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Physics Exam General Notes
1: Forces and Motion
● Kinematics: study of motion ● Basic types of motion: o Uniform (constant speed in straight line) o Non-uniform ● Scalar quantity: with magnitude & no direction o Distance, average speed ● Vector quantity: with magnitude (arrow above it) & direction (in square brackets after unit) o Position, displacement, acceleration ● Velocity: o Rate of change of position o Average velocity: displacement divided by time interval for that change o 2-D motion: using GPS (global position system) ▪ N/S/E/W to communicate directions ▪ Ex : 5.0 cm [25° S of E] or [E25°S] ● Acceleration: rate of change of velocity ● V-t graph to find other things: o Area under line gives displacement, slope gives acceleration ● Resultant displacement of 2 dimensions: o Vector sum of individual displacements o Use Pythagorean Theorem and SOH-CAH-TOA ● Relative motion: velocity of a body relative to a particular frame of reference ● Methods of writing direction: o GPS = [E25°S] or [25° S of E] o Bearing = [N 160°] (measure CW from North position)
2: Energy
● Dynamics: causes of motion ● Force: push or pull, vector quantity o 4 fundamental forces: gravitational, electromagnetic, strong nuclear, weak nuclear ● Unit of force: Newton (N) -> 1N = 1(kg x m)/s^2 ● Net force/resultant force: vector sum of all forces acting on an object ● Mass: quantity of matter in an object (standard: kg) ● Weight: force of gravity on an object (Fg), measured in Newton’s Newton’s Laws of Motion:
- If the net force acting on an object is zero, the object will maintain its state of rest or constant velocity.
- If the external net force on an object is not zero, the object will accelerate in the direction of that net force. The magnitude of the acceleration is proportional to the magnitude of the net force and inversely proportional to the object’s mass.
- For every action force, there is a reaction force equal in magnitude but opposite in direction. o Law of Universal Gravitation: Force of gravitational attraction between any two objects is directly proportional to the product of the masses of the two objects, and inversely proportional to the square of the distances between their centres. Friction: ● Static friction (Fs): force that tends to prevent a stationary object from starting to move o Starting Friction: max static friction, amount of force to overcome to get object to move ● Kinetic friction (FK): force that acts against an object’s motion in a direction opposite of the direction of motion o Sliding friction, rolling friction, fluid friction ● Coefficient of friction (μ): number that indicates the ratio of the magnitude of the force of friction (Ff) between 2 surfaces to the magnitude of the force perpendicular to these surfaces o μK for FK, μs for Fs; larger means more friction Energy: ● Energy: capacity to do work o 1 J (joule) = 1 Nm = 1(kg x m^2 )/s^2 o Forms: thermal, electrical, radiant, nuclear potential, gravitational potential, kinetic, elastic potential, sound, chemical potential ● Work: energy transferred to an object by an applied force over a measured distance
o Power: rate of doing work or transforming energy
▪ 1 W = 1 J/s
● Gravitational potential energy: energy possessed by an object because of its position relative to a lower position ● Kinetic energy: energy possessed by an object due to its motion ● Law of Conservation of Energy: energy cannot be created nor destroyed. When energy changes from one from to another, no energy is lost. o Valley problems, pendulum problems, objects dropped from a height ▪ (mvA^2 )/2 + mghA = (mvB^2 )/2 + mghB o Ramp problems
▪ Moving up: (F – Ff) ∆d = mgh
▪ Moving down: mgh – Ff∆d = ½mv^2
o Charge of -1, mass of about 1/2000th^ of a proton (same as electron)
o Ionizes atoms that they pass, but not as strongly as alpha particles
o Medium penetrating power, stopped by aluminum foil
● Gamma rays: waves
o No mass or charge
o Do not directly ionize other atoms
o High penetrating power, would take a thick metal to stop them
● Law of Conservation of Mass-Energy: for an isolated system, the total amount of mass-energy
remains constant
● Atomic mass (A) = # of protons (Z) + # of neutrons (N)
o Naming convention: mass above # of protons; left of chemical symbol
o Proton (^11 p), neutron (^10 n), electron (^0 -1e)
3: Waves and Sound
Vibrations: ● Vibration: periodic motion when it repeats a pattern of motion ● 3 types of vibrations: o Transverse: perpendicular to its axis at normal rest position (ex. pendulum) o Longitudinal: parallel to its axis of rest position (ex. pogo stick) o Torsional: around its axis at rest position (ex. motion of steering wheel) ● Cycle: 1 complete oscillation or 1 complete vibration/1 complete wave ● Frequency (f): # of cycles per second, measured in Hertz (Hz) ● Period (T): time for 1 cycle, measured in seconds ● Amplitude: distance in either direction from the rest position to an extreme position (max displacement) ● In Phase: objects have same period & pass through the rest position at the same time ● Out of Phase: objects don’t have the same period & pass through the rest position at the same time Waves: ● Wave: vibration/disturbance that can transfer energy over a distance ● Transverse waves: particles in the medium vibrate at right angles to the direction in which the waves travel (ex. water waves/waves in a rope) o Crest/trough, node/antinode, amplitude, rest axis ● Longitudinal waves: particles vibrate parallel to the direction of wave motion (ex. sound waves/compress coils in a Slinky) o Compression/rarefaction ● Wave interference: occurs when 2 act simultaneously on the same particles of a medium o Constructive interference: creates supercrests and supertroughs (add 2 together) o Destructive interference: waves diminish one another, amplitude decreases
● Standing waves: special case of inference in a one-dimension medium o If colliding waves are controlled so they have the same amplitude and wavelength but in opposite directions, it results in a “standing wave interference pattern” ● Principle of Superposition: at any point, the resulting amplitude of 2 interfering waves is the algebraic sum of the displacements of the individual waves ● Resonance: response of an object that is free to vibrate to a periodic force with the same frequency as the natural frequency of the object o Mechanical resonance: if physical contact between the periodic force & the object o Ex: Tacoma Narrows bridge, rock a car stick in snow, child moving on swing Sound: ● All sounds stimulate the auditory nerve ● Humans respond to sound frequencies between 20Hz – 20,000Hz o Infrasonic: lower than 20Hz, ultrasonic: above 20,000Hz ● Produced by vibrating objects (ex. guitar string, throat vibrating, stereo speaker) ● Needs a material medium for transmission ● Sound waves are longitudinal waves ● Larger amplitude: louder sound, higher frequency: higher pitch ● Intensity of sound: o Sounds audible to humans can vary in intensity ● Loudness measured in bels (B), most people use decibel scale (dB) o 1dB = 1/10B or 10dB = 1B ▪ 0dB: threshold of hearing (10-12W/m^2 ) ▪ 85dB: must wear eat protection for industrial safety ▪ 130dB: threshold of pain (10^1 W/m^2 ) ▪ 160dB: instant perforation of ear drum (10^4 W/m^2 ) o Each rise of 10dB: 10 fold increase in sound intensity ● Interference between identical sound waves: causes louder/softer sound regions o Can be done with 2 loudspeakers in phase ● Noise cancellation headphones use destructive interference (exactly out of phase with outside noise), can remove 70% of external noise ● Beat: periodic change in sound intensity ● Beat frequency: # of beats heard per second, in hertz ● Doppler Effect: observed frequency increases when source of sound approaches, and vice versa Sound Barrier: ● When flying at speed of sound, the wave fronts in the front of a plane pile up, producing an reap of very dense air/intense compression o Extra thrust required to break through barrier
Quality of sound: ● In a vibrating stretched string and the fundamental mode of vibrating, the string vibrates in one segment with a node on each end and one antinode in the middle. This creates f 0 or fundamental frequency. ● Different frequencies can be produced by forcing the string to vibrate in different patterns o Frequency produced depends on number of nodes/antinodes ● Second harmonic (2f 0 ) same as first overtone, 3 f 0 = second overtone, etc. o Frequencies of overtones are in simple whole numbered multiples of the fundamental and are called harmonics o Overtones can be more intense than fundamental in some instruments (ex. clarinet) ● Quality of a musical note depends on the # and relative intensity of the overtones it produces along with the fundamental ● Tuning fork only has one fundamental frequency Resonance in air columns: ● Closed air columns: o Caused by standing wave pattern with node at closed end & antinode at open end o For fixed length: resonance first occurs when air column is ¼ λ (wavelength) ▪ Then: 3/4 λ, 5/4 λ, 7/4 λ etc. ● Open air columns: o Created by standing wave patterns set up in a tube where an antinode exists at BOTH open ends o For fixed length open columns: resonance first occurs at λ/2 (first harmonic) o Then: λ, 3λ/2, 2 λ, etc.
4: Electricity and Magnetism
Electrostatics: ● Static electricity: a build-up of stationary electric charge o Charging by friction: rubbing 2 objects together ● Fundamental laws of electric charge: o Opposite charges attract, similar charges repel, charged objects attract some neutral objects ● Change in charge due to loss/gain of electrons only ● Conductors: solids in which charge flows freely (most metals, water) ● Insulators: solids that hinder the flow of charge (glass, rubber, wood, plastic, concrete) Electric fields and electric charge: ● Every charged object creates an electric field of force in the space around it
o Relative distance between adjacent field lines at a given point is an indication of the strength of the electric field at that point ● Magnitude of the electric force of the attraction or repulsion is: o Directly proportional to the product of the charges o Inversely proportional to the square of the distances between them ● One coulomb (C) of energy made up of 6.24x10^18 e- Electric current: ● Rate of movement of electrically charged particles past a point ● When electric charges move from 1 place to another ● In metals: moving charges are electrons ● Measured in amperes (A) o 1A = 1C/s o Standard household fuse: 15A ● Conventional current: positive charge from + to – (used in this course) o Electric flow: negative charge from – to + ● Can flow in either direction in liquids & gases ● Batteries: DC, wall sockets: AC ● Ammeter: measures amount of electric current in a circuit Electrical potential difference: ● Amount of work required per unit of charge (coulomb) to move a positive charge from one point to another in the presence of an electric field ● A 1V battery performs 1J of work to move 1C of charge between its terminals o 1V = 1J/C Electrical resistance: ● Opposition experienced when charges pass through a material or device, resulting in a loss of electrical potential energy ● Ohm’s law: The potential difference between any 2 points in a conductor varies directly as the current between the 2 points as long as the temp. remains constant. ● Unit for resistance: ohm (Ω) o 1 Ω = 1V/1A Electric circuits: ● Series: o VT = V 1 + V 2 + V 3 o IT = I 1 = I 2 = I 3 o RT = R 1 + R 2 + R 3 ● Parallel: o VT = V 1 = V 2 = V 3
▪ Domains: clusters of 10^17 atoms ● Non-magnetized: randomly pointing domains ● Effects: o Magnetic induction ▪ Permanent magnet near iron nail: temporary magnet ▪ Field of perm. cause dipoles in nail to align momentarily ▪ Soft iron: if nail loses magnetism as moved away ▪ Hard iron: if nail retains magnetism as moved away o Demagnetization ▪ Aligned dipoles return to random directions ▪ Caused by dropping or heating ▪ Some materials revert when removed from magnetic field (i.e. pure iron) ▪ Materials that instantly demagnetize: soft ferromagnetic materials ▪ Alloys used to make hard ferromagnetic materials (use aluminum or silicon) o Reverse magnetization ▪ Poles reversed when magnet placed in a strong enough magnetic field with reverse polarity o Breaking a bar magnet ▪ Creates mini magnet with identical dipole alignment o Magnetic saturation ▪ Peak of magnet’s strength: when max # of dipoles aligned o Induced magnetism by Earth ▪ Dipoles will align if a piece of iron with agitated atoms by heating or mechanical vibration in Earth’s magnetic field ● Point north & at angle of inclination + tapping with a hammer ▪ Steel columns, hulls, and railroad tracks tend to magnetize o Keepers for bar magnets ▪ Bar magnets demagnetize over time as poles start to reverse the dipoles’ polarity (random thermal motion of atoms) ▪ Store in pairs with opposite poles adjacent & small pieces of soft iron (keepers) across ends to prevent demagnetization ▪ Keepers become strong induced magnets, form closed loops
Factors affecting the magnetic field of a coil: ● Coil’s magnetic field can be turned on/off & alter strength ● Strength related to degree of concentration of its magnetic field lines ● More current in the coil = greater concentration of magnetic field lines in the core o 2x current = 2x magnetic field strength ● Number of loops in the coil: o Each loop of wire produces its own magnetic field o Magnetic field of a coil: sum of the magnetic fields of all its loops o 2x loops in coil = 2x magnetic field strength ● Type of core material: o Material of core affects coil’s magnetic field strength ▪ Cylinder of iron (instead of air) = 1000+ times stronger ▪ Aluminum core = no effect o Core material becomes induced magnet, magnetic field strength increases ▪ Dipoles align with magnetic field of the coil o Relative magnetic permeability (K): factor by which a core material increases the magnetic field strength that would exist in the same region if a vacuum replaced it o 2x relative magnetic permeability of the core = 2x strength ● Ferromagnetism, paramagnetism, and diamagnetism o Core materials divided into 3 groups according to their relative magnetic permeability o Ferromagnetic: high, strong induced magnets o Paramagnetic: slight increase, slightly greater than 1 ▪ Oxygen and aluminum o Diamagnetic: slight decrease, slightly less than 1 ▪ Copper, silver and water Motor Principle: ● A current carrying conductor that cuts across external magnetic field lines, experiences a force perpendicular to both the field lines and the direction of the electric current ● Applications: moving coil loudspeaker, galvanometer (armature forced to pivot with increased current) o Voltmeter: galvanometer + high value resistor in series o Ammeter: galvanometer + low value “shunt” resistor in parallel ● Electric motor: device that can convert electrical potential energy into mechanical energy o DC motor: needs DC electricity, uses “split right commutator” to reverse current through armature o AC motor: needs AC electricity, uses “slip rings” attached to armature since current switches direction, no need for split ring
● Step down transformer: o Used to decrease AC voltages o Ex: train set, car race car transformers, power adapters ▪ Adapter : step down transformer + rectifier (AC to DC convertor) in series
