University of Maryland, College Park

Fall 2008, Professor: Ted Jacobson

Homework

E1.4 means "Exercise 4 of Chapter 1"

P1.8 means "Problem 8 of Chapter 1"

C1.11 means "Case 11 of Chapter 1" - for these see Cases, at Textbook Companion Website

S5.1 means "Supplementary problem 1 for chapter 5, written out here".

HW13 - due at the beginning of class, Thursday 12/11/08.

E16.8 (beta decay)

E16.20 (X-ray tube energy)

E16.24 (MRI electromagnetic radiation)

E16.28 (magnetic field strength and MRI)

S16.1 An MRI machine could operate with a weaker magnetic field if it could employ more sensitive radio frequency electromagnetic wave detectors. How would the use of more sensitive detectors compensate for the use of a weaker magnetic field? (Use of a weaker field could lower costs, save space and weight, and operate more safely and with patients that have ferromagnetic metal inside them.)

HW12 - due at the beginning of class, Tuesday 12/09/08.

E16.2 (separating Cu-63 and Cu-65)

E16.6 (alpha decay)

E16.10 (size matters) (The question is, what sets the lower limit on the size?)

E16.18 (radioactive fallout)

P16.1 (gallium-67 decay after two days) (The numerical answer is in the book. (a) Show how this number is obtained. (b) How much gallium-67 remains after two weeks?)

S15.1 As mentioned in the textbook, IR laser light with a wavelength of 780 nm in air (effectively vacuum) has a wavelength of 503 nm in the clear plastic coating of a CD, while maintaining the same frequency. This happens because the speed of light is slower in the plastic. [See p. 492, and eqn. (13.2.1).] If future disc reading technology alows the use of laser light with wavelength 500 nm in vacuum, what will be the corresponding wavelength in the plastic?

S15.2 In order to fold a long optical path in binoculars into a small space the light must be reflected several times. This is done, for example, by a "double Porro prism" shown here: http://en.wikipedia.org/wiki/Image:Double-porro-prism.png (taken from http://en.wikipedia.org/wiki/Binoculars). There are no mirrored (metallic reflecting) surfaces --- only glass prisms are used. (a) How are the reflections accomplished without mirrors? (b) Why is it preferable not to use mirrors?

HW11 - due at the beginning of class, Thursday 12/04/08.

E15.24 (beam waist of blue vs. IR light)

S15.1 Write the answer to life the universe and everything as a binary number. (If you don't already know this answer, type "the answer to life the universe and everything" into a Google search.)

S15.3 The encoded surface area of a CD is about 90 square centimeters. Given that the shortest pit is 0.83 microns long, and that the sideways spacing is 1.6 microns (see Fig. 15.2.2), the area needed per bit is (0.83)(1.6) = 1.33 square microns. (a) Calculate how many bits of information can fit on the CD. (b) Using the fact that there are 8 bits in a byte, calculate how many bytes you can store. Your answer should come out to about 850 million, i.e. 850 MB of data. (A standard "700 MB" CD-ROM can hold about 847 MB of data. The "700 MB" referred to in the disc capacity does not include some data needed for error correction. Also, when data storage is discussed, 1 MB really means 2^20 bytes = 1,048,576 bytes, not 1,000,000 bytes. )

HW10 - Note: Multiple assignment: due at the beginning of class, Tuesday 12/02/08, just to be flexible for those with Thanksgiving break plans. However, you are welcome to hand in some or all of this on the previous Tuesday, 11/25/08.

E14.6 (seeing a laser beam)

E14.8 (reflection of light from water surface)

E14.10 (refraction of diamond)

E14.14 (colored rings from pair of glass surfaces)

E14.16 (seeing into water)

E14.20 (yellow paint)

E14.28 (incandescent vs. neon lamp colors)

E14.36 (hydrogen maser)

C14.1 (color of sky)

C14.2 (electronic flash)

C14.4 (paints and colors)

HW9b - due at the beginning of class, Tuesday 11/18/08.

E13.16 (AM vs. FM fadeout)

E13.28 (synchrotron radiation)

C13.4 (cell phones) Note: This "case" has 8 (interesting) parts, so begin early!

HW9a - due at the beginning of class, Tuesday 11/11/08.

E13.10 (sharp wire bends waste power)

E13.13 (waving a charged wand)

E13.14 (spinning magnet) (Hint: Two ways to see this: (i) Use the relation between electric and magnetic fields in an electromagnetic plane wave, p. 428, or (ii) think of the magnet as a current loop, and see how the charges in the loop are accelerated.

E13.22 (oven vs. microwave cooking of a potato) Take the question to be this: how is heat deposited in the potato using the two cooking methods?

S9.1 Maxwell inferred that electric and magnetic field propagate as waves at the same speed as does light, which led him to the discovery that light is in fact an alectromagnetic wave. We can glimpse that connection as follows. (a) Show that the ratio of the electric and magnetic Coulomb constants, k/(mu_0/4pi), has the SI units of squared speed, m^2/s^2. (b) Evaluate the square root of this ratio and show that it is equal to the speed of light, 2.998 E8 m/s.

HW8c - due at the beginning of class, Thursday 11/06/08.

E11.38 (AC current wire in magnet gap)

C11.2 (electromagnetic trash sorter) (Hint for (b): See Check your understanding #4 of section 11.2, p.362.)

C11.12 (electric shavers)

HW8b - due at the beginning of class, Tuesday 11/04/08.

E11.18 (DC toaster)

E11.19 (magnetic strip reader)

E11.24 (transformer in amplifier)

E11.26 (current in transformer coil)

P11.8 (energy of MRI magnetic field)

C11.1 (uninterruptible power supply)

C11.5 (audio speaker)

HW8a - due at the beginning of class, Thursday 10/30/08.

E11.2 (distance dependence of magnetic force between button magnets)

E11.4 (why don't magnet and iron repel?) Expand question: Explain why they attract no matter which pole of the magnet is next to the iron pipe.

E11.6 (hammering or heating a magnet)

E11.8 (net force on a compass in a uniform field)

HW7c - due at the beginning of class, Tuesday 10/28/08.

E10.32 (half a plug)

E10.36 (adding positive charge to a battery's positive terminal)

E10.40 (battery testing)

E10.42 (resistance of bulb wires)

P10.23 (voltage drop in extension cord)

P10.24 (wasted power in extension cord)

S10.3 If lightbulb consumes 60W of power when operating at 120V, (a) how much current flows through the filament, and (b) what is the resistance of the filament?

S10.4 If you double the voltage applied across the ends of a rear window defroster strip, what would happen to the rate at which heat is dissipated into the window?

S10.5 In HW7a, E10.4 asked why two bowling balls normally don't exert elctrostatic forces on each other, despite being full of charges. The answer was that the forces from equal numbers of positive and negative numbers of charges cancel. However, this is not fully correct. In fact, the balls attract each other a little bit due to the van der Waals force, which is electrostatic in origin. Give a brief explanation of how this attractive force arises, despite the equal numbers of positive and negative charges on each ball.

HW7b - due at the beginning of class, Thursday 10/23/08.

E10.14 (car battery voltage)

E10.20 (electric field at battery terminal)

E10.24 (screening electric fields) (Hint: Read pp. 319-20.)

E10.26 (electric field at tree top) (Hint: Read pp. 321-22.)

P10.10 (electric field from force) Consider the stated problem part (a), and give the answer in units of both N/C and V/m. Add (b) If the electric field is constant along a vertical line 1 cm long, what is the voltage drop from one end of the line to the other?

C10.3 (spark lighters)

HW7a - due at the beginning of class, Tuesday 10/21/08.

E10.4 (bowling balls and charges)

P10.2 (electrostatic force on socks)

C10.2 (Van de Graaff generator)

S10.1 A balloon rubbed on your hair will acquire negative charge, and will then stick to a neutral surface like a wall. Explain the origin of the force of attraction between the charged balloon and the neutral wall.

S10.2 An electron and a proton are attracted by both electric and gravitational forces, but the gravitational force is completely unimportant to the structure of an atom. To see why, compute the ratio of these forces. It doesn't matter what separation the electron and proton have, since both forces are inversely proportional to the square of the separation. (You'll need to look up the mass of the electron and proton. Newtons constant G is given on p. 126, the charge on the electron and proton is on p. 306, and the Coulomb constant is on p. 307.)

HW6b - due at the beginning of class, Thursday 10/16/08.

E9.14 (organ pipe filled with helium)

E9.16 (trumpet vs. tuba)

E9.30 (gong overtones)

E9.32 (string bass body)

E9.42 (pulsing pair of propellers)

S9.2 The speed of sound in air is determined by the restoring force of pressure, and the inertia of the air.

a. Use dimensional analysis to discover the combination of pressure p and mass density r to which the speed of sound is proportional. (Hint: Begin by writing down the SI units of pressure and of mass density, then figure out how you can combine these to get a speed.)

b. The dimensional analysis gives only a proportionality, it doesn't tell you the numerical coefficient. Find what the speed would be if this coefficient were one, and compare it to the speed of sound in air at standard temperature and pressure. (You can find the atmospheric pressure and mass density of air at standard temperature in Section 5.1, and the speed of sound in air in Section 9.2.)

HW6a - due at the beginning of class, Tuesday 10/14/08.

S9.1 The period of a pendulum is 2pi Sqrt[L/g]. If g is larger, then the period is shorter, which is easy to understand since larger g means stronger gravity, so a stronger restoring force. But why is the period longer if L is larger? It's not that the pendulum "has to go farther", since in fact the period is (approximately) independent of the amplitude of the swing. Explain using physics why a longer L produces a longer period, other things being equal. (Note: This will probably take some cogitation.)

S9.2 The speed of waves on the surface of deep water is determined by the restoring force of gravity, and the inertia of the water.

a. Use dimensional analysis to find out how the wave speed depends on the wavelength L and the gravitational acceleration g. (In class Thursday 10/09 I showed how one can use dimensional analysis to find how the period of a pendulum depends on the length of the pendulum and g. See the notes link at the course web page. The analysis for the water waves is similar.)

b. If you drop a stone in a lake, an expanding circle of waves is created. Based on your answer to (a), do you expect the longer wavelength waves to be leading the circle on the outside, or following up behind?

c. The dimensional analysis gives only a proportionality, it doesn't tell you the numerical coefficient. For the water wave speed this coefficient turns out to be 1/Sqrt[2pi]. Use this and your result from a. to calculate the speed of a wave with a wavelength of one meter. Does this speed seem to match with your experience?

Chapter 9

E9.9 (pitch of guitar string) Note that this is an odd-numbered problem, so the "answer" is in the back of the book. For this assignment explain, from first principles, WHY this is the answer, for the case of mass, tension, and length.

HW5 - due at the beginning of class, Thursday 10/2/08.

Chapter 8

E8.6 (car knocking on a hot day)

E8.8 (airplane air conditioning)

P8.4 (thermal energy) (Let the problem as stated be part (b), and add part (a) Why does the answer not depend on the mass of the ball? Note also you'll want to use Table 7.1.2.)

P8.6 (refrigerator work) Modify the problem:

a. By how much does the entropy of the food decrease?

b. By how much does the entropy of the room increase?

c. How much heat is added to the room?

d. The answer to c is greater than 100 J, since 300K is greater than 260K. The source of the extra heat must be the work done by the freezer. How much work is that?

P8.8 (heat pump work) Modify the problem:

a. How much does the entropy of the room increase?

b. How much does the entropy of the outdoor air decrease?

c. How much heat is extracted from the outdoor air?

d. The answer to c is less than 1000 J, since 260K is less than 300 K. The source of the extra

heat must be the work done by the heat pump. How much work is that?

P8.10 (airplane engine work) Modify the problem:

Let Q_engine be the heat that that leaves the engine, and Q_air be the heat that enters the air,

and let W be the work done by the engine.

a. Express W in terms of Q_engine and Q_air using the first law of thermodynamics.

b. Express Q_air in terms of Q_engine using the fact that the engine is ideal, and the

temperatures of the burned gases and the air.

c. Find the fraction W/Q_engine.

C8.2 (refrigerator)

C8.5 (sea breezes)

C8.8 (chinook winds)

Note on P8.6,8,10: These problems can be solved using the formulas in the book that relate

the heat transfer, work, and temperatures for ideal heat pumps and heat engines. However it

is more informative to use the concept of entropy and the second law of thermodynamics.

I have modified the problems to this end. As explained by Prof. Einstein in class, when heat

Q goes into (or out of) a system at temperature T, the entropy increases (or decreases) by Q/T.

Use this and the fact that the total entropy does not increase (or decrease) in an "ideally efficient"

heat pump or engine. (Such a device is reversible.)

HW4 - - due at the beginning of class, Thursday 9/25/08.

Chapter 5

P5.5 (fridge pressure change) (Hints: (i) Don't forget to use the absolute temperature scale. (ii) First find the ratio of the cold pressure to the room temperature pressure. (iii) Use the result of (ii) to figure the cold pressure given the room temperature pressure, and from this figure the pressure change.)

P5.7 (water displaced by boat) (Note: Give both the mass and the volume of the displaced water.)

Chapter 7

E7.12 (how space shuttle dumps heat)

E7.18 (blow dryer on a humid day) (Note: It seems to me two effects are involved, relating both to the density of the air and the temperature of the heated water in your hair...)

E7.20 (wine bottle in ice water)

E7.22 (covered pot boils faster)

E7.24 (steamed vegetables)

E7.30 (icy sidewalk)

C7.3 (electric oven)

C7.8 (duck warmth)

C7.9 (tight-fitting metal parts) (See page 229 for a discussion of thermal expansion, and the demo I showed 9/18, I1-11 THERMAL EXPANSION - BALL AND HOLE)

HW3a - - due at the beginning of class, Thursday 9/18/08.

E5.4 (grocery freezer displays)

E5.15 (hot food container in a fridge)

E5.16 (lowest thermometer readings)

C5.2 (bass air bladder) Assume the fresh and saltwater bass have the same mass.

C5.12 (floating mountains) (Note: The mantle of the earth is "molten" in the sense that over geologic times it flows as a liquid.)

S5.1 (melting icebergs) Ice floats on water because when water freezes and becomes ice, the density drops by about 10%. When a floating iceberg melts, the sea level does not go up (or down), but rather stays exactly the same. Explain clearly why this is so. (By contrast, if ice intially on land slides into the ocean and melts, then of course the sea level rises.)

HW2a - - due at the beginning of class, Tuesday 9/16/08.

E2.16 (bottle opener)

E2.22 (horse and cart)

E2.26 (force on bicycle) This is could be phrased more precisely. Let's make it: "What is exerting the forward force that accelerates the system consisting of you and the bicycle?"

E2.28 (friction on sled)

P2.6 (nutcracker)

HW1b - due at the beginning of class, Thursday 9/11/08

E1.34 (work when sawing)

P1.18 (hydroelectric power) Consider the book's problem to be part (a). Add two parts: (b) If a human can do work at at rate of 1000 J/s, how long would it take a human to deliver the same total energy as the ton of water falling off the dam? (c) How many pieces of cherry pie (see page 30) would you have to consume to obtain the energy required to do this much work?

P1.22 (work when sanding)

C1.5 (takeoff and landing on aircraft carrier)

C1.12 (cable cars in San Francisco)

HW1a - due at the beginning of class, Tuesday 9/9/08

E1.4 (toothbrush drying)

E1.8 (carousel velocity) Let's make this problem four parts: (a) How is your velocity vector is changing? (b) What is the direction of your acceleration vector at any moment? (c) What agent is exerting the force on your body making your velocity change? (d) What is the direction of that force vector?

E1.10 (coffee grinder)

E1.14 (falling ball)

E1.22 (force on Metro train cars)

E1.38 (roller skating uphill) Let's make this problem two parts: (a) What agent exerts the horizontal force that decreases your horizontal velocity? (b) What agent exerts the vertical force that initially increases your upward, vertical velocity as you start rollling up the hill?

P1.8 (sprinter acceleration)

P1.10 (mass and weight) (Give your answer in Newtons.)

C1.11 (high jumper and long jumper)

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