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General Physics PHY 114 Sub outcomes

1

PHY 114: Main sections 1

Mathematical background

2

Measurements and units

3

Waves (HRW9: 16 & 17)

4

Geometrical & physical optics (HRW 33 – 36)

5

Thermodynamics (HRW 18)

6

Calculus

7

Kinematics (HRW 2, 4)

8

Force and motion (HRW 5, 6)

9

Work and energy (HRW 7, 8)

10

Systems of Particles and collisions (HRW 9)

11

Rotational Motion (HRW 10, 11)

2

PHY 114: Sub-outcomes Note: (none) = Background information that will probably not be examined directly in exam, however you might need it to solve problems. * = Important concept / problem – ensure that you understand it. † = Will probably be tested in the exam. ‡ = Will certainly be tested in exam.

1

Mathematical background

Note: The aim of this section is to revise school work and ensure a good understanding of the concepts required later in the course. 1.1

Mathematical symbols and constants (LS 1.1, 1.2) a) explain what is meant by each of the mathematical symbols listed on page 1 b) * explain what is meant by the notation ∆x . c) * give the names and symbols of the following letters of the Greek alphabet: α, β, γ, δ, ε, θ, λ, µ, π, ρ, σ, τ, φ, ω, ∆, Σ, Ω

1.2

Exponents, logarithms and factorisation (LS 1.3, 1.5) a) explain the meaning of the terms “logarithm”, “base”, “exponent” b) explain what is meant by e x and ln x c) simplify expressions containing logarithms and exponents using the identities listed in LS 1.3 (e.g. LS problems 1.1 to 1.4) d) * factorise quadratic equations using the formula

1.3

Radian measure (LS 1.6) a) * explain how the radian measure is defined. b) * convert between angles given in revolutions, degrees and radians. c) ‡ calculate, in problems, θ , r or s given the other two values. (Formulae will not be given.)

1.4

Trigonometric functions (LS 1.7) a) * list the trigonometric ratios represented by the functions sin θ , cosθ and tan θ b) * draw a rough graph of y = sin x and y = cos x for −360 ≤ x ≤ 360 as well as − 2π ≤ x ≤ 2 π . c) * write down, without the use of a calculator the sine, cosine and tangent of the angles 0°, 30°, 45°, 60°, 90°, 180° d) * use the trigonometric identities LS 1.7(2) to 1.7(3) to solve problems (these identities won’t be given in exam). e) use trigonometric identities LS 1.7(4) to 1.7(17) to solve problems (identity will be given in exam) f) * explain what is meant by arcsin x and sin −1 x (as well as for cos and tan). g) * use the theorem of Pythagoras to calculate the length of a side of a rectangular triangle given the other two. 3

h) * apply the sine and cosine rule to determine angles and lengths of sides of a triangle. i) ‡ derive an approximate value for sinθ , cos θ and tan θ for small θ . 1.5

Geometric formulae (LS 1.8) a) explain (to a gr-1 pupil) what is meant by “area” and “volume” (operational definitions) b) Explain what is meant by an operational definition. c) * write down and use to solve problems: a formula for the area and the perimeter of the following: a rectangle, a triangle, a circle, a sector, an annulus and a narrow annulus. d) * write down and use to solve problems: a formula for the surface area and the volume of the following solids: a rectangular parallelepiped, a solid and hollow circular cylinder, a thin-walled hollow circular cylinder and a sphere.

Problems: LS 1: 1(a, d, g, j, m), 2 (c, f, I), 3 (a, d, g, j), 4 (a, d, g, j), 6(a, b, c, d), 7(a, b, d), 8(a, b, h, i), 10(a, d, j, g, m), 11(d, g , h (do you notice anything special with g & h? Can you explain it?)), 12, 13(a,d, e), 14(a,d), 16 (both exactly and using an approximation), 17 (there are two possibilities – can you find them?), 20, 21.

2 2.1

Measurements and units Units and Standards (WHR10: 1-1 to 1-6) discuss the properties required of a good standard. name five of the seven SI base units write a quantity in scientific notation. * give the values and symbol of the prefixes giga-, mega-, kilo-, centi-, milli-, micro-, nano- and picoe) † be able to convert between different units using the “chain link” method f) explain what is meant by “dimensions” g) † use dimensional analysis to check the correctness of an equation a) b) c) d)

2.2

Pressure and density (WHR10: 14-1) a) explain what is meant by a fluid (A: vloeier) b) define (in your own words) the concepts density and pressure, and state the units in which they are measured.

Problems: WHR10: Ch. 1: 1, 21, 28

4

3

Waves (WHR10: 16 & 17)

3.1

Introduction (WHR10: 16-1, 16-2, 16-4) a) explain what is meant by a wave and define the quantities wavelength, period and frequency. b) explain the difference between a transverse and a longitudinal wave c) † write down a general equation for a sinusoidal travelling wave with constant amplitude. d) ‡ derive and use to solve problems: The relationship between the angular wave number (k) and wavelength ( λ ), as well as the relationship between angular frequency ( ω ) and frequency (f). e) ‡ derive and use to solve problems: An expression for the speed of a wave in terms of ω and k or λ and f. f) † use the equation v = τ / µ to calculate the speed of a wave along a string. (The equation will be given, no derivation required.) Note: Transverse speed will be done later, derivation of (f), energy and wave equation not done.

3.2

Interference, standing waves and resonance (WHR10: 16-5, 16-7) a) explain what the superposition principle is b) † explain what interference is and derive an equation for the wave that is produced by interference between two waves having the same frequency, amplitude, wavelength, wave speed and direction but a phase difference φ . c) † use the equation derived in (b) to solve problems. (If the derivation is not asked, the equation will be given.) d) use diagrams to explain what standing waves are, and how they are formed e) † the wave equation. f) † use the equation derived in (b) to solve problems. (If the derivation is not asked, the equation will be given.) g) * discuss the reflection of waves and the boundary conditions that lead to inverted or non-inverted reflections h) † explain the phenomenon of resonance by referring to standing waves and derive an expression for the resonance frequencies. i) ‡ use the expression derived in (h), to solve problems. j) explain what is meant by the fundamental mode (= first harmonic), n-th harmonic. Note: Phasors not done.

3.3

Sound waves (WRH10: 17-1 - 17.5) a) describe what a wavefront and a ray is. b) use the expression v = B / ρ to calculate the speed of sound (the derivation is not covered in this course.) c) explain how a difference in path length between two sound sources (that are in phase) and an observer can lead to constructive and destructive interference. 5

Derive an expression for the path length difference that leads to constructive and destructive interference. d) define intensity of a sound wave and give its SI units e) ‡ define the decibel scale and use to solve problems f) ‡ derive expressions for the wavelength and frequency of standing waves with one or both ends open. Note: Derivation of speed of sound, pressure amplitude not done. 3.4

Beats (WHR10: 17-6) a) explain what beats are and how they are formed. b) ‡ derive an expression for the wave that is formed due to the superposition of two waves with different frequencies. Interpret the result and use to solve problems. (The identity for sinα + sin β will be given.)

3.5

Doppler effect (WHR10: 17-7) a) ‡ derive expression for the Doppler frequency change due to a moving detector, a moving source, and the case where both the source and the detector are moving. b) ‡ solve problems involving the Doppler effect. (Equation will be given, but without the sign rule.)

Problems: WHR 10: Ch. 16: 1, 3, 5, 9, 17, 19, 21 (optional challenge!), 25, 29, 31, 45, 53 (optional challenge!) Ch. 17: 1, 4, 9 (assume speed of wistle is 12 m/s), 12, 17(a), 21, 29, 31, 33, 37, 41 (optional challenge, some school kinematics required), 61, 65 (hint: calculate the ratios possible in the case of both ends open or only one end open)

4 4.1

Geometrical & physical optics (WHR10: 33 – 36) Introduction to waves & optics (WHR10: 33-1 (superficially), 33-4 (superficially), 33-5, 33-6; HRW 33-2, 33-3 (superficially), 33-7 to 33-9) a) * explain what is meant by a wave and define the quantities wavelength, period, freqency. b) explain what an electromagnetic wave is c) explain where visible light fits into the electromagnetic spectrum d) * name the colours at the extremes of the visible spectrum e) * state the (approximate) speed of light in vacuum f) ‡ define index of refraction, list its properties and use to solve problems g) explain what is meant by polarisation h) explain what is meant by reflection and refraction i) ‡ state the laws of reflection and refraction and use to solve problems j) explain qualitatively why light is refracted at an interface between two media k) explain what dispersion is l) † explain what is meant by critical angle and use concept to solve problems m) ‡ describe what happens during total internal reflection and use to solve problems 6

4.2

Real and virtual images (WHR10: 34-1; HRW 34-2) a) * explain the difference between a virtual and a real image b) * identify whether an image is real or virtual

4.3

Images formed in mirrors (WHR10: 34-2; HRW 34-3 to 34-5) a) * draw a ray diagram to show how an image of an object is formed by a plane mirror b) * explain the sign conventions used for object and image distances (i and p). c) * explain what is meant by the radius of curvature and the focal length of a spherical mirror and the sign conventions associated with these quantities. d) † derive an expression for the relationship between the radius of curvature and the focal length of a spherical mirror. (See WHR10: 34-6) e) † write down and derive an expression for the relationship between the focal length, object and image distances for a mirror and use to solve problems f) ‡ draw a principal ray diagram to show how an image of an object is formed by a spherical mirror

4.4

Images formed by thin lenses (WHR10: 34-4, 34-5; HRW 34-6 to 34-8) a) ‡ draw a ray diagram to show how an image of an object is formed by a thin lens b) * explain the sign convention used for focal length, object and image distances. c) * explain what is meant by the radii of curvature and the focal length of a thin lens and the sign conventions associated with these quantities. d) Use the lens maker’s equation (HRW eq. 35-10) to determine the focal length of a thin lens (equation will be given in exam) e) ‡ write down an expression for the relationship between the focal length, object and image distances for a thin lens and use to solve problems (no derivation) f) ‡ solve problems in which two lenses are involved. g)

4.5 a) b) c) d)

e) f) g) h)

Interference (WHR10: 35-1 (superficially), 35-2, 35-4, 35-5 (read); HRW 35-2 (superficially), 35-3 to 35-5, 35-7 (superficially), 35-8 (read)) ‡ Explain for which path length differenes constructive and destructive interference occur, and use to solve problems. * Explain what Huygens’ principle is. * Explain what diffraction at a single slit is and how it can be explained by Huygens’ principle. ‡ Explain the setup of Young’s experiment, and derive an expression giving the angles at which constructive and destructive interference occur. Use to solve problems. * Explain what coherence means. * Describe and calculate how the wavelength of light changes in media with different indices of refraction. * Explain qualitatively how interference occurs with thin films. † Solve problems in which thin film interference features: Single films and antireflection films. Start from first principles – do not just memorise equations. 7

i) * Describe the Michelson interferometer and explain how it works. 4.6

Diffraction (WHR10: 36-1, 36-5; HRW 36-2, 36-3, 36-8) a) † Explain how diffraction occurs at a single slit and derive an equation for the angle at which minima occur. Use the equation to solve problems. (If the derivation is not asked, the equation will be given.) b) † Describe what a diffraction grating is and derive an equation for the angles in which light is diffracted. Use the equation to solve problems. (If the derivation is not asked, the equation will be given.) c) † Briefly explain how a grating spectroscope works.

Problems: WHR10: 10th Ed: Ch 33: 9,13, 21, 25, 29, 33, 39 Ch 34: 10, 11, 28, 49, 58 – 65 (as many as you like), 67, 93 Ch 35: 25, 29, 45, 46 (slightly tricky), 47, 59, 60 (slightly hard), 76 Ch 36: 4, 7, 11, 26, 37, 42, 72

5

Thermodynamics (HRW 18)

5.1

The zeroth law of thermodynamics and temperature (HRW 18-1 to 18-2) a) * State the zeroth law of thermodynamics in your own words b) Explain why the zeroth law is essential to the introduction of the concept “temperature”. c) * Explain what is meant by the triple point of water. d) * Explain how the Kelvin temperature scale is defined. e) * Explain how temperature is measured by means of a constant volume gas thermometer f) * Give the relationship between the Celsius and Kelvin scales.

5.2

Thermal expansion (HRW 18-3) a) * describe linear expansion and define the coefficient of linear expansion b) ‡ write down and use to solve problems the equation describing the length expansion of an object c) ‡ write down equations describing area and volume expansion and derive them from the linear case and use to solve problems. d) * Explain how a hole in a plate and the volume of a hollow expands. e) * Describe and explain the implications of the anomalous behaviour of water between 0 and 4°C.

5.3 a) b) c) d)

Heat (HRW 18-4) * Explain what is meant by heat and explain the sign convention that is used. * Give the SI units of heat. Explain why it is not meaningful to refer to the “heat content” of a body. Define the heat capacity of an object 8

e) † Define the specific heat (capacity) of a substance and use to solve problems f) * Explain what is meant by heat of transformation, heat of vaporisation and heat of fusion. g) ‡ Calculate the final temperature, mass, heat capacity or heat of transformation in a heat problem involving temperature and phase changes. (See sample problems). 5.4

Heat transfer mechanisms (HRW 18-6) a) ‡ Write down an equation describing the rate at which heat is transferred by conduction. Explain the significance of all symbols. Apply the equation to problems as in HRW b) ‡ Calculate the heat flow through a layered system (composite slab) consisting of two or more layers, as in HRW Examples) c) Explain how heat is transferred by convection d) ‡ Use an equation to calculate the amount of heat radiated as thermal radiation by a warm body. (Equation will be given.) e) * Explain the significance of the T 4 in the Stefan-Boltzmann equation.

Problems HRW 9th Ed Ch 18: Q1, Q3, Q4, Q5, Q6, Q9, Q11, 9, 10, 15, 17, 23, 25, 28, 29, 35, 36, 37, 41, 54, 55, 59

6

Calculus

6.1

Differential calculus (LS 2) a) * Calculate the derivative of functions of form axn , sin ax , cos ax , eax and ln x . b) * Apply the sum, product and chain rule to calculate the derivatives of more complicated functions. c) * Give a geometrical interpretation of the first and second derivative of a function. d) * Use calculus to find the extreme values of a function and classify them as minima or maxima. e) * Explain what is meant by a differential and use them to calculate the change in a function due to a (small) change in on of its parameters.

6.2

Integral calculus (LS 3) a) * Calculate the “anti-derivative” (indefinite integral) of functions of the form ax n , x −1 , sin ax , cos ax , e ax . b) * Calculate the integration constant given the necessary boundary condition. c) * Use the definite integral to calculate the area under a curve and interpret the result geometrically. d) * Use the definite integral to calculate the area and volumes of various objects. e) ‡ Use integration to calculate the amount of work done by an ideal gas during (i) an isobaric, (ii) an isothermal and (iii) an adiabatic process.

6.3

Vector algebra (LS 4, HRW Ch. 3) a) Define a vector (in your own words) 9

b) * Perform vector addition and subtraction graphically and algebraically using components. c) Describe what is meant by a co-ordinate system and unit vectors d) Give the geometric meaning of the dot and cross products. e) Write down expressions for the dot and cross product both in terms of magnitude and angles as well in terms of components. f) Use the dot product to calculate the angle between two vectors. 6.4

Vector calculus (LS 5, 6.1, 6.2) a) Calculate the derivative of a vector function. b) Integrate a vector function. c) Applications to kinematics (see Theme 6)

Homework / Huiswerk: LS Ch 2: 3(a, b), 7, 8, (9), (10), 11, 12(a-e), 14, (17), 18. LS Ch 3: 1(a, f, i), 2(g, h, i, j), 3(a, b, c), 4, 7, English book 8 / Afrikaanse boek 9. LS Ch 4: 1, 2, 3, (4), (5), (6), 10, 11, 14, 17. LS Ch.5: 2, 3, 4, 5, 6. LS Ch 6: 1, 3, 4, 5, 6

7

Kinematics (Ch. 2, 4)

7.1

One dimentional kinematics: A review of Gr 12 Kinematics (HRW 2) a) Position, velocity, acceleration b) Graphs

7.2

Coordinates, position, path length and displacement (HRW 4-2) a) Explain what is meant by a position vector b) * Explain what is meant by path length and the displacement vector and point out the differences between the two and use to solve problems. c) Explain what the difference is between an instant and a time interval

7.3

Velocity and acceleration (LS 6-2, HRW 4-3, 4-4) a) Define the average velocity over an interval b) * Write down an expression for the velocity in terms of the position vector in both vector and component form. c) Explain why the velocity v of a particle is always tangential to the path of the particle and show that the magnitude of the velocity is equal to the speed. d) * Write down an expression for the acceleration in terms of the velocity both in vector and component form. e) ‡ Calculate the velocity and acceleration of a body given its position as a function of time f) ‡ Calculate first the velocity then the position given the acceleration of a particle and suitable initial conditions

10

7.4

Motion under constant acceleration (HRW 4-5, 4-6) a) † Do problems on free fall from rest (or with an initial velocity) calculating position, velocity, acceleration, time of flight. (Review of school work.) b) ‡ Do problems on projectile motion, calculating position, velocity, acceleration, the equation of path, horizontal range, maximum height etc. of a projectile. (All these problems have to be solved from first principles – no credit will be given for formulae that you “happen” to remember. See LS Section 6.2.1 – 6.2.3 for examples.)

7.5

Circular motion (HRW 4-7) a) ‡ Write down an expression for the position as a function of time for an object undergoing circular motion. b) Derive a relationship between the angular velocity ω and the speed v for an object undergoing circular motion. c) ‡ Calculate the velocity and acceleration of the object d) * Explain what is meant by centripetal acceleration e) ‡ Write down an equation for the centripetal acceleration of an object moving along a circular track giv...