Workshop #1: 28-30 January 2004Physics 100, Spring 2004

Prof. McFarlandDiscussions:

1. Take your text book and a half-sheet of notebook paper. Hold them in separate hands at an equalheight and drop them. Compare the result to what happens if you place the paper on top of the bookand drop both at once. Working in small groups, form a hypothesis to explain the result and suggestanother experiment to validate or refine this hypothesis. Discuss in the whole workshop. Can youthink of more experiments as a group to refine your hypotheses?

Problems I:1. A moving bus carrying passengers comes to a sudden stop. The standing passengers will lurch

forward. Explain why this happens. Be sure to use key words from our discussion of Aristotle’s andGalileo’s theories of motion.

2. It takes light from the sun 8 minutes to travel to the earth. Light travels at a speed of 300,000km/second. How far is the earth from the sun?

Measurements (break into groups, reconvene to discuss when finished):1. In class, you learned how to measure speed, (change of position)/(change of time). and how to define

acceleration. (change of speed)/(change of time). Divide into groups with the goal of measuring thespeed of one of your group sprinting down the hall a short distance. Perform measurements basedon the above definitions of speed and acceleration. Document your measurement technique. Whatcan you say about the speed of the running from your measurements? What can you say aboutacceleration?

2. You can use simple geometry to show that for the similar triangles ABC and ADE, it is true thatDE=BC*(AE/AC). (Here “DE”, for example, is the length of the line segment DE.) Use this fact tomeasure the height of a building on the quad. Document your measurement.

B

C

D

EA

Problems II:1. An object falling near the surface of Mars starts from rest and falls with constant acceleration ac-

cording to Galileo’s Law of Falling. After 1 second, the falling object has fallen 4 m and has avelocity of 8 m/sec.

(a) What is its velocity after 2 seconds? 3 seconds?(b) How would you calculate the average velocity over the first second? What is the average

velocity over the first two seconds? First three seconds? (Making a graph of speed vs. timemay help.)

(c) How far has the object fallen after two seconds? After three seconds?

Workshop #2: 4-6 February 2004Physics 100, Spring 2004

Prof. McFarland

Discussion I:

1. Take a spring scale with a weight on the end and place it so that the weight is just above but nottouching the ground.

(a) Slowly lift the weight at a nearly constant speed. Observe the scale.(b) Lift the weight quickly reaching a constant speed. Observe the scale.(c) Try to constantly accelerate the weight upward. Observe the scale.

Discuss the observations. What do you conclude that a spring scale actually measures? Can youexplain this using the Galilean and Newtonian language introduced in lecture?

Measurements I:Break into groups, each with its own spring scale. Load the scale up with enough key rings or otherweights so that it reads between 150 and 250g on the scale.

1. Jump off a low height such as a table or chair and observe the reading of the spring scale

(a) before jumping(b) during your fall(c) as you hit the ground(d) sometime after you hit the ground

Make a graph of the reading vs. time. Make sure that you repeat this experiment several times withdifferent observers and that your observations agree. Explain the features of the graph.

2. Spin rapidly holding the weighted spring scale and observe the reading of the scale.

(a) How does the reading vary with your rate of rotation?(b) How does it vary with the distance between your “center” and the scale (e.g., hold it close to

you, and hold it at arms length)

What conclusions can you draw about circular motion and acceleration?

Problems I:

1. A Mack truck weighing 20000 kg is stopped in intersection facing east. A Mini weighing 1000 kgtraveling 20 meters/sec and heading south collides with the truck. When the two collide, they sticktogether.

(a) Determine the total momentum of each vehicle before the collision.(b) Determine the total momentum of the two vehicle together after the collision.(c) Determine the velocity of the two vehicles after the collision.(d) How would the last answer differ if the Mack truck had been moving at 5 meters/sec before

the collision?

Discussion II:

1. What is the role of a “crumple zone” in automobile crash safety?

Measurements II:Break into groups, each with its own spring scale and skateboard.

1. Attach the skateboard to the scale. Pull the skateboard in such a way that you keep the spring scalereading a constant non-zero value. Describe the motion.

2. Place some books on the skateboard and repeat. What is different?

3. Place a member of your group on the skateboard and repeat. (Don’t break the scale!) What isdifferent?

Discuss and explain in terms of Newtonian concepts discussed in class.

Workshop #3: 11-13 February 2004Physics 100, Spring 2004

Prof. McFarland

Measurement I:

1. Your spring scale can measure force in Newtons (kilogram*meters/sec2). Place a key ring or othersmall object on the end of your spring scale. Work individually.

(a) Compare the spring scale reading in Newtons and in grams on the reverse. Show that theconversion is correct if the acceleration due to gravity on the earth’s surface is 9.8 meters/sec2.

(b) Slowly lift the spring scale from the floor straight up so that it is eye level with you. Calculatehow much work you just did.

(c) How long could you run a 100 Watt light bulb with that amount of energy?

2. Now work in a small group to answer the following questions.

(a) Where did the energy go when you did the work to lift the key chain? Where did it come from?(b) Drop the key chain from eye level. Using conservation of energy and the transformation from

gravitational potential (or stored) energy to kinetic energy, how fast should the key chain begoing when it hits the ground.

(c) Convince yourself with a speed measurement that this answer is approximately correct. (Theexact technique for doing this was in Problem II.1 of Workshop #1, but you don’t need to do itthat carefully.)

Problems I:

1. The earth orbits the sun in (roughly) a circle with a radius of 160 × 109 meters. The radius of theearth is (roughly) 6.4 × 106 meters. The mass of the earth is (roughly) 6 × 1024 kilograms. Theacceleration of the earth towards the sun is roughly 0.0064 meters/second2.

(a) Calculate the total kinetic energy of the earth in its orbit.(b) Use Newton’s Third Law to calculate the force exerted on the sun by the earth.(c) How much work would it take to pull the earth one earth radius further away from the sun?

Compare your answer to the kinetic energy of the earth. (Don’t worry about the fact thatNewton’s Law of gravity says that the force of gravity will change (slightly) as you move theearth away from the sun.)

Discussion I: Conserved or not conserved.Sometimes conservation laws are helpful for a given problem, and other times they are apparently

violated, puzzlingly enough. In the cases where there are apparent violations, there actually are not anyviolations of course, but for some reason or other, the conservation laws aren’t useful for the problem athand.

For each of these situations, consider which conservation laws are apparently valid and which areapparently violated. If they are apparently violated, what do you need to do to show that they are actuallyconserved.

1. Two identical cars collide at the same speed but opposite directions. They lock bumpers and areboth at rest after the collision.

2. A superball bounces off of the floor

3. A bag full of ball bearings falls onto the floor

4. A bowling bowl strikes a single bowling pin head on. After the collision, the bowling ball continuesforward (a little bit more slowly), and the bowling pin moves forward at higher speed than the ball.

Measurements II:Break into groups; each group needs a stop watch and a tape measure.

1. Have one member of your group race up several flights of stairs as fast as possible. Do all themeasurements necessary to calculate the power expended by work against gravity to go up the stairs.

Discussion II:In your group from the previous exercise, answer the following question.

1. If you did the above experiment but ran on a flat surface, would the runner be expending energy? Ifthat energy doesn’t go into working against gravity, where does it go? What does that tell you aboutthe limitations of your previous measurement?

2. Compare the energy required to run horizontally with the energy expended in going up the samedistance on stairs. Justify your answer.

Meet together as a big group to discuss your answers and to compare results from the stair power.

Workshop #4: 18-20 February 2004Physics 100, Spring 2004

Prof. McFarland

Measurement I: Electric and magnetic charges (work in groups of two or three at most)Each group should work with a pair of bar magnets and several balloons.In lecture, it was asserted that there are no free magnetic charges in a magnet that can move the wayelectric charges can. You may remember from your youth that you can produce excesses of electric charge(negative charge, in fact) on an inflated balloon by rubbing it against your hair. Perform the followingexercises.

1. Do an experiment or make an observation to demonstrate that your hair also acquires a static electriccharge when you rub a balloon against your hair.

2. You can stick the balloon to non-conducting surfaces like painted walls. You know that positiveand negative charges must be involved to make this attractive force. If the negative charge is on theballoon, where is the positive charge? Draw a diagram. What happens after you remove the balloon?Test your ideas with experiments.

3. Do an experiment to observe the interaction between two charged balloons. What do you see?

4. With your permanent magnets, stick them to a ferromagnetic surface. Thinking of North and Southpoles attracting each other, where is the north or south pole on the surface? Draw a diagram? Whathappens when you remove the magnet?

5. Test the interactions between the magnets? How is it different than what you saw with the balloons?

Discussion I: Are the observations above sufficient to convince yourself that there are no magnetic freecharges present in the permanent magnets? Are there any loopholes? What other experiments could youimagine?

Problem I: The force between two electric charges has a mathematic form just like Newton’s law ofgravity. Putting together what we discussed in class, the gravitational force between two masses can bewritten as

Fgravity = GNM1M2

r2

where GN is a constant, 6.7 × 10−11 Nm2/kg2, r is the distance between the two masses, and M1 and M2are the masses. The force between two electric charges (“the Coulomb force”) is

Felectric = kQ1Q2

r2

where Q1 and Q2 are the electric charges and k is a constant, 9×109 Nm2/(Coulomb)2, where the Coulomb(C) is the unit of electric charge.

A proton has a mass of 1.67 × 10−27 kg and a charge of 1.60 × 10−19 C. Compare the electric andgravitational force between two protons.

You have lots of protons in your body and so does the earth, but of course that positive charge isbalanced by negative charge in electrons. What does this answer tell you about the excess or deficit ofelectrons in your body or the earth compared to the total number.

Measurement II: Wavelength, wave speed and frequencyWork in groups. Stretch a slinky about 25 feet (5 paces) to make the following measurements.PLEASE be careful not to stretch the slinky past its elastic limit so that it won’t recompress...

1. Send a transverse (horizontal is easiest since the slinky will probably be touching the floor) travelingwave down the slinky and measure its speed. (The wave will reflect at the far end and return withthe same speed which may help your measurement.) Measure with several different amplitudes andrepeat several times to ensure your measurement is accurate.

2. Now set up standing transverse waves. (Easiest if one person drives the slinky.) Depending on thefrequency you will get some number of “nodes” (places where the slinky doesn’t move). For a givennumber of nodes (I would start with two or three), measure the frequency of the oscillations and thewavelength of the oscillations.

3. Repeat the previous experiment with at least two different node numbers

4. Check that the relationship between wave speed, frequency and wavelength that we learned in classholds for each measurement.

Reconvene in a big group to compare results

Problem II: FM Radio Stations broadcast at a frequency of about 100 MHz. (A Megahertz (MHz) is onemillion cycles per second.) The wave speed of FM Radio, as we will see later, is 3 × 108 meters/second.What is the wavelength of FM radio?

Measurement III: Work in groups to measure the speed of sound outside by two methods. First, haveone member of your group go a long distance away (the length of the quad for example) and compare thearrival of the sound from a clap with the visible evidence of a clap. Second, attempt to time an echo of aclap against one of the buildings on the quad. What do you conclude about direct measurements of wavespeed as compared to the method of the previous experiment?

Workshop #5: 25-27 February 2004Physics 100, Spring 2004

Prof. McFarland

Apparently, the mechanics of this attempt at a measurement totally didn’t work. Chalk didn’t markon the floor. Problems with marking string. Only looking at peaks, etc. Need a better way to do thismeasurement.

Measurement I: In class, we showed how to determine which distance and wavelength combina-tions would result in two sources in a plane giving two destructive interference minima separated by thedistance of the source. Now we’ll see the full interference pattern and how it varies with the wavelengthof the light and the separation distance.

Start with the following parameters: wavelength of 10 cm (4 inches), source separation of 20 cm(8 inches). Using the provided string, marker and chalk, your assignment is to mark (in chalk) in a 2 meterby 4 meter (with the sources part of one 2 meter side) the interference minima with a “0” and maxima withan “x”. At each distance from the sources there are minima and maxima somewhere, so only mark themevery 10 or 20 cm and join the paths between the related minima and maxima by lines, but fill in morepoints close to the sources.

1. Develop a method and check with your workshop leader before proceeding. Use the marker to markonly the string, and use the chalk only to mark the floor.

2. Make a map of the maxima and minima with the initial parameters given above

3. In class we assumed that the distance from the sources was much bigger than the separation ofthe two sources. Doing this we got a linear relationship between distance from the sources andseparation of minima. Can you now see why we had to make this assumption? Explain.

4. In a different color of chalk, make the same map for the case where you double the wavelength.(Hint: you should see a pattern that allows you to relate your previous map to this one.)

5. Pick one of the following three changes and remake your map. (Check with your workshop leaderbefore proceeding so that someone in the workshop does each.)

(a) Halve the spacing between the sources(b) Double the spacing between the sources

6. Generalize from your result to develop a hypothesis about the effect of changing the spacing on theinterference pattern

Discuss and compare your results as a group.

Problem I: Several problems related to the speed of light.

1. TV signals are beamed from the source to a local TV station by satellite. These satellites are in ahigh orbit, typically with a radius of 30000 km (the radius of the earth is about 6000 km). Assumingfor simplicity that the signals just travel straight up and down, how long a delay does this introducein “live” TV?

2. You call your good friend in Perth, Australia which is approximately directly opposite New York onthe earth.

(a) Estimate how long a delay you might expect from phone signals traveling the speed of lightfrom you to your friend and back.

(b) Is this the delay you often hear in international communications?(c) Estimate how long it would take sound (speed 300 m/sec) to travel this same distance.

Discussion I: Galilean Relativity of Light

1. Galileo is in a rocket ship and is completing his morning grooming. He is facing a mirror in thedirection of motion of the ship. Suddenly he says, “Pezzo di merda! I keep telling them not to goover the speed of light when I’m shaving!” Discuss this Galilean dilemma.

Measurement II: You are about to do a light clock experiment. Work in a room where you can mark onthe walls with chalk in groups of two or three.

In this experiment a person on a Segway scooter traveling 0.3 m/sec is being watched by an ob-server who is stationary. However, the speed of light is 0.5 m/sec in this experiment!

1. In the frame of the passenger, mark second by second the location of a light pulse emitted at timezero from the passenger’s foot travels up to the height of his or her head, and reflects back down tobe absorbed at the foot.

2. From the point of view of the observer if Galilean relativity were correct, what would the speed ofthis light be?

3. Now redo the experiment from the point of view of the observer, remembering that Einstein says allobservers measure the same speed for light.

4. Compare the amount of time that each observer thinks the light takes on its path.

Reconvene in a big group to compare results. Measuring how long light takes to travel this path is one wayto define the length of a clock “tick”. We have (or will soon) derive a formula for time dilation in classwhich says t′ = t√

1−v2/c2where v is the velocity of the moving observer. Does this formula match your

observations of the “light clock” here?

Discussion II: Points for discussion as a group

1. If you repeated this experiment, but with the light clock in the possession of the of the observer noton the Segway, what would be the outcome.

2. How can you use time dilation to make two twins age differently? Does this really work?

Problem II: Cosmic ray muons are produced in the upper atmosphere at a high of about 10 km from thesurface of the earth. The muon is a particle with a lifetime of 2 × 10−6 seconds. These muons are very

energetic and travel near the speed of light. Notice that the muon travels only a small fraction of 10 km inits mean lifetime.

If we want the muons to make it to the surface (they do at a rate of about 1 per second through yourhand) what is the minimum velocity required to make their (lifetime)*(speed) at least 10 km? You maymake the approximation that the muon speed is very close to the speed of light (except when you calculatethe time dilation effect!).

Workshop #6: 10-12 March 2004Physics 100, Spring 2004

Prof. McFarland

Problems I: Using γ to calculate time dilation and length contraction

1. Casey is driving his train nearly at the speed of light. Ishmael is watching Casey approach andis standing between two telephone poles driven into the ground parallel to the tracks. How doesIshmael’s measurement of the distance between the two poles compare to Casey’s? Longer, shorteror the same? Can you explain this in terms of time dilation of Casey’s clock from Ishmael’s pointof view?

2. Terra and Astra, our twins, were placed into identical cradles before their journeys. Each cradlewas 1 meter long and 0.5 meters high. The cradle is placed in Astra’s spaceship so that its lengthis oriented along the direction of motion, and Terra’s cradle is equipped with a special device so itslength is always pointing towards Astra’s ship.Astra is then accelerated to 90% of the speed of light.

(a) Find the length and height of Terra’s cradle as viewed by Astra(b) Find the length and height of Astra’s cradle as viewed by Terra(c) Is it possible, based on these measurements, that one twin will conclude that the other doesn’t

fit in the cradle anymore? Explain.

Measurement I: The Garage Paradox RevealedWork in groups of two or three to explore the garage paradox! You will need to step through a timesequence, like you did with the light clock, to figure out why Dudley and Percepta can disagree aboutwhether or not the car fits in the garage.

Dudley

Door Closer Door Closer

Door Closer Door CloserLL

Percepta

v=0.9c

v=0.9c3L

In this setup, the garage doors close in response to a well-timed signal from flash lamps at thecenter of the garage. When light reaches the “door closer” the door is considered “closed”. We say thatthe car “fits” in the garage if there can be a time when the car is in the garage and both doors are “closed”.

1. From Dudley’s viewpoint, find the length between the flash lamp and a door closer (L according toPercepta). From Dudley’s viewpoint, should the Humvee fit?

2. From Percepta’s viewpoint, find the length of Dudley’s gas guzzler. You should find a result thatsays the Humvee will fit!

3. As Dudley is driving through, Percepta arranges for the lamp to flash to that the doors close whilethe Humvee is inside, proving from Percepta’s point of view that it fits. We said that in this sameexperiment, Dudley would agree that the front door of the garage doesn’t hit his car, but he woulddisagree that this door closed before his Humvee went out the back of the garage. From Dudley’spoint of view, how long should it take from the lamp flash for the back door to close? How muchlonger (approximately) does it take after this for the front door to close?

4. As with the light clock, use time steps to work out the position of the doors with time with respect tothe Humvee and when the doors close to see the experiment work from Dudley’s viewpoint. Flashthe lamp when the front of the Humvee passes the lamp.

Reconvene as a group to discuss your resultsProblem II: E = mc2 estimate

1. The Ginna nuclear power plant down the road has a thermal output of 20 Billion Watts. To a goodapproximation, this energy comes from converting mass to energy in nuclear fission. How muchmass does this plant convert to energy in a day?

Discussion I: The age of the universe is approximately 13 billion years. What would you expect to seein a telescope if you could see light from a distance of 13 billion light-years away. (One light year is thedistance that light travels in a year.)Measurement II: Work in groups of two or three. Inflate a balloon to the point where it is roughlyspherical.

1. Mark the north pole. Now draw the equator. Mark two more points on the equator that are 1/4 ofthe circumference apart from each other.

2. Draw “straight lines” between each pair of marked points by determining the shortest distance onthe sphere between the two. You can do this by stretching a string on the surface of the spherebetween the two points. This is a triangle.

3. Measure the angle of all the angles of the triangle. What is the sum? What is the sum on a triangleon a piece of paper?

4. Look at your triangle from above its center and try to draw what you see on a sheet of paper. Whathappens to your straight lines?

Reconvene in a big group to compare results and discuss what this means. What sort of a path would lighttake on the surface of this sphere? What would it look like if we thought the sphere was “flat”?

Workshop #7: 31 March - 2 April 2004Physics 100, Spring 2004

Prof. McFarland

Problems I: The deBroglie Wavelength

1. Pick a macroscopic object moving with a realistic speed. Calculate the deBroglie Wavelength.h = 6.6 × 10−34 Joule-sec. (Remember that a Joule is a kg-m2/sec2 and verify that the units workout correctly in your calculation!)

2. Now do the same for a hydrogen atom. Remember that a mole of hydrogen has a mass of a gramand Avagadro’s Number is 6.023 × 1023 atoms/mole. At what speed would the wavelength of ahydrogen atom be comparable to the wavelength of visible light (∼ 5 × 10−7 meters)?

Measurement I: Using Polarizing films to simulate quantum mechanical measurementsWork in groups of three or four to try the following exercises with three polarizing films. Your workshopleader will briefly review what you learned in class about polarizing films and light.

1. Put two films on top of each other and rotate them.

• If you rotate both films together, does the light transmission change?• Describe what happens as you rotate one film with respect to another.• Explain what you are seeing in each case by drawing “polarization vectors” corresponding to

the polarization of light after the light passes through each polaroid.

2. Place two films on top of each other so that no light can pass through the pair. Now add a third filmto the stack either before or after the original two (keeping their angles fixed). What do you see?Explain by drawing diagrams of polarization vectors like the ones above.

3. Now place the third film in between the original two (keeping the angles of the original two fixed).What do you see? Explain by drawing polarization vectors.

4. Polarizing puzzle I. Can you orient three films so that in one order they transmit light but in anotherorder (without rotating them) they do not? Explain by drawing polarization vectors.

5. Polarizing puzzle II. Place three polaroids side by side in a particular order. Arrange them in anorientation so that between both adjacent pairs, if they are stacked on top of each other, at leastsome light is transmitted. Now if you stack all three up in order, preserving their orientation, mustlight be transmitted? Explain with polarization vector diagrams.

Discussion I: Interpretations of Quantum Mechanics

1. “If a tree falls in a forest, does it make a sound?” Discuss the Zen of Quantum Mechanics. Can youtie this concept into examples from class?

Problem II: Heisenberg Uncertainty principle

1. Return back to your calculations in Problem I. For your macroscopic system and a hydrogen atom,imagine that you have a speed uncertainty of 1 meter per second in your measurement. What thenis your uncertainty in a position measurement?

2. For each of your two systems, imagine you have a position measurement uncertainty of one de-Broglie wavelength. What is your speed measurement uncertainty then?

Can you see the connection between deBroglie wavelength and the uncertainty principle of Heisenberg?

Measurement II: Quantum DiceIn quantum mechanics, we may not always be able to predict the outcome of a measurement, but onaverage we can predict it and get it right. Try some dice games in workshops in groups of two.

1. Throw one die a large number of times, and record the values. What is the average value youobserve? Calculate what the average value you expect is. Is this a possible value

2. Throw two dice. When die number 1 comes up a one or a 2, plot the value of the other die. What isthe result? Now repeat the game, but this time throw only one die, and use the value on the bottomface of the die as the second measurement. Does this change your experimental result? How?

3. Here’s another game to play. Throw two dice and record their sum, except we are going to introducedifferent rules to correlate the results. Play the game many times which each rule and record thesum of the two dice for the rolls that are “kept”.

Rule 1: Discard the roll unless one of your two die is odd and one is even.Rule 2: Same as rule 1, except that you one light colored die and one dark colored die. Discard the

roll unless the light colored one is odd and the dark one is even. Does it change the result fromrule 1?

Rule 3: Put on your hump... one of you gets to play Igor. Before the roll of the two main (differentcolored dice) Igor rolls a “secret” die. If it the secret die is odd, then the light-colored die mustbe odd or the roll is discard. If the secret die is even, than the dark colored die must be odd orthe roll is discarded. Does this game give different results from rule 1? Does it matter if Igorshows you the secret die?

Reconvene to discuss as a group. Can you see an analogy between the spin of an atom in the Stern-Gerlachexperiment and game 1? In game 2, you are exploring uncorrelated quantum measurements vs. correlatedmeasurements. Can you see a connection between game 3 and the concept problem involving Igor the labassistant who won’t tell you the answers?

Workshop #8: 7 April - 9 April 2004Physics 100, Spring 2004

Prof. McFarland

Problems I: Atomic Spectra

Answer the following questions about the energy level diagram shown for hydrogen above. Energy levelsare given in electron volts (eV). 1 eV is 1.6 × 10−19 Joules, a very small number. Remember that h =6.6 × 10−34 Joule-seconds.

1. Imagine that transition #5 takes place because a photon is absorbed by an electron, thus giving itmore energy. What frequency must that electron be? Where is that on the spectrum?

2. How does the frequency of the photon absorbed in transition #1 differ from that emitted in transition#2?

3. Which transitions shown cannot be achieved by absorption of a photon by an electron in Hydrogen?Explain.

Discussions I: Forces of Nature1. Which is stronger: the strong force holding the nucleus of a Helium atom together or the repulsive

electric force between the two protons in a Helium nucleus (10−15 m apart)? How do you know?

2. For two hydrogen atoms in a molecule separated by 10−10 m is the strong force or the electric forcebetween the two protons greater? How do you know?

3. Imagine that all of the electrons were removed from the earth. Which would be stronger; the electri-cal force pushing the protons in the earth apart or the gravitational force binding them together. Howdo you know? What does this tell you about the behavior of very ionized (atoms lacking electronsare said to be “ionized”) matter?

Problem II: If Plancks’ constant (h) were big. . .If Planck’s constant were 1 J/Hz instead of 6.6 × 10−34 J/Hz,

1. What would your deBroglie wavelength be if you were walking? Express your answer in meters.

2. If your position were known to an uncertainty of 1 mm, how uncertain would a measurement of yourspeed be by Heisenberg’s uncertainty principle?

3. Invent an amusing or bizarre physical situation that could arise if Planck’s constant had this largevalue. Be creative! Your workshop leaders will have a prize for the best ideas!

Measurement II: Another Dice Game: Radioactive DecayTry a simple model for radioactive decay in groups of two.

1. Start with ten dice. Throw the dice, and remove each die that comes up a 1, 2 or 3. Throw theremaining dice again, as many turns as it takes to get rid of all the dice. Play this game several timesrecording the number of dice at each step. On average, how many turns does it take for you to getrid of half of your dice? On average, how many turns to get rid of all the dice?

2. Start with ten dice, but this time only remove a die when it comes up a 1. This time play only onceso it’s not so tedious... How many turns does it take you to get rid of half the dice? How many turnsto get rid of all the dice?

3. Repeat the ten dice game again, but this time only keep a die in play if it comes up 6. Play severaltimes. How many turns on average does it take you to get rid of all your dice?

Reconvene to discuss as a group. What can you say about the relationship between the “decay” outcomeof a single throw and the outcome of the big population of dice based on your measurements.

Workshop #9: 14 April - 16 April 2004Physics 100, Spring 2004

Prof. McFarland

Problems I: Half-Life and Radioactive Decay Problems

1. Use a periodic table (back cover of Hobson) to find the daughter nucleus from each of the followingradioactive decays:

• 3H beta decay• 222Rn alpha decay• 238U beta decay

Remember that beta decay is emission of an electron when a neutron turns into a proton, and thatalpha decay is emission of an alpha particle which is made of two neutrons and two protons.

2. The half-life of 222Rn (Radon) is 4 days. If you go into a mine and inhale 200 atoms of 222Rn, howmany atoms of Radon would you expect to still be present in your lungs 12 days later?

3. The half-life of 238U is 4.5 × 109 years. One gram of 238U contains 2.5 × 1021 atoms. How manydecays do you expect in one second? (Use scientific notation and your calculator.)

Discussion I: Scientists and Moral ResponsibilitiesScientists working on the Manhattan project faced a number of moral and ethical dilemmas concerningtheir choice to work on the development of the fission bomb.

1. Brainstorm a list of these dilemmas

2. Can you come of with arguments to support each side of these dilemmas?

3. What would each of you have done?

Problem II: Energy and fission

1. When an atom of 235U undergoes nuclear fission, about 1% of its mass is lost. In a Uranium bomb,like the one dropped by the U.S. on Hiroshima, assume that 10 kg of Uranium undergoes fission.How much energy is released? Express this answer in the equivalent of tons of TNT, where one tonof TNT releases 4.2 × 109 J when it explodes.

2. A small hydrogen (fission+fusion) bomb in the U.S. nuclear arsenal would release 10 Megatons (107tons of TNT equivalent) of energy if exploded. Estimate the total mass in buildings in the Rochesterarea, and calculate how high off the ground 10 Megatons of energy (conversion factor given above)could lift all the buildings in Rochester.

Measurement I: Another Dice Game: Chain ReactionsChain reactions are important in the self-sustaining nature of fission devices. The purpose of this exerciseis to explore how concentration of fissile material (material that can undergo fission) affects the ability tocreate a self-sustaining or runaway reaction. This requires a lot of dice, so work in a large group.

1. Roll all the dice on a table and organize them (randomly, without looking at the numbers!) into a“road” of dice in a rectangular grid, four dice wide and as long as you can make it with the numberof dice available.

2. Starting from one end of the road, the rules of the game are that at each turn you remove (throughfission) a die if it is adjacent to a spot on the grid where a die has undergone fission and if the diehas a certain value. You continue playing until the chain reaction dies out or until it reaches theopposite end of the road.

3. Play the game where the rule is that dice showing 1–4 spots can undergo fission, does the reactionreach the end?

4. How about if only dice showing 1–2 spots can undergo fission?

5. Try other required number of spots. Is the outcome random or is it fairly predictable?

6. What if you tried shapes of dice grids other than a long “road”. (E.g., starting from the middle of asquare grid of dice.)

This is a qualitatively realistic model for a chain reaction. The concentration and physical arrangementfissile material is the most important consideration in whether a reaction is self-sustaining and how quicklyit spreads.

Discussion II: Scientists and RiskWhen the fission bomb was being developed, it was suggested that the heat of the explosion could triggerfusion reactions in the atmosphere of the earth, causing a chain fusion reaction which would burn up theentire atmosphere of the earth. Calculations showed that the temperature of the fission weapon would beabout a factor of 100 too low for this to happen. Because of the secrecy of the Manhattan project, this riskwas never disclosed to the public before the first bomb test in New Mexico.

1. What are the implications of imposing this risk on the general population? Was this justified? Listarguments for and against this decision.

2. Can you come up with other examples where such a decision (to withhold information from thepublic based on science) is justified or not justified in your opinion?

Workshop #10: 21 April - 23 April 2004Physics 100, Spring 2004

Prof. McFarland

Problems I: Anti-matter EnginesIn Star Trek, the starship enterprise uses a drive system based on combining anti-matter (frozen anti-hydrogen atoms) with regular matter to release energy. The mass the Enterprise is approximately 2 ×10

6 kg. The mass of a single hydrogen atom is 1.7 × 10−27 kg.

1. How much anti-hydrogen mass must annihilate with hydrogen to make the Enterprise go from 0to 0.1c. How many anti-hydrogen atoms is this? (Hint: first find the kinetic energy change of theEnterprise.)

2. Imagine that the Enterprise needs to be able to accelerate from 0 to 0.1c in 1 second. What is thepower required to do this in units of Watts? Compare that to the output of a typical nuclear powerplant (1-10 Billion Watts).

3. The Enterprise can only carry so much anti-hydrogen in its tanks, say 105 kg (that’s about 100 tons).How many times during its five year voyage can it accelerate from 0 to 0.1c. Does the answer fitwith your impression of the Enterprise’s capabilities from the TV series?

Experiment I: Scattering ExperimentsA good analog for a scattering experiment using particle beams is the determination of a hidden shape bybouncing marbles off of it. Work in pairs on this one...

1. Scatter marbles off of your shape and try to determine the shape (no peeking!)

2. After you start work and experiment a little, stop to think about the techniques you are using. Whatis it you consider exactly when you shoot in a marble? How could you improve your measurements?

3. Did you get the shape right?

4. How would you expect your result to be different if you had used hockey pucks instead of marbles?

Reconvene as a group to compare results and techniques.

Problem II: Exchanging a particle to carry a forceIn the Rutherford-Geiger-Marsden experiment which showed back-scattering of α particles in a gold foil,imagine that the force between the α particle and the nucleus was from the exchange of a single photon.To answer the questions, you will need to know:

• The mass of an alpha particle is 6.7 × 10−27 kg.

• The velocity of the alpha particle in Rutherford’s experiment was 1 × 107 m/sec.

1. If an alpha particle changes its direction 180 degrees but keeps the same initial velocity, how muchdoes its momentum change?

2. A photon has momentum equal to p = E/c. If a single photon caused the change of momentumabove, what was its energy?

3. What is the wavelength of this photon? Where on the electromagnetic spectrum does it lie. Doesthis answer surprise you?

4. What does this answer tell you about how close the alpha particle must have gotten to the nucleus?

Experiment II: Cosmic Ray ExperimentsYou can form a cosmic ray telescope with two paddles by requiring a signal in both paddles. In this way,you select only cosmic rays from a particular direction. Your job is to use the paddles to demonstrate thatmore cosmic rays are traveling up and down than horizontally.

1. Discuss as a group how to design your experiment. Consider (and test):

• The effect of distance between the two paddles• The effect of the orientation of the two paddles• How to make the two measurements you want to compare

2. Run your experiment. Collect data.

3. While collecting data, speculate about the implications of the fact that cosmic rays go up and downrather than horizontally. You may use the fact that the cosmic rays you see in your paddles arecreated at all points in the top of the atmosphere by interactions of high energy protons as a startingpoint. . .

Workshop #11: 28 April - 30 April 2004Physics 100, Spring 2004

Prof. McFarland

Problems I: Quantum and Measurement in ReviewWork in groups to answer each of these questions.

1. Film is exposed photon by photon to make a photograph as illustrated below. As the photograph isgradually exposed, do you know where the next photon will go? What do you know about the nextphoton? Explain.

2. Young’s double slit experiment is performed, and again you can watch the pattern build up photon-by-photon. Looking at the photographs, would you necessarily be able to see interference with asingle photon? Explain.

3. Imagine that you blocked one of the two slits for each photon. How would the experiment bedifferent? Is it different only on the “average” level or is it also different photon by photon? Explain.

4. Erwin Schroedinger, one of the pioneers of quantum mechanics proposed a paradox known as“Schoedinger’s cat”. If we place a cat in a sealed box for an hour with the device below, thereis a 50-50 chance that the cat will be alive when we open the box. Before we open the box, what dowe know about the cat? Is it alive or dead or both?

Problems II: Protons and ElectronsWork in small groups. Pick one problem or the other to work out.

1. A proton is part of a single gold nucleus which has a diameter of 10−14 meters. You measure itsspeed. Describe what you are likely to measure and why.

2. An electron is part of a single gold atom which has a diameter of 10−10 meters. You measure itsspeed. Describe what you are likely to measure and why.

Reconvene to discuss. What do these answers tell you about the speeds of the respective objects?

Problems III: Energy of a FlyWork in small groups. Compare results at the end.

1. A fly is buzzing around the room. Your task: list all the forms of energy of the fly and estimate howmuch energy in each form.

(Hints: what if the fly encountered an antimatter fly? does a fly burn as well as a Frito(TM) which has 40Joules per gram? where is the fly and how fast is it going? serious joke: do you know both of those?)