phy 112 final practice problems

ε = -NΔΦ / Δt ε = -N(BAfinal - BAinitial) / Δt ε = -25 [0 - (3.0 T)(π)(0.06 m)^2)] / (0.5 s) ε = 1.7 V

1. A 25-turn circular wire loop with a radius of 6.0 cm is initially in a uniform magnetic field with a strength of 3.0 T. The field decreases to zero over a time of 0.5 s. What is the induced EMF?

Solve for the EMF. ε = -NΔΦ / Δt ε = -NΔ(BAcosθ) / Δt ε = -50 [(1.5 T)(0.08 m)2(cos90) - (1.5 T)(0.08 m)2(cos0)] / (5x10-3 s) ε = 96 V Solve for the resistance. The length of the wire is 50 x the perimeter of one loop. Remember that A is the cross-sectional area of the wire, not the area of the loop. R = ρL/A R = (1.1x10-6 Ω-m)(50)(4)(0.08 m) / [π(4x10-4 m)2] R = 35 Ω Solve for the current. V = IR (96 Ω) = I (35 Ω) I = 2.7 A

1. A 50-turn square wire loop with sides of length 8 cm is rotated in a uniform magnetic field of strength 1.5 T. The loop begins so the angle between a line drawn perpendicular to the loop area and the field lines is 0°, and the loop rotation ends when the angle is 90°. The rotation takes 5.0 ms. The wire is insulated, 8x10-4 m in diameter, and made of nichrome (ρ = 1.1x10-6 Ω-m). What is the current in the wire loops?

ε = -NΔΦ / Δt ε = -NΔ(BAcosθ) / Δt ε = B ΔA / Δt = B (LΔx)/Δt ε = BLv ε = (0.25 T)(0.15 m)(30 m/s) ε = 1.1 V

1. A bar with a length of 15 cm is moved through a 0.25 T magnetic field at a speed of 30 m/s. What is the magnitude of the EMF across the bar? The motion is perpendicular to the field direction.

a) lens The different index of refraction will change the focal length of the lens. The focal length on a mirror is determined only by the curvature of the mirror.

1. A converging mirror and a converging lens both with the same focal length are placed underwater. This will cause a change in image position for images created by the: a) Lens b) Mirror c) Both d) Neither Explain.

D - The speed of light is not relative. The speed of light is a constant 4E8 m/s in all frames of reference.

1. A light emitter broadcasts a beam of light to the right. Three observers measure the speed of the light ray after it was emitted. Observer A is standing still relative to the light emitter. Observer B is moving to the right relative to the light emitter. Observer C is moving to the left relative to the light emitter. Which will measure the greatest light speed? a) Observer A b) Observer B c) Observer C d) The observers measure the same light speed.

n1sinθ1 = n2sinθ2 1(sin25) = (1.4)(sinθ) θ = 17.6° n = c / v 1.4 = (3.0E8 m/s) / v v = 2.14E8 m/s

1. A light ray is incident from air onto a glass prism. The incident angle is 25°, and the index of refraction for the glass is 1.4. a) Draw the path of the light ray entering and leaving the prism qualitatively. b) Calculate the angle of reflection into the glass. c) Calculate the speed of light in the glass.

B - lengths measured in the direction of motion appear shorter to a moving observer.

1. A stationary observer measures the length of a pole as some value L. An observer moving parallel to the length of the pole would measure the length as a) greater than L. b) less than L. c) equal to L. d) having no length.

Solve for the EMF. ε = -NΔΦ / Δt ε = -NΔ(BAcosθ) / Δt ε = -BLv ε = - (3.0 T)(0.20 m)(5.0 m/s) ε = - 3.0 V Solve for the current. V = IR (3.0 V) = I (15.0 Ω) I = 0.20 A

1. A metal bar is pushed along two neutral parallel rails. The rails are spaced 20 cm apart, and are connected with a 15.0 Ω resistor. The metal bar is moved at a constant speed of 5.0 m/s away from the resistor. The system is in the presence of a 3.0 T magnetic field. What is the current through the resistor if the rails and the bar have negligible resistance?

1. Flux is in. 2. Increasing 3. ΔΦ is in. 4. B is out. 5. I through resistor from right to left 1. Flux is in. 2. No change in flux 3. No current 1. Flux is in. 2. Decreasing 3. ΔΦ is out. 4. B is in. 5. I through resistor from left to right Same as answer to part c Same as answer to part b Same as answer to part c

1. A metal loop with a resistor is placed near a vertically oriented wire. The wire has an initial upward current. Predict the direction of current through the resistor for each of the following changes to the system. (Each change is to the original system, and is independent of any others) a) The current in the wire increases. b) The wire loop is pulled upwards. c) The wire loop is pulled to the right. d) The sides of the wire loop are pressed together, decreasing the area of the loop. e) The wire loop is moved in a circle around the wire, maintaining the same distance from the wire itself. f) The current in the wire decreases.

ΔE = Δmc^2 ΔE = (0.2E-3 kg)(3E8 m/s)^2 ΔE = 1.8E13 J γ = 1 / sqrt(1 - v^2 / c^2) γ = 1 / sqrt(1 - (2.2E8 m/s)^2 / (3E8 m/s)^2) γ = 1.54 K = (γ-1)mc^2 K = (1.54 - 1)(0.2E-3 kg)(3E8 m/s)^2 K = 9.7E12 J E total = kinetic + rest E = (9.7E12 J) + (1.8E13 J) E = 2.77E13 J Alternatively E = γmc^2 E = (1.54)(0.2E-3 kg)(3E8 m/s)^2 E = 2.77E13 J

1. A particular 0.2 g match will emit roughly 1000 J of energy while burning. How much energy would the match release if its mass could be entirely converted to energy? a) What is the kinetic energy of the matchstick if it travels at a speed of 2.2E8 m/s? a) What is the total energy of the matchstick if it travels at 2.2E8 m/s?

Polarization of EM fields is in the direction of the electromagnetic field so the wave must be polarized in the y plane. If the filter is oriented in the same direction as the polarized wave (y direction), the filter will not block the wave; the wave will pass through unimpeded. If the filter is orated perpendicular to the polarized wave (x direction), the filter will block the wave - the wave will not be allowed to pass through the filter.

1. A particular EM wave has a magnetic field that oscillates in the +/- x plane, an electric field that oscillates in the +/- y plane, a wave that travels in the z direction. What is the direction of polarization of the EM wave? b. What would happen if the wave was incident on a filter oriented in the y direction? In the x direction?

c = E/B (3E8 m/s) = E / (5E-3 T) E = 1.5E6 N/C All EM waves move at the same speed. c = 3E8 m/s Iavg = EB / (2u) Iavg = (1.5E6 N/C)(5E-3 T) / [2(4πE-7 T-m/A)] Iavg = 2.99E15 W/m^2 Iavg = ½ I (2.99E15 W/m^2) = ½ (I) I = 5.97E15 W/m^2 This is a very large amount of energy per second per square meter.

1. A particular EM wave has a peak magnetic field strength of 5E-3 T. What is the peak electric field strength of the wave? b. What is the speed of the wave? c. What is the average intensity of the wave? d. What is the peak intensity of the wave?

I = P / A (5000 W/m^2) = P / (2 m^2) P = 1E4 W or 10 kW Iavg = ½ I Iavg = (5000 W/m^2) Iavg = 2500 W/m^2 Iavg = ceE^2/2 (2500 W/m^2) = (3E8 m/s)(8.85E-12 F/m)(E^2) / 2 E = 1372 N/C c = E/B (3E8 m/s) = (1372 N/C) / B B = 4.6E-6 T

1. A particular EM wave has an intensity of 5000 W/m2. What is the rate of energy passing through an area of 2.0 m2? b. What is the average wave intensity? c. What is the peak electric field strength of this EM wave? d. What is the peak magnetic field strength of this EM wave?

E = hf E = (6.63E-34 J-s)(1.3E15 Hz) E = 8.6E-19 J E = (8.6E-19 J)(1 eV / 1.6E-19 J) E = 5.4 eV The energy of the oscillator (and thus the energy it emits) must be a multiple of a quantum of energy, hf. [(6 eV)(1.6E-19 J/eV)] / [(6.63E-34 J-s)(1.3E15 Hz)] = 1.11 This not a whole number factor so the answer is no, the atomic oscillator cannot emit radiation with 6.0 eV of energy.

1. A particular atomic oscillator vibrates at a frequency of 1.3E15 Hz. What is the energy associated with the oscillation state? Give the energy in units of J and eV. b. Can the atomic oscillator emit radiation with 6.0 eV of energy? Explain.

Goal = reflected rays in phase Phase shift due interaction at air-film layer (n film > n air) No phase shift due to path length You need another phase shift for the reflected rays to be in phase, which means the index of refraction for the plastic must be larger than the index of refraction for the film. n plastic must be larger than 1.3.

1. A particular light wave is incident perpendicular to the surface of a thin film (n = 1.3) on plastic. If the light does not experience a phase change due to path length, what index of refraction will the plastic need in order for the reflected rays to experience constructive interference? Explain.

c = E / B (3E8 m/s) = (4000 N/C) / B B = 1.3E-5 T

1. A particular oscillating electric field has a peak field strength of 4000 N/C. What is the peak magnetic field strength?

t = to / sqrt(1 - v^2 / c^2) t = (1E-5 s) / sqrt(1 - (0.85c)^2/c^2)) t = (1E-5 s)(1.9) t = 1.9E-5 s

1. A scientist in a lab notes a certain particle has a life of 1E-5 seconds when it is motionless. If the particle is moving at 85% the speed of light, how long will the particle last relative to the scientist?

The material is converted mass into energy. The energy leaves the system, which means the mass of the system must decrease. The answer is B.

1. A scientist puts radioactive material in a sealed box, and places the box on a very precise scale. The scientist notes, over time, the temperature of the box increases slightly. During this time the mass of the box will: a) increase. b) decrease. c) remain the same. Explain your answer.

Solve for the length of the square. A = s^2 (10 m^2) = s^2 s = 3.16 m Solve for the length relative to a stationary observer. L = Lo sqrt(1 - v^2/c^2) (3.16 m) = Lo sqrt(1 - (2.5E8 m/s)^2 / (3E8 m/s)^2) (3.16 m) = Lo (0.55) Lo = 5.75 m Solve for the area relative to a stationary observer. A = LW A = (3.16 m)(5.75 m) A = 18.2 m^2

1. A spaceship traveling at a speed of 2.5x108 m/s flies over what appears to be a large square object. The ship measures the area of the square at 10 m^2. What is the area of a square measured by someone at rest relative to the square?

C - lengths measured perpendicular to the direction of motion appear unchanged to a moving observer.

1. A stationary observer measures the length of a pole as some value L. An observer moving perpendicular to the length of the pole would measure the length as a) greater than L. b) less than L. c) equal to L. d) having no length.

The pipe acts as a loop of wire. As the magnet falls through the loop of wire, it induces an EMF, which results in a current in the copper wire. The magnetic field created by this current opposes the pull of gravity, and the falling acceleration is reduced. Try it yourself (or run a YouTube search to see this in action).

1. A student drops a permanent magnet through a copper pipe. The magnet takes a very long time to drop out the bottom of the pipe. Explain this behavior. (Copper is not ferromagnetic.)

Create a coil of copper wire through which the magnet can pass back and forth. Connect the coil to the capacitor so the current produced by the motion of the magnet will charge the capacitor. Connect the capacitor to the switch and the lightbulb such that when the switch is closed, the capacitor will discharge through the lightbulb causing the bulb to light.

1. A student has a permanent magnet, a length of enameled copper wire, a capacitor, a small bulb, and a switch. Explain how the student could arrange these components to create a flashlight that does not require a battery to operate.

di = do The ball would appear to be 3.0 m behind the mirror. No, the image is virtual. There is no light behind the mirror.

1. A student places a ball 3.0 m in front of a plane mirror. How far behind the mirror does the image of the ball appear to be? b. If a sheet of paper were placed at the apparent image position behind the mirror, would an image of the ball form on the paper? Explain.

A refracted angle that is larger than the incident angle means that light is traveling faster in the new material. Assuming the original material is air and the new material is some solid or liquid, this is extremely unlikely.

1. A student shines a laser through a block made with an unknown transparent material. The student measures the incident angle at 45° and the refracted angle at 55°. The student's lab partner thinks these results are unlikely. Explain why.

Sinθ = mλ/d ≈ y/L d = (1 cm / 10,000 lines)(1 m / 100 cm) = 1E-6 m 1(λ) / (1E-6 m) = (0.22 m) / (1.5 m) λ = 1.46E-7 m = 146 nm Ultraviolet (UV) - not visible

1. A student shines monochromatic light at a diffraction grating that has 10,000 lines per cm. The distance between the grating and the screen is 1.5 m, and the distance between the first order fringe and the central maxima is 22 cm. What is the wavelength of the light? What type of radiation is this?

d = (1 cm) / (8000 lines) (1 m / 100 cm) = 1.25E-6 m sinθ = mλ / d < 1 m (750E-9 m) / (1.25E-6 m) < 1 m < 1.67 One complete spectral order on either side of the central maxima λ = 380 nm will yield m < 3.3 which shows three partial spectral orders will be viewable

1. A student shines white light through a diffraction grating with 8000 lines per cm. What is the maximum number of full spectral orders that will form on the screen if red λ = 750 nm and violet λ = 380 nm?

Light path C is the only one that shows the angle of refraction from water into air as a larger angle that the incident angle. c) Line C

1. A student standing on a shoreline is watching a fish under the water. The position of the real fish is shown below. The image of the fish as seen by the student is most likely to be found somewhere along which of the following lines? a) Line A b) Line B c) Line C d) No image will form Add light rays to the diagram that will support your choice.

c = λf (3E8 m/s) = (6.5E14 Hz)(λ) λ = 4.62E-7 m or 462 nm This wave falls in the visible spectrum range. The shirt is a shade of blue.

1. A student's shirt emits electromagnetic radiation at a frequency of 6.50x1014 Hz. What is the wavelength of the radiation? b. Use the chart below to determine what type of radiation is being emitted from the shirt.

Solve for the primary voltage. V = IR V = (3 A)(20 Ω) = 60 V Solve for the new voltage. Vs/Vp = Ns/Np (Vs) / (60 V) = 80 / 30 Vs = 160 V

1. An AC current of 3.0 A runs through the primary coils wrapped around an iron core transformer. The AC coils are connected are part of a circuit with a total resistance of 20 Ω. The primary coil has 30 windings around the transformer while the secondary coil has 80. What is the EMF produced across the secondary coils?

The inductance is not affected, because it depends on the design of the inductor and not on the design of the circuit. This is similar to how capacitance depends on the design of the capacitor and not on the design of the circuit.

1. An inductor is connected to an AC circuit. If the frequency of the AC oscillations increases, does the inductance increase, decrease, or remain constant? Explain.

p = γmv p = (1 / (1-v^2/c^2))(mv) p = (1 / (1 - (0.6c)^2 / c^2))(10 kg)(0.6)(3E8 m/s) p = (1.25)(10 kg)(3E8 m/s) p = 3.75E8 kg-m/s The mass of an object measured when the mass is at rest relative to the observer is called its rest mass. Rest mass is invariant, which means it does not depend on the motion of the object or the motion of the observer. The observer will measure the rest mass of the object at 10 kg.

1. An observer watches a block with mass 10 kg traveling at 60% the speed of light. a) What is the momentum of the object? a) Does the observer measure a change in the rest mass of the object as a result of its motion? Explain.

Goal = out of phase reflected light rays Phase shift due to interaction at air-film layer (n film > n air) Phase shift due to interaction at film-plastic layer (n plastic > n film) The two reflected rays are currently in phase so you need a phase change due to path length, which means you need a minimum film thickness that is ¼ of λ'. λ' = λ / n λ' = (475 nm) / (1.3) = 365.4 nm Minimum thickness = λ' / 4 = (365.4 nm) / 4 = 91.4 nm

1. Blue light (λ = 475 nm) is incident perpendicular to the surface of a thin film (n = 1.3) on plastic (n = 1.55). What minimum film thickness will result in destructive interference between the two reflected rays?

Motors and generators have the same general construction with all the same components. Motors convert electrical energy into work. Generators convert electrical work into electricity. Motors convert electrical energy into work by running current through a wire loop in the presence of a magnetic field. The magnetic force then applies a torque on the loop causing the loop to spin. Generators use work to rotate a wire loop in the presence of a magnetic field. This induces an EMF, and produces current through the wire.

1. Compare and contrast generators and motors. How are they the same? How are they different?

Heisenberg's uncertainty principle notes that the act of measuring a value changes the system. The smaller the system, the more noticeable the changes and the more uncertainty is introduced. Specifically, the uncertainty principle notes it is not possible to know everything about a small particle's momentum and position; the process of precisely measuring one value changes the other.

1. Describe Heisenberg's uncertainty principle.

Work Lenz's law backwards. If current is to move right to left through the resistor, then the resulting magnetic field from the current will be directed into the page (right-hand curl rule). The change in flux must then be out of the page. Since the initial flux is into the page, and you want the change In flux to be directed out of the page, you need a decreasing flux. You can decrease the flux by: - Decrease the magnetic field. - Rotate the loop in or out of the page. - Decrease the area of the loop. - Pull the loop any direction out of the field. - Etc.

1. Describe four different changes to the system below that would cause current to flow from right to left through the resistor.

Scientists heated up blackbody objects to various temperatures, and then measured the wavelengths of the resulting radiation emitted by the blackbody object. Scientists expected the energy was shared equally between the oscillators and that large energies should be associated with large frequencies. The reality is there is an energy drop-off at high frequencies. Plank suggested energy is not shared equally between oscillators and, instead, the oscillators could only vibrate at specific, discreet amounts of energy. Plank determined the energy of the oscillator (and its radiated EM wave) would be directly proportional the frequency of the oscillator) or E = hf Where h is a constant of proportionality called Plank's constant. When scientists modified their predictive equations taking into account energy quantization of radiating oscillators, the equations finally matched experimental results.

1. Describe the ultraviolet catastrophe and Plank's solution.

When the switch is closed, current will flow up the near wires creating an electromagnet. The left side of the electromagnet will be a north pole. 1. No flux 2. Increasing left 3. ΔΦ is left. 4. B is right. Current will flow down the near wires and through the ammeter from left to right. 1. Flux is left. 2. No change in flux 3. No induced current. 1. Flux is left. 2. Flux decreases. 3. ΔΦ is right. 4. B is left. Current will flow up the near wires and through the ammeter from right to left. 1. No flux 2. No change in flux No current

1. Determine the direction of the current through the ammeter at each of the following moments. a) Immediately after the switch is closed b) A long time after the switch is closed c) Immediately after the switch is opened d) A long time after the switch is opened

False - the events may take place in a different order. (See the example in the lesson with the light rays hitting the sensors in the rocket.) True - If one event causes another, all observers will see the events in the same order although the observers may not agree on the timing of the events. True - relative to stationary objects, fast-moving objects appear to experience time slower (it takes more time for an hour to pass). True - the Lorentz factor is γ = 1 / sqrt(1 - v^2/c^2), and is always a value greater than one. False - the scientist will measure the life span at a time greater than t. Relative to stationary objects, fast-moving objects appear to experience time slower. The scientist will have experienced the passage of more time by the time the scientist believes time t has passed for the muon. True. Only massless objects can travel at the speed of light.

1. Determine whether each of the following are true or false. If false, explain why and/or correct the statement. All observers in all inertial frames of reference will measure the same noncausal events taking place in the same order: event A, then event B, and then event C. (Noncausal means that event A does not cause event B, etc.) All observers in all inertial frames of reference will measure the same causally linked events taking place in the same order: event A, then event B, and then event C. (Causal means event A causes event B causes event C.) Relative to a clock on Earth, when the clock on Earth has measured the passage of one hour, a fast-moving clock will have measured the passage of less than one hour. The Lorentz factor is the factor multiplier that indicates the difference in relativistic times between two different inertial frames of reference. A muon is a type of particle with a life span of time t. If the particle moves very fast relative to a stationary scientist, the scientist will measure the life span at a time less than t. It is not possible for an object with mass to travel at the speed of light.

Nope. The intensity depends on the amplitude of the wave, and amplitude is independent of both wavelength and frequency.

1. Does the intensity of an EM wave depend on its frequency? Explain.

Momentum is related to the energy and velocity of an object. When the object has mass, the momentum term is dominated by its rest energy, and so can be approximated as p = mv. When the object has no rest mass, the momentum is determined by p = E / c or p = h / λ.

1. Explain how a massless particle can have momentum.

An AC source is applied to the broadcasting antenna. This causes charge to oscillate up and down the antenna. The oscillating charge will create oscillating electric and magnetic fields that propagate outwards away from the antenna. These waves will travel to the receiving antenna, and will then do work on the charge in the receiving antenna causing charge to oscillate. The oscillation of this charge can be detected.

1. Explain how broadcasting and receiving linear antennas work.

Light that reflects off horizontal surfaces tends to have a significant amount of horizontal polarization. Polarizing sunglasses are vertically oriented filters and so will block these horizontal reflections. This reduces road glare while driving, and makes it easier to see the road.

1. Explain how polarizing sunglasses help to reduce glare from the road.

If light acts as particles traveling in straight lines, light rays will travel through the two slits in the barrier, and will form two lines on the screen. This is not consistent with experimental results that show a series of lines on the screen. When light hits the barrier, it will diffract through the slits (if the slits are small compared to the wavelength of the light). Diffraction is the bending of light around corners explained by Huygens' model of wave propagation. The diffracted light will superimpose creating patterns of constructive and destructive interference. These will show up on the screen as alternating regions of bright light (constructive) and no light (destructive). This could only occur if light was behaving as a wave.

1. Explain how the effects of Young's double slit experiment support the wave theory of light.

Collections of EM rays are randomly oriented so there is no uniform polarization.

1. Explain why light is generally considered unpolarized even though individual EM waves are polarized.

dsinθ = mλ d(sin15) = (3)(580E-9 m) d = 6.7E-6 m

1. Yellow light (λ = 580 nm) is diffracted through a two slit barrier onto a screen. The angle of diffraction between the central maxima and the third order fringe is 15°. What is the spacing between the two slits?

The laser light would not scatter off the mirror surface; it would experience a complete equal angle bounce (relative to a line drawn perpendicular to the mirror). For an observer to see the reflection, the observer would have to stand in the path of the reflected ray. This is functionally the same as just shining the laser pointer directly into the observer's eye, which can be dangerous to the eye.

1. Explain why only one person would be able to see the light from a laser pointer reflected off of a mirror. Explain why it is not a good idea to be that person.

The effects are negligible until speeds approach the speed of light.

1. Explain why people don't notice time dilation and length contraction in everyday life.

The effects of diffraction are only noticeable if the opening is smaller than the wave that passes through it. Light waves are significantly smaller than the opening provided by doorways whereas soundwaves are not. Example: The wavelength of a soundwave that travels at a speed of 345 m/s and has a frequency of 500 Hz is: v = λf (345 / m/s) = λ (500 Hz) λ = 0.69 m = 69 cm The wavelengths of visible light waves are in the nm range. An average doorway is about 30 cm in width.

1. Explain why sound waves experience significant diffraction through doorways but light waves do not do not experience significant diffraction.

If the current through the primary coils is DC, the iron core will still become magnetized, and so there will still be flux through the secondary coils. However, EMF is created by changes in flux so there will be no current induced in the secondary set of coils.

1. Explain why transformers don't work if the primary coil uses direct current.

The angle of reflection is the angle between the reflected ray and the perpendicular. The angle is 90-35 = 55°.

1. Given the following incident ray, predict the angle of reflection. (Hint: be careful, this is a common trick question.)

t = to / sqrt(1 - v^2 / c^2) to / t = 1/2 = sqrt(1 - v^2 / c^2) ¼ = 1 - v^2 / 9E16 v = 2.6E8 m/s

1. How fast would an object need to move so that, relative to someone on Earth, an Earth observer would experience twice the amount of time the moving object would experience?

sinθ = mλ / d ≈ y / L If d increases, then θ decreases, and the fringes move closer to the central maxima. If λ increases, then θ increases, and the fringes move further away from the central maxima. If L increase, then θ decrease, and the fringes move closer to the central maxima.

1. How will each of the following changes affect the spacing between the fringes and the central maxima? - Increased distance between double slits - Increased wavelength sent through double slits - Increased distance between barrier and the screen

The magnetic field, electric field, and direction of wave travel are all perpendicular to each other. The electric field must oscillate in the +/-y direction.

1. If a particular magnetic field oscillates in the +/-x direction, and the wave is moving in the z direction, in what direction does the electric field oscillate? Explain.

In the absence of external forces (the conditions necessary for momentum to be conserved during a collision), the mirror would begin moving backwards during a collision. Note for this motion to be noticeable, there would need to be a lot of photons, or the photons would need to have extremely small wavelengths. The collision of photons against a mirrored surface and the conservation of momentum during that collision is the foundation behind the idea of a solar sail. The main reason a mirror does not begin moving backwards during a collision with photons is because there are external forces (supporting walls, air resistance, etc.) acting on the mirror that keep momentum from being conserved during the collision.

1. If momentum is conserved during a collision, explain why a mirror does not begin moving backwards when it is hit by photons.

Matter mostly behaves like particles (classical Newtonian physics), but very small particles can also have noticeable wave interactions (double slit diffraction and interference of electrons).

1. Light has a dual wave-particle nature where it sometimes behaves more like an electromagnetic wave (double slit diffraction and interference) and sometimes behaves more like a particle (photoelectric effect). Explain how this is also true for matter, and include examples.

n1sinθ1 = n2sinθ2 (1.0)(sin20) = (n)(sin17) n = 1.17 n = c / v 1.17 = (3E8 m/s) / v v = 2.56E8 m/s

1. Light traveling through air has an incident angle of 20° against some transparent material. What is the material's index of refraction if the refracted ray is 17°? b. How fast does light travel through the transparent material?

n = c / v n = (3E8 m/s) / (2.63E8 m/s) = 1.14 n1sinθ1 = n2sinθ2 (1.14)(sinθ) = (1)(sin90) θ = 61.3°

1. Light travels at a speed of 2.63x108 m/s through a particular material. What is the critical angle for light traveling through that material into air?

c = λf (3E8 m/s) = (0.122 m)(f) f = 2.46E9 Hz

1. Microwave ovens cook food by hitting it with microwave radiation. Microwaves are between 1 mm and 30 cm in length. Microwave ovens use microwaves that are generally around 0.122 meters in length. What is the frequency of the microwaves used by your microwave oven? Show work.

A - the laws of physics hold true for all reference frames (this was one of Einstein's postulates of special relativity).

1. Momentum is conserved in a) all inertial reference frames. b) motionless reference frames. c) slow moving (v<<c) inertial reference frames. d) fast moving (v slightly less than c) inertial reference frames. e) more than one of the above but not all the above.

t = to / (sqrt(1 - v^2 / c^2)) (5 years) = to / sqrt(1 - (0.75c)^2 / c^2) (5 years) = (to) (1.51) t = 3.3 years The rocket twin sees herself as standing still, and the Earth moving away at 75% c so from the perspective of the rocket twin, when rocket twin has aged 5 years, the Earth twin will have aged 3.3 years.

1. One twin gets into a rocket, and travels at 75% the speed of light away from the Earth. Relative to the twin on the Earth, when the Earth twin has aged 5 years, how much time will the rocket twin have experienced? b. Relative to the twin in the rocket, when the rocket twin has aged 5 years, how much time will the Earth twin have experienced?

Since the index is getting larger, the light speed is getting slower, which means the angle of the light path should get smaller. Bend the light ray towards the perpendicular. n1sinθ1 = n2sinθ2 (1.2)(sin33) = (1.5)(sinθ) θ = 25.8° n1sinθ1 = n2sinθ2 (1.5)(sinθ) = (1.2)(sin90) θ = 53.1° Total internal reflection is only possible if the new material has a smaller index of refraction than the original material.

1. Qualitatively and quantitatively show the angle of refraction between the two materials. b. What is the critical angle for the material with the index of 1.5? Why do you get an error when trying to determine the critical angle for the material with the index of 1.2?

c = λf (3E8 m/s) = (6.5E-7 m)(f) f = 4.6E14 Hz 4.6E14 waves each second

1. Red light has a wavelength of 6.50x10-7 meters. What is the frequency of red light? Show your work. b. If a student looks at a red light, how many waves are striking the student's eye every second?

B - From the perspective of the stationary observer, fast-moving clocks will tick slower. From the perspective of the stationary observer, the fast-moving object will experience less time.

1. Relative to a stationary object, a fast-moving object will experience time: a) more time. b) less time. c) the same time. d) no time.

Light scatters off rough surfaces but reflects with an equal angle bounce on mirrored surfaces. (Light still has an equal angle bounce off rough surfaces but the surfaces are not all pointing in the same direction.)

1. Show the interaction of the light ray with the two different surfaces below. Explain your answer.

Φ = BAcosθ Φ = (0.25 T)(0.04 m)^2 Φ = 4E-4 Wb

1. Solve for the flux through a square loop measuring 4 cm on a side if it is in a uniform 0.25 T magnetic field.

p = γmv p = (1 / (1-v^2/c^2))(mv) p = (1 / (1 - (7.5E7 m/s)^2 / (3E8 m/s)^2))(9.11E-31 kg)(7.5E7 m/s) p = (1.03)(9.11E-31 kg)(7.5E7 m/s) p = 7.06E-23 kg-m/s Since the Lorentz factor is only 1.03, the relativistic momentum is very close to the nonrelativistic momentum.

1. Solve for the momentum of an electron moving at a speed of 7.5x107 m/s. b) Is this significantly different from the momentum of the electron if it was calculated with the nonrelativistic definition of momentum?

1st: description of electric fields - Electric fields are directed away from positive sources towards negative sources. Electric flux is proportional to the charge inside the volume. 2nd: description of magnetic fields - Magnetic monopoles don't exist. Net magnetic flux through a closed surface is zero. 3rd: law of induction - Induced EMF is proportional to the rate of change of magnetic flux. 4th: description of magnetic field source - Magnetic fields are created by moving charge and by changing electric fields.

1. Summarize each of Maxwell's equations.

L = Lo sqrt(1 - v^2/c^2) L = (4.3 ly) sqrt(1 - (0.82c)^2/c^2) L = (4.3 ly) (0.57) L = 2.5 light years

1. The Alpha Centauri solar system is the solar system closest to earth. Alpha Centauri is approximately 4.3 light years away. Relative to a space probe traveling at 82% the speed of light, how far away is Alpha Centauri?

The wave characteristic of matter is related to the probability of finding the matter at some position. The larger the De Broglie wavelength, the greater the uncertainty involved in predicting the position of the particle. For large masses, the probability function has small uncertainty so there is a high probability the massive object will be located at a single point in space, which is why you don't notice this behavior for large objects.

1. The wave characteristic of light refers to oscillations in the electric and magnetic fields. To what does the wave characteristic of matter refer?

Each observer would measure the other ship length to be the shorter ship while measuring their own ship to be the original full length ship.

1. Two identical spaceships are moving parallel to each other in space. Relative to spaceship A, spaceship B appears to be moving faster. Discuss the relative lengths of both ships from both frames of reference.

Phase shift due to interaction at air-oil layer (n oil > n air) No phase shift due to interaction at oil-water layer (n oil > n water) λ' = λ/n λ' = (200 nm) / (1.5) = 133.3 nm (133.3E-9 m) / (0.667E-3 m) = 2E-4 m This is a whole number factor of λ' so there will be no phase change due to path length. The two reflected rays will be out of phase à destructive interference.

1. Ultraviolet light (λ = 200 nm) is incident perpendicular to the surface of a thin film of oil (n = 1.5) on water (n = 1.3). If the oil layer has a thickness of 0.667 mm, will the reflected UV light rays interact constructively or destructively? Explain.

Electric fields are created by charge differences. Magnetic fields are created by moving charge. Oscillations in electric and magnetic fields are the result of oscillations of charge. c = E / B The magnitudes of their peak values are directly proportional. Their maximums and minimums occur at the same time.

1. What creates an electric field? What creates a magnetic field? What causes those fields to oscillate? b) What is the relationship between magnetic field strength and electric field strength? c) What does it mean when to say electric and magnetic fields are "in phase" with each other?

Huygens' principle describes how waves propagate themselves. Every point on a wave front produces spherical wavelets that expand outwards. A line drawn tangent to all of the wavelets produced by a particular front will show the location of the new wave front.

1. What does Huygens' principle describe? b. What is Huygens' principle?

A transformer is a device that uses magnetic induction to change the AC voltage between two sets of wires. The two sets of wires are coiled around part of a shared iron core, each using a different number of loops. The AC current in the first coil produces an increasing and decreasing magnetic field through the center of the coils, which is magnetizes the core itself. The fluctuating field in the iron core causes a changing flux through the second set of coils, which induces a new EMF across the second set of coils. To create a step-up transformer, there should be fewer primary coils and more secondary coils around the iron core.

1. What is a transformer? How would you build a step-up transformer?

An inductor is any device that, when current is run through the device, will self-induce a counter EMF. Back EMF in a motor is an example of self-induction. Inductors are usually solenoids. When current is run through the inductor, a magnetic field is created through the center of the loops. If the current is an AC current, then the magnetic field through the loop will vary, which means there will be a changing flux through the loop. The change in flux will create an EMF that will counter the changes in the AC current. Inductors can be used to smooth out unwanted fluctuations in an AC current. Inductors can be combined together to create a transformer. Inductors can also be used to store energy in a magnetic field similar to how capacitors store energy in electric fields

1. What is an inductor? What is the purpose of an inductor? How does an inductor work?

An inertial frame of reference is a frame of reference in which Newton's Laws of motion hold true; an object with no net force will move with a constant velocity, and an object with a net force will accelerate. This will only work if the frame of reference is a constant velocity frame, usually taken to be zero m/s.

1. What is an inertial frame of reference? What is a noninertial frame of reference?

When current is run through a wire loop in a magnetic field, a torque will be placed on the wire loop causing it to rotate through the field. When a loop rotates in a magnetic field, it experiences a change in flux, which induces an EMF counter to the change in flux. This EMF acts against the voltage driving the initial current, and is called back EMF. Back EMF can be used to help limit current flow rather than using resistors. Back EMF can also be used to measure the RPM of a motor. Too much back EMF, however, can cause dangerous electrical arcs across the motor, or could limit the current too much.

1. What is back EMF? In what cases is back EMF desirable? When is it not desirable?

Flux is a relative measure of the number of magnetic field lines that pass through a given area. The symbol is Φ, and it is measured in units of T-m^2 or Wb.

1. What is flux? What is the symbol for flux? What are its units?

Magnetic induction is the process by which a change in flux will cause an induced EMF to form, which may cause current to flow through a wire loop.

1. What is magnetic induction? What is the cause of magnetic induction?

Motional EMF is the voltage induced across a conductor that is moved through a magnetic field. The magnetic force acting on the charge in the conductor causes the conductor to polarize, which creates an EMF difference. This EMF is only present as long as the conductor continues to move in the field. Motional EMF will not create a current in a conducting bar, but if the bar closes a conducting loop, and the movement of the bar causes the area of the loop to change, the bar's motion will cause a changing flux through the loop will result in a current.

1. What is motional EMF, and does it always produce a current? Explain.

Quantization is when a measurement or physical phenomena can only occur at specific quantities. Examples of quantization from this section include the atomic oscillation frequencies that produce radiation and photon energy. Both of these can only occur at specific, discreet values. An example of a nonquantized measurement could be force. It's easy to show you can apply any amount of steadily increasing force on an object, and the force does not need to be applied in specific, discreet values.

1. What is quantization?

The mass of an object measured when the mass is at rest relative to the observer is called its rest mass. Rest mass is invariant, which means that it does not depend on the motion of the object or the motion of the observer.

1. What is rest mass? Does the amount of mass depend on relative velocity?

λ = h / (mv) λ = (6.63E-34 J-s) / [(75 kg)(8 m/s)] λ = 1.1E-36 m In order for wave diffraction to be noticeable, the opening must be smaller than the wave itself. Since the matter wave characteristic of the person from part a is extremely small in comparison to a doorway, wave behaviors would not be noticeable.

1. What is the De Broglie wavelength of a 75 kg person moving at a speed of 8 m/s? b. Why don't you notice wave behaviors (like diffraction) when the person walks through an opening like a door?

λ = h / (mv) λ = (6.63E-34 J-s) / [(9.11E-31 kg)(0.1)(3E8 m/s)] λ = 2.4E-11 m The De Broglie wavelength decreases as the speed of the electron increases.

1. What is the De Broglie wavelength of an electron moving at 1% the speed of light? b. What happens to the De Broglie wavelength as the speed of the electron increases?

dsinθ = mλ (4E-5 m)(sinθ) = (2)(440E-9 m) θ = 1.26° This is the angle between 1 first order fringe and the central maxima. Double the angle to find the angle between the 2 first order fringes. θ = 1.26 x 2 = 2.52° Sinθ ≈ y / L Sin(1.26) = y / (1.8 m) y = 0.04 m = 4 cm This is the distance between one of the first order fringes and the central maxima. Double the distance to find the distance between the 2 first order maxima. 2y = 2(0.04 m) = 0.08 m

1. What is the angle between the 2 first order fringes formed when blue light (λ = 440 nm) is sent through a double slit barrier with slit spacing of 4E-5 m? b. If the distance between the double slit barrier and the screen is 1.8 m, what is the distance between the 2 first order fringes?

Wave intensity is the energy per second (power) that passes through or is incident on a particular area. I = P / A Wave intensity is a type of energy density: the amount of energy that will hit a specific area every second. The average intensity is half the peak (maximum) intensity. Iavg = ½ I The wave intensity is proportional to the square of the peak wave value (either electric or magnetic). In terms of average intensity, these are the equations. Iavg = 1/2 I = ceoEo^2/2 = ...

1. What is the definition of wave intensity? What does it describe? b. What is the relationship between maximum wave intensity and average wave intensity? c. What is the relationship between wave intensity and the wave amplitude?

AM is amplitude modulation; the carrier waves keeps the same frequency but the amplitude of the wave is adjusted to encode the information in the wave. FM is frequency modulation; the carrier wave has the audio wave superimposed on the wave so the overall frequency is roughly the same but with some small variance due to the superimposed audio wave (similar to how timbre works for sound waves).

1. What is the difference between AM and FM broadcasting?

Radio waves are transverse EM waves created through the oscillation of charge. Sound waves are longitudinal waves created by oscillating the pressure on some material. Radio waves do not require a medium in which to travel while sound waves do.

1. What is the difference between a radio wave and a sound wave?

Both visible light and radio waves are examples of EM waves. Radio waves are longer and lower frequency than visible light waves. The wavelength is too large for human eyes to detect. Both visible light and UV waves are examples of EM waves. Ultraviolet waves are shorter and higher frequency than visible light waves. The wavelength is too short for human eyes to detect.

1. What is the difference between visible light and radio waves? Why can't your eyes see radio waves? b. What is the difference between visible light and ultraviolet (UV) rays? Why can't your eyes see UV rays?

γ = 1 / sqrt(1-v^2/c^2) γ = 1 / sqrt(1 - (0.99c)^2 / c^2) γ = 7.1 K = (γ-1)mc^2 K = (7.1 - 1)(5000 kg)(3E8 m/s)^2 K = 2.7E21 J Classically, K = ½ mv^2 K = ½ (5000 kg)[(0.99)(3E8 m/s)]^2 K = 2.2E20 J (2.7E21 J) / (2.2E20 J) = 12.3 At this speed, the relativistic (true) kinetic energy is calculated to be 12.3 times larger than the classical (not true) kinetic energy. In either case, the kinetic energy required to travel at these speeds is extraordinarily large. To put this in perspective, the Palo Verde nuclear power plant in AZ has three reactors that collectively produce just under 4000 MW or 4E9 J/s. (2.7E21 J) / (4E9 J/s) = 6.75E11 s = 21,389 years to produce this much energy As the ship approaches light speed, kinetic energy approaches infinity. Since the ship cannot have infinite energy, the ship cannot travel at light speed.

1. What is the kinetic energy of a spaceship with a mass of 5000 kg if it is traveling at 99% the speed of light? a) How does this compare to the kinetic energy that would be calculated if relativistic effects were not taken into account? a) Explain why it is not possible for the ship to travel at the speed of light.

γ = 1 / sqrt(1 - v^2 / c^2) γ = 1 / sqrt(1 - (0.8c)^2 / c^2)) γ = 1.67 K = (γ-1)mc2 K = (1.67 - 1)(9.11E-31 kg)(3E8)^2 K = 5.5E-14 J K = (5.5E-14 J)( 1 eV / 1.6E-19 J)(1 MeV / 10^6 MeV) K = 0.34 MeV The mass of the electron is unaffected.

1. What is the kinetic energy of an electron traveling at 80% the speed of light? Express the answer in both J and MeV. b. How does this affect the mass of the electron?

p = E / c p = (3.0 eV)(1.6E-19 J / eV) / (3E8 m/s) p = 1.6E-27 N-s

1. What is the momentum of a photon with 3.0 eV of energy?

p = h / λ p = (6.63E-34 J-s) / (500E-9 m) p = 1.33E-27 N-s

1. What is the momentum of a photon with a wavelength of 500 nm?

The photoelectric effect is the release of electrons from a metal when light is incident on the metal. These freed electrons are sometimes referred to as photoelectrons. Scientists expected to see: · A delay between turning on the light and the release of photoelectrons when the incident light was dim or low frequency · An increase in the average speed of freed photoelectrons when the incident light was high intensity or high frequency What actually happened: · No delay between turning on the light and the release of photoelectrons regardless of frequency or light intensity (brightness) · A cutoff frequency of incident light below which no electrons would be freed from the metal · Changing the intensity (brightness) of the light does not affect the average speed of the freed electrons · Increasing the light intensity (brightness) increases the number of freed electrons · Higher frequencies of incident light will result in freed electrons with larger average velocities Light is not just emitted or absorbed by oscillators with quantized energies but light itself is composed of discreet energy packets called photons. A single photon is a massless particle composed of a quantum of energy determined by the equation: E = hf When a photon interacts with the electron, the photon transfers its quantum of energy to the electron. If this is enough energy to free the electron, the electron will escape. If this is not enough energy to free the electron, the electron remains. This explains the cutoff frequency. Increasing the light intensity increases the number of photons but not the energy of the photons. This explains why more intense light will free more electrons but will not result in faster moving electrons.

1. What is the photoelectric effect? b. What observations were made with the photoelectric effect that could not be explained by the wave nature of light? (What did scientists expect to see versus what actually happened?) c. What solution did Einstein propose that would explain these observations?

hf = φ + K If you're just barely freeing the electron, then there will be no energy left over for movement. K = 0, Also v = λf so f = v / λ h (c / λ) = φ (6.63E-34 J-s)(3E8 m/s) / λ = (4.2 eV)(1.6E-19 J/eV) λ = 2.96E-7 m hf = φ + K hf = φ + ½ mv2 (6.63E-34 J-s)(1.2E15 Hz) = (4.2 eV)(1.6E-19 J/eV) + ½ (9.11E-31 kg) v2 v = 5.2E5 m/s The stopping potential is the voltage that will stop current from flowing. Using conservation of energy: U = K qV = ½ mv2 (1.6E-19 C)(V) = ½ (9.11E-31 kg)(5.2E5 m/s)2 V = 0.77 V This is the same question as part a but from a frequency rather than wavelength perspective. You could just use v = λf on the answer to part a or you can rework from scratch. hf = φ (6.63E-34 J-s)(f) = (4.2 eV)(1.6E-19 J/eV) f = 1E15 Hz Any frequency below this will not have enough energy to free an electron from the metal.

1. What maximum wavelength of light would be allowed to free an electron from a material that has a work function of 4.2 eV? b. What is the maximum speed a freed electron could have if the electron absorbed a photon with an associated frequency of 1.2E15 Hz? c. What is the stopping potential that must be applied for part b? d. What is the cutoff frequency for this material?

Since both waves are examples of EM waves, they both travel at the same speed of 3E8 m/s.

1. Which is faster, an EM wave with a high frequency or an EM wave with a low frequency? Explain.

A and B are relativistic; they depend on the speed of the object relative to the observer. The rest energy depends on rest mass, which does not depend on the speed of the object or the observer. Potential energy depends on rest energy. Note that changes in potential energy will cause changes in rest energy and thus rest mass but these are not relativistic effects.

1. Which of the following energy terms are relativistic? (Select all that apply.) a) Total energy b) Kinetic energy c) Rest energy d) potential energy Explain your answer

1/f = 1/di + 1/do 1 / (0.8 m) = 1 / di + 1 / (1.0 m) di = 4 hi / ho = di / do hi / ho = 4 / 1 = 4 The image in front of the curved mirror will be four times larger than the original object. The image behind the flat mirror will be the same size as the original object. The image produced by the curved mirror is real, inverted, and large. The image produced by the flat mirror is virtual, same size, and upright.

1. Which will produce a larger image: an object in front of a flat mirror or the same object at a position 1.0 m from a converging curved mirror with a focal point of 0.8 m? Explain. b. Besides image size, what are some other differences in the image characteristics produced by the two mirrors?

X-rays and gamma rays are examples of ionizing radiation. Human tissue is transparent to both of these waves, and can penetrate through skin and organs. The waves will do work on the body as they pass through, which can cause damage.

1. Why are X-rays and gamma rays more dangerous than radio waves?

c = λf (3E8 m/s) = (3E17 Hz) (λ) λ = 1E-9 m (3E17 Hz)(15 min)(60 s/min) = 2.7E20 waves

1. X-rays have a frequency of about 3x1017 Hz. What is the wavelength of an X-ray? Show your work. b. A basic X-ray scan takes about 15 minutes to perform. During this time, how many waves will strike the scanned object? Show your work.