation – energy emitted by the hydrogen fusion sun reaction
wind energy – result of the uneven heating of the surface of the Earth
water energy – result of the heating of the surface water by the sun
biomass – any form of organic matter such as wood, crops, seaweed, algae, animal wastes etc.
fossil fuels – all fossil fuels were formed from plants and animals that lived millions of years ago
b. Non-Solar Energy Sources
energy sources having no relationship to the sun
nuclear energy – using fission of uranium
geothermal energy – energy generated in the Earth
tidal energy – result of the gravitational pull of the moon
renewable energy sources are continually and infinitely available
eg) solar, wind, water, geothermal, tidal and biomass
non-renewable energy sources are limited and irreplaceable eg) fossil fuels
several factors have placed demands on our energy supplies:
1. amount of energy consumed per person has been increasing exponentially
2. world population is growing exponentially
3. many societies now use renewable energy sources rather than non-renewable energy sources as their primary source of energy
the efficient use of energy involves maximizing conservation of resources and minimizing waste
we can conserve energy by:
1. reducing usage
2. search for new fossil fuel reserves 3. search for alternative energy sources
4. increase cogeneration (process of using waste energy form one process to power a second process)
we must come up with a sustainable solution
