Geoff Wan's Physics 12 notes
These are the notes that Geoff painstakingly
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Physics 12
Table of Contents:
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Significant Figures
- Pure Numbers (ie defined numbers [60 sec in a minute] and counting numbers [27 people]) do NOT obey the sig fig rules
- measured quantities - have errors or limits to the degree of accuracy - therefore you must obey the sig fig rules when using...
- 1 Addition and Subtraction - round off to the last accurate digit...for example...
430.061 + 17.82 + 5.1 = 452.981 (arithmetic answer - WRONG!)
the RIGHT answer would be 453.0
- 2 Multiplying and Dividing - round off to the least number of sig figs in the data...for example...
4.37 * 2.6 * 3 = 34.086 (arithmetic answer - WRONG AGAIN! HAHAHAH!)
the RIGHT answer would be 3 * 10^1 (must have 1 sig fig, and "30" is considered as 2 sig figs)
- ZERO is not a sig fig if it is used only to locate a decimal point. Avoid confusion by writing numbers in scientific notation! DO NOT USE ALL DIGITS FROM CALCULATOR!!
Checklist for Graphs
1 Title
2 Name and label axis with appropriate quantities and units (do NOT use "x" and "y")
3 Include the origin
4 Use at least half the page
5 Choose axis and scale that creates a line at about 45 degrees
6 Do not join points. Draw a "best fit" line
7 Show slope interval and calculation
8 State an equation - include units for slope and intercept
Problem Solving
1. What is happening?
a) Read
b) Draw / Sketch
c) Graph
d) Identify your givens and unknowns
2. Equation
a) Select equation that relates known and unknown quantities....eg v = d/t
b) Solve algebraically for unknown.......eg t = d/v
c) Possibly search for second equation (2 step problems)
3. Substitute
a) Numbers and units
b) Estimate answer
c) Use dimensional analysis to check units
4. Evaluatuate
a) Use calculator
b) Check answer
c) Congratulate yourself <-------- VERY IMPORTANT!!!
Kinematics
Uniform Motion
Uniform Acceleration
- v(avg)=d/t.......OR......v(avg)=[v(f) + v(i)] / 2
- a= [v(f) - v(i)] / t
- d= 1/2(at^2) + v(i)t
- v(f) = v(i) + at.....OR.......v(f)^2 = v(i)^2 + 2ad
Vectors
- quantities that have both magnitude (size) and direction
- scalars (speed, distance) have magnitude only
- vectors are represented by arrows that are drawn to scale and pointing
in the required direction
Methods of solving Vector problems
1.) Graphical analysis
- draw vector to scale
- place head to tail and draw resultant
2.) Analytical Method
- break each vector into its horizontal and vertical
components (use trigonometry on a scale diagram
- define positive and negative directions
- add all vertical components
- add all horizontal components
- use Pythagorus's Law to find the resultant
Forces
- force is a vector quantity
- therefore it has magnitude and direction
- measured in Newtons: 1 N = 1kg * 1m/s^2......1N is the force
required to accelerate 1kg at 1m/s^2
Newton's Laws
1.) Inertia - an object moves at a constant velocity until an external force is acted upon it (external force can be a push, pull, or friction)
2.) F=ma - as you already know, Force = mass * acceleration
3.) Equal and Opposite Forces - and you probably already know that "for every action, there is an equal and opposite reaction" (but they MIGHT not be acting parallel to each other - that's why organisms can move...they exert a force diagonal to the ground, and the ground exerts an equal force upwards...that's how animals move...)
(but for stuff like a rock on the ground - the rock exerts a force straight down, and the ground exerts a force straight up - that's why stuff like rocks don't move unless there is some other force acting on it...confusing ain't it??)
Tension
Q: How the hell do you calculate tension???
A: first, you have to tell which of two situations apply:
1.) the object is moving up
2.) the object is moving down
- For situation number 1, the answer is: T(ension) = W(eight) - m(ass)a(cceleration)
where acceleration is the actual acceleration in which the system is accelerating
- For situation number 2, the answer is: T = W + ma
where acceleration is the actual acceleration in which the system is accelerating.....clear as mud?
- you're probably asking yourself, how the hell do I get the acceleration? simple!
- a(cceleration) = g(Msin[angle1] - Msin[angle2]) / (M + m)
keep in mind that:
- g=9.8m/s^2
- M = the first mass
- m = the second mass
- [angle1]= the angle at which the first mass is exerting a force (0-90)
- [angle2] = the angle at which the second mass is exerting a force (0-90)
Forces on Slopes
- F(g) = m.g.sin[theta] =====> a=g.sin[theta]
- F(f) = u.m.g.cos[theta] ===> a=u.g.sin[theta]
That's it!! That's all there is to forces on slopes!! Yay!
Work and Energy
(W)ork = (F)orce * (d)iplacement
- where F & d are in the same direction (ie parallel)
- measured in Joules
1 J = 1Nm
one Joule is the energy required to apply a force of 1 Newton over a
distance of 1 meter
(P)otential (E)nergy = (m)ass * g * (d)isplacement
work is done on an object by lifting it to a higher position
the work done on it is the change in potential energy
(K)inetic (E)nergy = 1/2 * (m)ass * (v)elocity^2
the amount of work done on an object in motion is the change in Kinetic
Energy
Circular Motion
Uniform Circular Motion
- Uniform motion occurs when an object travels in a circle with a
constant speed and with a fixed radius
- Speed is constant but direction is constantly changing.
Therefore, a force is required and acceleration occurs.
- In uniform circular motion, acceleration and force are directed
towards the centre of the circle of rotation. These are centripetal
acceleration and centripetal forces.
a = v^2 / r |
OR |
a = 4(pi^2)R / T^2 |
where a is the centripetal acceleration,
v is the speed at which the object moves (?)
R is the radius of circular path at which the object orbits
and T is the time for one full period
Newton's Universal Gravitation Law
- an apple falls in the same way that the moon falls. Gravity keeps
the moon in orbit (and Earth around the sun). Cavendish measured "G" by
using a torsion balance. From this, he was able to calculate the
mass of the earth!
Fg (Force of gravity on earth): = mg = GMm / R^2
where m is the mass of the object,
g is the acceleration due to gravity,
G is the universal gravitational constant (6.7 * 10^-7 Nm^2/kg^2)
R is the radius of the earth, or any other large piece of mass, like
another planet, the sun, or even Rush Limbaugh. (radius of the earth = 6.4 * 10^6m)
and M, which is the mass of the same big object (mass of the earth = 5.98 * 10^24 kg)
Gravity
- On the earth's surface g (acceleration due to gravity) is approximately
9.8m/s^2 (((6.67*10^-11)(5.98*10^24)) / (6.4 * 10^6)^2)....go on, calculate it and see for yourself..!
- but when the object is WAAAAY above the earth's surface, g = GM / R^2
and one can infer that... GM = g(1)R(1)^2 = g(2)R(2)^2
Kepler's Laws
- Some scientist named Kepler was the first person to look for
physical laws based on measureable phenomenoa to describe the universe. Until
then, it was thought that spirits were responsible for the motion
of objects. So, he formulated 3 laws...
- The paths of the planets around the sun are elliptical
- The planets sweep equal areas around the sun in equal intervals of time
- For any planet, the ratio of the cube of their mean radius and the square
of their period is a constant.
ie R^3 / T^2 = K
Satellites and Weightlessness
- people in a space shuttle are not weightless (g = [approx] 8.4m/s^2)...but they are in an
environment of relative weightlessness
ie both the shuttle and the astronauts are falling to the earth at the
same rate (see the elevator analogy on P.112 if you like pictures instead
of words)
- they are weightless with respect to each other
- if it stopped, it would fall towards the earth and start accelerating at 8.4m/s^2 (assuming
an altitude of 500km)
- if it is travelling too fast, it would escape the earth's gravitational
field, never to return
- assume satellites move in circular orbits
- centripetal acceleration is supplied by gravity...thus a(c) = a(g)
Electrostatics
Static Electricity
- there are two types of charges: like and unlike, or
in lamen's terms, positive and negative
- unlike charges attract, like charges repel
- "charged" objects have a net charge...that is, they
have more positively particles than negatively charged
particles, or vice versa
- neutral objects contain both positively and negatively
charged particles, both of which are equal in number
- charged objects often attract neutral objects - why?
say an positively object is brought near a neutral object,
the positively charged particles (from the charged object)
is attracted to the negatively charged particles (from
the neutral object) and thus, the two objects attract
each other...
Coulomb's Law
- defines the force between point charges
- where k is Coulomb's constant of 9.0 * 10^9 Nm^2/C^2
- Q and q are the point charges measured in coulombs
- and R is the distance between the points
Electric Fields
- the electric force described by Coulomb extends in space to create
the electric field invented by Faraday
- the direction of the field is the direction in which a positive
point charge would move when placed around a charge
- the electric field between two parallel plates is constant
- the electric field inside a conductor is zero
- the electric field outside a conductor is perpendicular to the
surface area
- the field strength, E, is defined as the force exerted on a
small test charge, q, placed in the field
E = | F -- q |
=> | (kQq)/r ---------- q |
=> | E = |
kQ ---- r^2 |
- measured in N/C
The Superposition Principle
- when the field is due to more than one charge, the individual fields
are added together according to the rule of vector addition
Electric Potential
- at infinity, the electric potential between two charges is zero
- as q approaches Q, the electric potential increases and the force
between them increases
For a finite value of r:
- the potential energy between like charges is positive because you
do work on them by forcing them together
- the electric potential between unlike charges is negative because
you do not do work to bring them together
electric potential
- the voltage on q at r is the potential per unit charge
V = | Ue --- q |
=> | V = | kQ --- r |
work can be expressed in terms of voltage; W = Vq
Electric potential for 2 or more charges:
Vt = kQ1/r1 + kQ2/r2...
+q = positive potential
-q = negative potential
Vt is the arithmetic sum (as opposed to vectoral) sum of
the individual potentials
Between parallel plates:
- Voltage is work per charge (J/C)
- the field is uniform
- the force required to move a charge from the positive plate to the
negative plate is F = Eq (remember, E=kQ/r^2)
- if the plates are a distance d apart,
the work done to move a charge is Fd = Eqd
- one electron volt (eV) is the energy acquired by an electron
moving through one potential difference of one volt
Electrical Energy
Current
- current is the rate of flow of charge
- measured in Coulombs per second.....so, 1A = 1C/s
- flows from positive to negative
- electron flow goes from negative to positive
Voltage
- voltage is energy per charge
- measured in Joules per Coulomb......so, 1V = 1J/C
Resistance
- Ohm's Law defines resistance in terms of voltage and current
- V = IR
- resistance is measured in ohms.....so, 1 ohm = 1V/A
Circuits
Series Circuits
- Current is same through each resistor...that is I(t) = I(1) =
I(2) = I(3)...
- Voltage is completely used up by each of the resistors...
that is V(t) = V(1) + V(2) + V(3)...
- Resistance is the sum of resistances from all the resistors...
that is R(t) = R(1) + R(2) + R(3)...
Parallel Circuits
- Current is the sum of the currents at each resistor... that is
I(t) = I(1) + I(2) + I(3)...
- Voltage stays the same... that is V(t) = V(1) = V(2) = V(3)....
- Resistance is weird. Here goes... R(t) = [R(1)^-1 + R(2)^-1 +
R(3)^-1...]^-1
Terminal Voltage & EMF
EMF is...
- electromotive force - maximum voltage that can be created by a cell
- never obtained in practice because of the internal resistance,
r, of the cell
Terminal Voltage is...
- the voltage that is actually supplied to the external circuit...
- V = E - Ir
- where V is the terminal voltage, E is the EMF, I is the current in
the circuit, and r is the internal resistance of the cell
Meters
Galvanometer
- a very sensitive meter - only 25-50 microamps are required for
full scale deflection
- deflection of the needle is directly proportional to the current
(duh)
- Current Sensitivity is the current required to cause full
scale deflection
Ammeter
- used to measure large currents
- a galvanometer is connected in parallel with a shunt resistor
- shunt resistors are very low in value
- Ammeters are always connected in series
Voltmeters
- a galvanometer connected in series with a resistor called a
multiplier, which happens to have a relatively high
value (unlike the shunt resistor)
- voltmeters are always connected in parallel
Voltmeter Sensitivity
- this is a value printed on the meter - measured in ohms/volt
- it states how many ohms of resistance are in the meter when
it is registering full deflection
eg 30,000 ohm/volt means that on the 10V scale, the meter has a resistance
of 300,000 ohms
- sensitivity can also be used to measure current sensitivity
eg 1V / 30,000 ohm = 0.000 033A
- the higher the ohm/volt, the less current is disturbed
Power
- heat is generated as a result of collisions between electrons
and atoms in a wire - this accounts for power lost in a circuit
- power is the rate of using or supplying energy
- measured in watts....1W = 1J/s
- in electrical terms, P = VI (according to Joule's Law)
- one can re-arrange this by using Ohm's Law..
- P = (I^2)R or P = (V^2)/R
- energy is the product of power and time... E = Pt
- 1kWh = 1000J/s * 3600s = 3.6 * 10^6J
questions? comments? send them to
gwan@yahoo.com