Honors Physics Semester 2 Final Study Guide PDF

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Summary

This contains all information learned in the second semester of this course (it is a compilation of notes used for the final exam); it has diagrams, practice problems, and example scenarios for each concept...

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Guo + Kriplani 1

I. II.

III.

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V.

VI.

Circular Motion Momentum and Energy A. Momentum B. Impulse C. Momentum Practice D. Energy Electric Charge A. Electric Charge Model B. Electric Force/Coulomb's Law C. Electric Fields D. Electric Potential Difference E. Charge Separation F. How to Charge Something G. Electric Charge Practice Circuits A. Ranking of Bulb Brightness B. Current Model C. Voltage Model D. Circuits Practice Magnetism and Waves A. Magnetic Field Lab(and Right Hand Rules #1 and #2) B. Magnetic Force Math Models C. Magnetism Model General Math Models/Potentially Useful Information

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A. Circular motion occurs when an object’s velocity is perpendicular to its acceleration. B. The acceleration always points towards the center of the circle C. a=v2/r 

A. Momentum 1. Momentum is the “quantity of motion” a) Composed of the velocity and the “quantity of matter” b) “Quantity of matter” is defined as the density or bulk 2. Momentum is a v ector a) Always points in the same direction as the velocity 3. p=mv a) Momentum = Mass * Velocity 4. Units a) kg*m/s 5. Needs subscripts a) X, y, total, object name, and initial or final b) Examples (1) px (2) pball (3) pi (4) ptotRandi 6. If ∑F=0, then ∆p=0 7. CONSERVATION OF MOMENTUM - momentum is a conserved quantity → in a system that has no  external force acting on it, the total momentum of the system stays  B. Newton’s 2nd Law 1. ∑F = ma (both F and a are vector quantities) 2. p = mv (both p and v are vector quantities) a) “Motion” is the product of mass and velocity which is momentum  C. Impulse 1. ∆p/∆t = ∑F therefore ∆p = ∆t * ∑F (impulse - change in momentum equation) 2. sad ball(the one in physics) vs. happy ball(the one in chem) a) sad ball: (1) Vf = 0 (2) ∆p =mvf - mvi (3) ∆p = -mvi (4) ∑F is less → the ball doesn’t knock over the block

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b) happy ball (1) ∆p = mvf - mvi (both equate to less than 0) (2) Impulse is bigger than sad ball → ∑F is greater → knocks over the ball

3. How safety agents in cars work: a) airbag increases the time of impact to lower the force, since the change in momentum is the same b) seat belt exerts ∑F (external) on parts of the body that can sustain it (chest) 4. bungee cord vs. stiff cord a) stiff cord - large force over a small amount of time b) bungee cord - smaller force over a larger amount of time

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c) 5. PRACTICE

a) b) In Case A, a metal bullet penetrates a wooden block. In Case B, a rubber bullet with the same initial speed and mass bounces off of an identical wooden block. (1) Will the speed of the wooden block after the collision be greater in Case A, greater in Case B, or the same in both cases? Explain (a) The speed of the wooden block will be greater in Case B because their momentum is the same, but in Case B, the bullet recoils in the opposite direction with a velocity, so the velocity of the block must be greater in order for momentum to be conserved (2) Your friend drops her phone on the concrete floor in Nichols hall, which causes the screen to shatter. Later that day, you accidentally drop your own phone on the carpet at home from approximately the same height. Your phone survives the fall unscathed. Using the ideas of impulse and momentum, describe why your friend’s phone broke but yours did not. (a) The carpet allows your phone to take a longer time to receive the impact, so the force on your phone is less than the force on your friend’s phone. ∆p=∑F*∆t

Guo + Kriplani 5 (b) When dropping on a concrete floor, the time that the phone takes to land is much shorter. Since there is less time, the force is greater. ∆p=∑F*∆t (c) Alternative Answer (i) Your friend has a ZTE Zinger and you have a Nokia or other non-trash phone so theirs shattered and yours didn’t. (3) A Mack Truck and a MINI cooper have a head-on collision (a) Which vehicle will experience the greatest force of impact (magnitude)? Explain

(b) (i)

They will experience the same force of impact due to Newton’s 3rd  law (c) Which will experience the greatest change in momentum (magnitude)? Explain. (i) The change in momentum for both will be the same because the force and time are the same. (d) Which will experience the greatest change in velocity (magnitude)? Explain. (i) The change in velocity of the MINI cooper will be greater because the momentum is the same and the velocity should be greater to counter the smaller mass.  D. Energy 1. Types of Energy a) Mechanical Energy (1) Kinetic Energy, Ek (a) Due to macroscopic motion (b) Ek=0 when v=0 (2) Gravitational Potential Energy, Eg (a) Due to relative position of object to another object(Earth) (b) Eg=0 where we choose (c) Best place is the lowest position (3) Elastic Potential Energy, Eel (a) Due to the compression or stretching of an object (b) Eel=0 in a relaxed state

Guo + Kriplani 6 b) Other Energy (1) Thermal Energy, Et (a) Due to microscopic motion (b) Et=0 when and where we choose (c) In a system, Et can only ever increase. (2) Chemical Potential Energy, Echem (a) Due to energy released or absorbed during chemical reactions (3) Electric Energy, Eelec (a) Due to movement of electrons (4) Electric Potential Energy (a) Due to the relative location of charges 2. Changing the energy of the system a) 1st law of thermodynamics (AKA Law of Conservation of Energy) (1) ∆Esys = Q + W (determined experimentally) (2) Q - heat (3) W - work (a) w = F · ∆d (can’t write it as w = F x d) because work is a scalar quantity (i) Dot product results in a scalar (b) w = F∆*d*cos θ (c) θ - angle between F and ∆d (d) ∆d - magnitude of the displacement (e) F - magnitude of the force b) Example: system - chair, earth (1) Dr. Brada picks up the chair (he does positive work on the system) - w = mg∆h*cos (0) (a) ∆Esys = mg∆h (b) ∆Eg = mg∆h

(2) If he sets the chair down, the force is still up (but the displacement is down) (a) θ = 180 (cos θ = -1) so there is negative work

Guo + Kriplani 7 (3) If he picks up the chair and walks around, the force is still up and the displacement is horizontal (a) θ = 90 (cos θ = 0) so there is NO work done c) Units: J = N *m (Joules - the unit of energy and work) 3. Energy General Math Models a) Ek = 1/2 mv2

b) (1) How to find/derive it: (a) ∆Esys = ∆Ek (b) ∆Ek = W + Q (Q is 0) (c) ∆Ek = F * ∆d * cos θ (d) ∆Ek = m * a * ∆d * 1 (e) ∆Ek = m ((vf 2 - vi 2)/2) (f) ∆Ek = ½ mvf 2 - ½ mvi2 (g) Ekf - Eki = ½ mvf 2 - ½ mvi2 (h) Ek = ½ mv2 c) Eg=mgh 4. General Math Model of a Spring a) Fspring = k∆x (1) k - spring constant (stiffness of a spring) (2) ∆x - stretch (3) This only occurs for an ideal spring (Hookean spring), where the y intercept is zero. b) Hooke’s Law - Hookean spring (example: rubber band) (1) Our springs are not Hookean because you can pull them a little bit before they start to stretch

(2) W = ½ ∆x * Fspring

Guo + Kriplani 8 (3) W = ½ ∆x * k * ∆x (4) W = ½ * k * ∆x2 (5) Positive work → increase in the Energy of the system (a) Work is also positive if it’s in the same direction as the displacement (b) Esys = W + Q (Q is 0) (c) ∆Eel = ½ * k *∆x2 c) Elastic Energy (1) Eel=½ * k * x2 (a) When the object is not stretched or compressed, x=0 so therefore Eel = ½ * k * x2 = ½ * k * 0 = 0

5. Defining Systems a) The amount of energy as well as the types of energy in your system are both affected by how you define it (1) For example, you should define your system where h=0 in the first image or the lowest point (2) Something inside a system cannot exert a force or work on it. 6. Factors a) When no work is done on the system, ∆E = 0 b) As a general rule, try to set Eg to zero in the first image or the one where the height is the lowest (1) It depends. Setting h=0 where the height is the lowest is more preferable, but you can also set it at the first image so you have no Eg there. (2) Rule of thumb, try to keep the energy always above or at zero c) If you are including friction or air resistance in your system, you must include the surface or air in your system (1) Therefore, they do no work on the system 

A. Model for electric charge 1. There are two types of charge a) Positive and negative 2. Opposite charges attract and like charges repel 3. There are two categories of materials a) Conductors - cannot be charged when held and rubbed b) Insulators - can be charged when held and rubbed 4. How to test for charge a) Hold the object in question over paper dots b) If there is an interaction, the object is charged c) If there is no interaction, the object is not charged 5. The strength of the interaction decreases with increasing distance

Guo + Kriplani 9 6. Neutral and charged objects attract each other 7. The charge on an object dissipates with time 8. Objects (insulators) can be discharged by rubbing them all over with bare hands and breathing on them 9. Charge is a CONSERVED quantity (same set of charge is being transferred) a) Neutral objects contain equal numbers of positive and negative charge 10. Charge cannot be created or destroyed B. Force of Electricity 1. Coulomb’s Law a) Fe = (k*|q1|*|q2|)/distance2 (1) k - Coulomb's constant (units N*m2/C2 ) (2) k = 8.99 * 109 ( N*m2 /C2 ) (3) q1 and q2 are the charges of the two objects we are trying to find the interaction between 2. Fe is similar to Fg in that it is a non-contact force, except Fe has the ability to repel while Fg does not  C. Electric Field 1. Charge automatically creates electric field everywhere (electric field points away from positive point charges and towards negative point charges) a) Start on positive charge or infinity b) End on negative charge or infinity

 D. Electric Potential Difference

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1. ∆v = w/q 2. ∆Esys = W + Q (Q is 0) 3. Moving away from (-) plate to (+) plate → increasing electrical potential difference 4. +q: w = q * Eo * D a) ∆v = (q * Eo * D)/q b) ∆v = EoD 5. +2q: w = 2q * Eo * D a) ∆v = (2q * Eo * D)/2q b) ∆v = EoD  E. Charge Separation 1. Why do charged objects attract neutral objects like paper dots? a) When a charged object, take for example a positively charged object, is brought near a neutral object, the excess positive charges in the charged object attract some of the negative charges in the neutral object towards it. b) Some of the positive charges in the neutral object are repelled to the other side of it by the excess positive charges in the charged object c) Since some of the negative charges in the neutral object are now closer to the positive charges in the charged object than some of the positive charges in the neutral object, the attraction between the negative and positive charges overpowers the repulsion between the two positives. d) So, the objects attract.

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F. Configuration of a light bulb

G. 1. Fluorescent → gas 2. Incandescent → based on heat that produces light 3. Short circuit → pathway has no resistance from the terminals  H. How To Charge Something 1. Charge by Induction a) This is similar to charge separation, except you basically steal the other charges b) Only works with conductors c) Basically, you hold a charged object near an uncharged one to induce charge separation d) Then you ground the uncharged object WITHOUT removing the charged object e) The repelled charges in the uncharged one are grounded away f) Remove grounding THEN the charged object g) Left with two oppositely charged objects

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I.

2. Scrape A Charged Rod Across It a) Simple, the excess charges are transferred b) The two objects are charged the same  PRACTICE 1. A small ball is positively charged on one side, and equally negatively charged on the other side. The net charge of the ball is zero. The ball is then placed near a positive point charge as shown. a) Would the ball be attracted toward, repelled from, or unaffected by the positive point charge? Explain your reasoning (1) The negative side attracts the positive charge and is closer to the charge and the positive side repels the positive charge and is further away → the attraction is greater than the repulsion b) Is the positive point charge affected by only the negative side of the ball, only the positive side of the ball, or both sides of the ball? (1) Both because the net change of the object is still zero and you need to account for the whole ball c) Does your answer to Part B or support your answer to Part A? Explain

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J.

(1) Supports because for both we argue that the net charge is zero and that the ball is neutral 2. A charged rod is held near an object that has been cut in half. While the charged rod is held close, the object is separated and the net charge of each half is determined a) What is the net charge of each half when the object is a conductor? (1) The one closer to the negatively charged rod was positively charged and the other is negatively charged b) What is the net charge of each half when the object is an insulator? (1) Both are neutral → charges CANNOT MOVE AROUND BECAUSE THEY ARE LAME Circuits 1. Ranking

a) Rank the brightness: A = D = E > B = C b) Rank the current: A = D = E > B = C c) Current through battery: 3 > 1 > 2 d) Rank the resistance: 2 > 1 > 3  2. Current Model a) The same amount of current flows through light bulbs in series because they are on the same pathway b) The way that current splits at a junction is dependent on the relative resistance of the pathways (1) Less resistance means more current (2) More resistance means less current c) If the total resistance of the circuit increases, the current through the battery decreases. If the total resistance of the circuit decreases, the current through the battery increases. d) Adding a bulb in series increases the total resistance of the circuit. Removing a light bulb that is in series and replacing it with a wire lowers the total resistance of the circuit. e) Adding a bulb or network of bulbs in parallel decreases the total resistance of the circuit. Removing a pathway from a circuit increases the total resistance. f) Bulbs are independent when they have their own connections to the battery.

Guo + Kriplani 14  3. Voltage Model a) The voltage across a battery does not change b) Kirchoff’s 2nd Law/Loop Theorem: The voltage across a battery in a current loop is equal to the sum of the voltages across all of the other elements of the circuit. c) As the current through a resistor or bulb increases, the voltage across the resistor or bulb increases.  4. PRACTICE a) The diagram shows a two-bulb circuit with the two bulbs connected one after the other. When bulbs are connected this way, they are connected in series (1) Explain how the brightness of the two bulbs compare to each other (a) They will have the same brightness because the current is the same amount throughout (2) Explain how the brightness of each of these bulbs compare to the brightness of an identical bulb in a single-bulb circuit. (a) The bulbs in series are less bright because the bulbs in series share the current. b) The diagram shows a two-bulb parallel circuit (1) Explain how the brightness of the two bulbs compare to each other (a) They will be the same (current is the same) (2) Explain how the brightness of each of these bulbs compare to the brightness of an identical bulb in a single-bulb circuit (a) It would be the same because they are independent loops  K. Magnetism and Waves 1. Magnetic Field Lab a) Vector arrow facing me☉(out of the page)

b) Vector arrow facing away ⊗ (into the page) c) Right Hand Rule #1: for determining the direction of the magnetic field surrounding a current carrying wire (1) Hold right hand flat with your right thumb at 90 degrees to your fingers (imagine the wire runs through your right thumb) (2) Point your fingers into the region of space where you would like to know the direction of the field (3) Curl your fingers 90° to the palm of your hands; they now point in the direction of the field (4) IF THE ELECTRIC CHARGE IN QUESTION IS NEGATIVE, USE THE LEFT HAND RULE

Guo + Kriplani 15 d) Right Hand Rule #2: predicting the direction of the magnetic force on a moving charge (1) Hold your right hand flat with your thumb and fingers 90 degrees apart (2) Point your fingers in the direction of the moving charge (3) Rotate your hand so you can curl your fingers towards the head of the magnetic field vector (4) Your thumb now points in the direction of the magnetic force 2. Magnetic Force Math Models a) Fm = Iℓ ×   B (cross product) b) Fm = IℓB sine Ө + direction determined by RHR2 (1) I = current (2) ℓ = length of wire within the field (3) Ө = angle between vector ℓ and vector B (4) B = magnetic field vector  3. Magnetism Model a) A current loop has magnetic poles b) Magnetism is called by the movement of electrons c) In a ferromagnet or permanent magnet, there are small domains d) In a permanent magnet, these domains are aligned in one direction e) In a ferromagnet, these domains are jumbled around but become aligned when near a permanent magnet f) Non-magnets have no magnetic domains g) How to make a magnet (1) To Magnetize (a) Heat above the Curie temperature and cool in the presence of a magnetic field (b) Place in a strong constant magnetic field and vibrate or tap (c) Stroke with another permanent magnet (2) To Demagnetize (a) Heat above the Curie temperature and cool in the absence of a magnetic field (b) Place in a strong alternating magnetic field and slowly decrease magnitude (c) Mechanical disturbance(hit with hammer or drop)

Guo + Kriplani 16 General Math Models

k = 9.0 * 109Nm2 /C2 g = 10. N/kg 1µC = 10-6 C Mass of a proton = 2 * 10-27  kg Mass of an electron = 9 * 10-31  kg v = ∆d/∆t s = distance/∆t a = ∆v/∆t ∆d = vi ∆t + ½a∆t2 vf2 = vi 2 + 2a∆d Fg = mg ∑F = ma Fs(max)  = µsFN Fk = µkFN a = v2/r Fg = GmM/distance2 g = GM/distance2 p = mv Impulse = F∆t ∑F*∆t = ∆p ∑W = ∆E W = F∆dcos Ө Eg = mgh Ek = ½mv2 Eel = ½kx2 Fspring = kx Fe = kqQ/distance2 E = Fe/q E = kQ/distance2 ∆v = w/q ∆v = EoD Req = nR Req = R/n Req = R1 + R2 + … Req = (1/R1 + 1/R2 + …)-1 V = IR I = q/∆t V = ∆E/q P = ∆E/∆t P = IV FB = qvBsin Ө F = 1/T

Guo + Kriplani 17 V = λ/T = λ * f # of g’s = FN/Fg...