Homework for PHY 309L

Welcome to homework assignments for the Elementary Physics (II) course, PHY 309 L. The homeworks on this page are for the section taught by Professor Vadim Kaplunovsky in Spring 2010 (unique #56970). Other sections assign different homeworks.

Many homework problems are taken from the Griffith and Brosing textbook; such problems are listed by chapters and numbers, for example Q4 at the end of chapter 12. Please note the letter in the beginning of each number: Q4, E4, and SP4 are different problems. Also, the numbers are according to the 6^th edition; if you use an older or a newer edition, the number in your book will be different.

In addition to the textbook problems, I will make some problems of my own, or copy problems from other books. All such non-textbook problems will be written down on this page.

Please note that the physical laws and the formulae you use and the way you put them together are more important for your grade than the numbers you calculate. If you understand the physics governing a problem, use correct formulae, and properly put them together, you would get a high partial score even if your arithmetic is faulty. But you would get a low score for a numerical answer without a clear explanation of where it came from, even if the number happens to be correct.

Update 9/9: Starting with homework set 3, I am giving more points to more difficult problems. The pointage will be shown after each problem; if the pointage is not shown, the problem is worth 10 points. For example, in homework set 3, problem SP4 is worth 15 points, problem SP5 is worh 12 points, and all the other problems are worth 10 points each.

Schedule of Homeworks and Exams.

Each homework set should be posted by the "assigned" date in this schedule. If it is not, let me know ASAP.

The textbook chapters in the schedule are tentative. They may change if the class goes faster or slower than I expect.

Note: The above table reflects schedule changes made on 9/28 and 11/1. The original schedule had an extra homework set, and the midterms were on slightly different adtes.

Exams

• First mid-term, September 30; solutions.
• Second mid-term, October 26; solutions.
• Third mid-term, November 23; solutions.
• Final exam, December 11 (2-5 PM), not yet posted.

Homework sets

Set 1

Textbook problems: Q4, Q14, E8, SP1, and Q20 at the end of chapter 12.

No non-textbook problems this time.

Due September 2; solutions.

Set 2

Non-textbook problems:

1. (a) Four electric charges are placed at the corners of square ABCD with 20 cm sides. The charges at corners A and B are positive, q_A=q_B=+0.10 μC, while at the other two corners C and D the charges are negative, q_C=q_D=-0.10 μC. Find the electric field vector (both the magnitude and the direction) at the center of the square.
   (b) Now let's replace the positive charges at corners A and B with equal and opposite negative charges so that all 4 charges are equal, q_A=q_B=q_C=q_D=-0.10 μC. Find the new electric field vector at the center of the square. Hint: Use symmetry of the configuration.
2. In old-style TV tubes and computer monitors, the picture on the screen was produced by electrons beams striking the back of the screen at high speeds. The electrons were emerging from a hot cathode (hence the name cathode ray tube (CRT) for the monitor) with negligible speeds, but then were accelerated to high speeds by big voltages between the cathode and the other electrodes.
   Suppose the cathode has electric potential −2500 volt, while the screen (which acts as the anode) has zero electric potential. With what speed do the electrons strike the screen in this monitor?
   Use energy conservation to answer this problem. For your information, every electron in the Universe has charge q_e=−e=−1.60·10^-19 C and mass m_e=9.11·10^-31 kg.
   Updated 9/4: The cathode has negative electric potential −2500 volt relative to the screen.
3. Consider a capacitor made out of two parallel metal plates of area A=500 cm² separated by an air gap of thickness d=1.00 mm. (a) Suppose the voltage (i.e., potential difference) between the two plates is 1,000 volts. What is the electric fields between the plates?
   (b) What electric charges should the two plates have to create such a field?
   (c) What is the capacitance (charge/voltage ratio) of this capacitor?
   (d) Now let's fill the air gap between the plates with glass having dielectric constant ε=4.5. The new capacitor is charged till the potential difference between the two plates reaches the same 1,000 volts as before. What is now the electric field in the glass between the plates?
   (e) What electric charges should the two plates have to create such field in the glass?
   (f) What is the capacitance of the new capacitor?
4. Car batteries are often rated in ampere-hours (a-h). What physical quantity can be measured in ampere-hours: The current? The voltage? The electric charge? The electric energy? The power? Something else? Also, convert 150 ampere-hours into the standard metric (SI) unit for this quantity.

Textbook problems Q1 and E5 at the end of chapter 13.

Due September 9; solutions.

Set 3

Non-textbook problems:

1. Consider two resistors, R₁=10.0Ω and R₂=15.0Ω. (a) What would be the net resistance of these two resistors connected in series? (b) What would be the net resistance of these two resistors connected in parallel?
2. At room temperature, copper has resistivity ρ=17·10^-9Ω m. Calculate the resistance of a copper wire of diameter 2r=1.0 mm and length L=1.6 km (1 mile).

Texbook problems E8, SP4 (15pt), Q22, E15, SP5 (12pt) at the end of chapter 13.

Update 9/9 at 8 PM: non-existent problem E22 is replaced with SP5. Also, extra points given to problems SP4 and SP5.

Due September 16; solutions.

Set 4

Texbook problems Q8, SP1 (15pt), Q17, SP2 (15pt), Q26, E12 at the end of chapter 14.

No non-textbook problems this time.

Due September 23; solutions.

Set 5

Non-textbook problems:

1. (12pt) A 400-loop coil of area A=12 cm² rotates in a uniform magetic field B=1.5 Tesla with angular velocity ω=377 rad/s (60 rev/s). The axis of rotation is parallel to the coil's loops but perpendicular to the magnetic field. Explain how this coil can be used as an AC generator and calculate the peak EMF induced in it. For your information, Δsin(ωt)/Δt=ω×cos(ωt).
2. (15 pt) The input coil of a transformer has 200 loops while the output coil has 400 loops. The input coil of this transformer is plugged into a 120 Volt AC outlet while the output coil is connected to a 300 Ω load. For simplicity, ignore the internal resistances of the coil or any other losses in the transformer.
   (a) Is this a step-down or a step-up transformer?
   (b) What is the voltage on the output coil of the transformer?
   (c) What is the current through the output coil?
   (d) What is the current through the input coil?
   (e) How much electric power does this transformer deliver to the load and how much power does it get from the electric grid?
   (f) Finally, what would happen if this transformer were plugged into a DC rather than an AC outlet?
3. (15pt) One of the demos I have showed in class had a metal ring jumpint almost to the ceiling because of magnetic forces on eddy currents induced in the ring. Suppose the ring is horizontal (i.e., its axis is vertical) while the magnetic field is directed mostly vertically up but also has a smaller horizontal component away from the ring's axis. The average vertical field through the ring increases with time at the rate ΔB_z/Δt=120 T/s, while the horizontal outward field also increases with time but at a smaller rate. The ring itself has radius r=2.5 cm and electric resistance R=0.40 mΩ (to the current flowing around the ring).
   (a) Calculate the EMF induced in the ring and the eddy current flowing through it.
   (b) Use Lenz rule to find the direction of the eddy current.
   (c) Show that the magnetic force on the eddy current is mostly horizontal but also has a smaller upward component.
   (d) Calculate the net upward force on the ring at the moment when the horizontal component of the magentic field (at the ring's location) reaches B_r=0.15 T.

Texbook problems Q8, Q11, and E4 at the end of chapter 15.

Due October 7; solutions.

Set 6

Textbook problems Q20 and SP2 (15pt) at the end of chapter 15, and problem SP1 (12pt) at the end of chapter 16

Non-textbook problems:

1. (12 pt) The atmosphere of Mars is rather dilute — average surface pressure P=600 Pa, less than 1% of the air pressure on Earth. It constist mostly of carbon dioxide CO₂ (molecular weight 44, adiabatic coefficient γ=1.3). During a winter night, the temperature on Mars drops to 170 Kelvin — about 153 degrees Fahrenheit below zero. According to the universal gas law, the density of CO₂ under such conditions is ρ=18 g/m³ (note units).
   Calculate the speed of sound on Mars.
2. (15 pt) Consider two organ pipes: The first pipe is open at both ends, while the second pipe is open at one end and closed at the other. Both pipes have the same length L=1.5 meter (about 5 feet).
   (a) Find the wavelength of the lowest harmonic for each pipe.
   (b) Find the wavelengths of the next two harmonics for each pipe.
   (c) Find the frequencies of all those harmonics when the speed of sound in the air is u=340 m/s.
3. Two out-of-tune musical instruments try to play the same note — middle C — but the sounds they produce have slightly different frequencies, f₁=261 Hz and f₂=264 Hz.
   (a) Explain why playing these two instruments at the same time produces beats.
   (b) Calculate the beat frequency: how many times does the sound intensity go up and down in one second.

Due October 14; solutions.

Set 7

Textbook problems Q10, SP2 (15 pt), Q20, E10, and E14 at the end of chapter 16.

One non-textbook problem (15 pt):

• Surface of a crystal is covered by a thin layer of oil, just 450 nm (nanometers) thick. Light shines on this surface and some of it is reflected back; For simplicity, assume that both the incoming and the reflected light waves move perpendiculary to the surface.
  (a) Both sides of the oil layer reflect light, but the light waves reflected by different sides travel through different distances. Find the difference between the two distances.
  (b) The oil has refraction coefficient n=1.488, which means the light travels through it at reduced speed c/n (cf. problem SP1 from the previous homework set). Find the wavelengths in the oil of the red, green, and blue light waves with respective frequencies 448, 560, and 672 TeraHertz. (1 THz=1·10¹² Hz.)
  (c) For each of the three colors of light, compare its wavelength to the difference between distances traveled by the two reflected waves, and find if the interference between those two waves is constructive or destructive.
  (d) Suppose the light shining on the oil-covered crystal is white. What is the color of the reflected light?
  Update 10/14 at 7 PM: An oil slick floating on top of water is changed to a similar oil layer on top of a crystal. Consequently, there are no phase reversals when the light is reflected from either side of the oil layer.

Due October 21; solutions.

Set 8

Two textbook problems: Q8 and Q26 at the end of chapter 17.

One non-textbook problem (15 pt):

• A concave mirror has curvature radius R=30 cm.
  (a) If a parallel beam of light (from a laser, or from a very distant lamp) shines on this mirror, would the reflected rays converge or diverge? Where would they cross or appear to cross?
  (b) An object is placed 10 cm in front of the mirror. Where is the image of this object: in front of the mirror or behind it, and at what distance? Is this image real or virtual? Is it up-right or upside-down?
  (c) Another object is placed 20 cm in front of the mirror. Where is the image of the second object: in front of the mirror or behind it, and at what distance? Is this image real or virtual? Is it up-right or upside-down?

Four more textbook problems: E4, Q16, Q17, and E7 at the end of chapter 17.

Due November 2; extended to November 4; solutions.

Set 9

Two textbook problems from the end of chapter 17:  Q29 and E16.

A non-textbook problem (15pt):

1. Consider a two-lens microscope. The objective lens has focal distance 12.0 mm while the ocular (eyepiece) lens has focal distance 25.0 mm. An object — an infusoria fixed to a glass slide — is held at distance 13.0 mm from the objective lens.
   (a) Where is the image of this infusoria in the objective lens?
   (b) What is the magnification of this image?
   (c) Where would you put the ocular lens relative to this image so that its image would be 25 cm in front the observer's eye (which is just behind the ocular)?
   (d) How much further magnification do you get from the ocular?
   (e) The infusoria is 0.2 mm long. How long is its image in the microscope?

Three textbook problems from the end of chapter 18:  Q13, Q17, E4.

Another non-textbook problem (12pt):
Update 11/9: This problem is postponed to the next homework set.

2. Natural copper is a mixture of the two isotopes, about 69% of ⁶³₂₉Cu and 31% of ⁶⁵₂₉Cu.
   (a) Find the numbers of protons, neutrons, and electrons in a single neutral atom of each isotope.
   (b) Find the atomic weight of a natural copper.
   

Due November 11; solutions.

Set 10

Non-textbook problem II from the previous homework set.

Five textbook problems at the end of chapter 19:  SP2 (12pt), Q13, E9, Q16, E11.

Another non-textbook problem (12pt):

• In 1952, the US tested the very first fusion device (Ivy Mike, not weaponized) and blew up the Elugelab island. The explosion energy was about 47·10¹⁵ J — the equivalent of 11 megatons of TNT or 750 Hirosima bombs. 23% of that energy came from deuterium fusion; the rest came from secondary fission in the uranium tamper.
  The deuterium fusion reactions can be summarized as
               3D → α + p + n
  where D is a deuteron (deuterium ²H nucleus) of mass 2.014,102 amu, α is an alpha particle (helium ⁴He nucleus) of mass 4.001,506 amu, p is a free proton of mass 1.007,276 amu, and n is a free neutron of mass 1.008,665 amu.
  (a) When 3 deuterons participate in this reaction, how much mass is lost and converted to energy?
  (b) How much energy do you get from this conversion? For your information, 1 amu=1.6605·10^-27 kg, c=2.9979· 10⁸ m/s.
  (c) How much deuterium (in kilograms) was fused during the Ivy Mike test?

Due November 18; solutions.

Set 11

Textbook problem SP2 (12pt) at the end of chapter 18.

Two non-textbook problems:

1. (15 pt) An electron microscope uses beams of fast electrons instead of light to view very small objects. Typically, the electrons are accelerated by a 100 kilovolt potential difference, made into a tight beam aimed at the object, and then manipulated by sideways electric and magnetic fields that act like lenses to form a magnified image on the screen.
   (a) Find the kinetic energy, the speed, and the momentum of an electron accelerated by a 100 kilovolt potential difference. For simplicity, ignore the relativistic effects and use Newtonian formulae for the kinetic energy and momentum.
   (b) Find the de Broglie wavelength of such electron.
   (c) If an electromagnetic wave had such a wavelength, would it be infrared, visible light, ultraviolet, X-ray, or gamma-ray?
   (d) What would be the frequency of such EM wave?
   (e) Find the energy of one photon of this wave and compare it to the electron's energy.
2. (15pt) Consider 3 jet planes flying at similar airpeeds 570 MPH in a strong wind blowing from West to East at speed 100 MPH.
   (a) The first plane due East. Find its grounsdpeed.
   (b) The second plane flies due West. Find its groundspeed.
   (c) The third plane heads due North. Find the direction of its flight relative to the ground.
   (d) Find the groundspeed of the third plane.
   Note on terminology: The airspeed of a plane is the magnitude of its velocity relative to the moving air, while the groundspeed is the magnitude of its velocity relative to the ground. The heading of the plane is the direction of its velocity relative to the air, while the direction of the plane's velocity relative to the ground is called the flight direction.

Three more textbook problems from the end of chapter 20:  Q8, Q10, SP2 (15pt).

Due December 2; solutions.