SPECIFIC HEAT
Is the specific heat of liquid water constant? Fill a 600mL beaker with 400mL of water, and measure the temperature before and after several successive one-minute exposures inside a microwave oven, repeating until you get above about 90oC. Be sure to stir the water with the thermometer to ensure that all the water is at the same temperature. Is the specific heat constant? Double the mass of water in the oven and measure the temperature change for two separate one-minute trials. Is the result consistent with the calorimetry equation? Using your best values for the temperature change in the beakers, calculate the power output of the oven in watts. How does this power output compare to a typical lightbulb or to the rated output of the oven (if known)?
LATENT HEAT
Measure out 100mL of water, using a graduated cylinder. Put it in a large beaker (at least 200mL) to avoid spills. Bring it to boiling in a microwave oven, and continue boiling for exactly two minutes. (Boiling does not start all at once in all parts of the water, since the microwave heats the water unevenly: use your best judgement of when the boiling starts.) Measure the mass, m, (or, equivalently, the volume) of water that has boiled off. Calculate the latent heat of vaporization in cal/kg, using the value you calculated for the power of the oven last time. The accepted value of Lv is 540cal/kg, which means that if you put a mass, 10m, in the oven, its temperature should rise 54oC when cooked for two minutes. Test this.
MASS OF A BALLOON
Assuming air to be an ideal gas of molar weight 29g/mole, calculate the pressure of the air inside a balloon by measuring its mass. Be sure to subtract off the mass of the part of the balloon which is not air. If you calculate a pressure less than 1atm, you have fallen into an obvious trap. What is it? Recalculate the pressure. How close to 1atm is it?
LAUNCHING A HOT-AIR BALLOON
Today we will inflate a 0.95m3 tissue-paper hot air balloon, the shell of which has a mass of 138g. In order for the thing to float, we need to heat the air inside to 62oC, if the surrounding air is 22o C. (You should be able to calculate these values, but I'm not asking you to.) Calculate the amount of heat needed to get the balloon to float. (We will start with the balloon filled with cold air, rather than uninflated, to simplify your calculation. Is the air heated at constant pressure or constant volume?) Measure the amount of time it takes for a blowtorch to get the balloon to lift. From this, calculate the power output of the torch in W. Does this answer make sense? (How does it compare, for example, to the power output of a lightbulb?)
CAUTION: Use the stovepipe assembly with the blowtorch to avoid fire hazard, and remove the stovepipe from the balloon before turning off the torch. The stovepipe gets very hot once there is no air rushing through it, tissue paper burns very rapidly, and this balloon took hours to piece together.
ENTROPY
Calculate the probability of seeing 1, 2, 3, 4, or 5 'heads' after 5 throws of a coin, assuming that an individual coin toss is exactly 50% likely to yield 'heads'. How many coins would you have to toss to be able to prove whether the probability is exactly 50%?
Throw a fist full of five coins 40 times (for a total of 200 individual coin tosses), counting the number of heads in each batch. Calculate the experimental probability of throwing 1, 2, 3, 4, or 5 'heads' out of five. Also calculate the experimental probability of throwing 5 'heads' out of ten (by grouping together adjacent data). Compare this probability to theory (63/256). Finally, calculate the total probability of tossing a head, using all 200 events in your experiment. Does this tell you anything about how averages depend on the sample size? What does all this have to do with ideal gases and physical materials? (Hint: how many "coin tosses" are there inside a balloon?)
CALCULATING ELECTRIC FORCE
Consider two charges, each +1mC, located at x=0, y=1cm. Calculate the force felt by a +3mC charge along the x-axis for x>0. Set up a spreadsheet with columns x, F1 , F2, cosq1, cosq2, F1x, F2x, SFx. (SFy=0, so we'll ignore the y-components for this example.) Find the value of x (to three significant figures) for which the force is a maximum, and find the value of the force there. Calculate the magnitude of the force at x=0, 0.1, 0.2, 0.3,...,1.0cm. You will need these values in a later lab, so hold onto them. If you have a floppy disc, save you may want to save this spreadsheet for future reference.
CHARACTERISTICS OF THE ELECTRIC FIELD
Your instructor will show you a computer program which plots the electric field near an array of charges by placing a positive test charge near each positive charge and following where it would go if released. Have this program sketch several such diagrams for different sets of three or four charges. You should be able to take at least one of these diagrams and notice a few mistakes in the diagram as drawn. Referring to the properties of electric-field lines mentioned in the text, describe as many of these errors as you can find in the diagrams, and tell how you would alter the diagrams to fix them up. (If a red marker is handy, use it.) Be sure to mark the direction of each line while you're at it.
THE ELECTRIC FIELD NEAR A DIPOLE
Back to the spreadsheet! Consider an electric dipole which consists of a +1mC charge on the y-axis at y=1cm, and a -1mC charge on the y-axis at y=-1cm. Set up a spreadsheet to calculate the electric field along the x-axis and along the y-axis. (Notice: in both cases, Ex=0. Can you see why?) How quickly does the electric field go to zero, relative to the field around a single electric charge? Calculate the electric field along the x-axis and along the y-axis, doubling (several times) the distance of the test charge from the origin, and checking whether the field decreases by a factor of 2, 4, 8, 16, or whatever. Does the E-field obey a power law? If so, what is the power? Does the E-field obey the same power law along the x-axis as along the y-axis? In your writeup, try to explain why the E-field would drop off faster or slower than for a single charge.
DO IT YOURSELF CAPACITORS
The capacitance of a parallel-plate capacitor is C=eoA/d=A/(4pkd). Make your own capacitor by sandwiching a piece of notebook paper between two sheets of aluminum foil. Clip some alligator clips and banana plugs onto each piece of foil and measure the capacitance. If the meter reads an overflow, the two plates are probably touching somewhere. Measure the capacitance, then lean on a book on top of the plates to push them together. What does the capacitance do? Using this technique of leaning on the plates, measure the capacitance as you increase the gap between the foil plates to two, three, or more pieces of paper. Calculate the thickness of a sheet of paper from the equation above. Is this thickness consistent with, for example, the thickness of your text? (divide the thickness of the text by half the number of pages.)
VOLTAGE AND RESISTANCE MEASUREMENT
To measure resistance, you can either (a) measure both the current through and the voltage across an element, and divide R=DV/I, or (b) use an ohmmeter, which does all these steps for you. We'll do it both ways, just to ensure that they are equivalent. Voltage measurements are different from current measurements, because voltage is the energy difference per electron across a circuit element. Thus, the meter has to have one 'foot' on either side of the circuit element, unlike the current meter which has to sit right in the path of the circuit in order to ensure that it counts every single electron that passes. Hook up an ammeter and a voltmeter to the circuit element you are given. Measure current and voltage for a 9V battery source, for two 9Vs in series, and for three 9Vs in series. Calculate the resistance for each. Now, use an ohmmeter to measure the resistance directly. How do these two approaches compare?
SERIES AND PARALLEL RESISTORS
Resistors in series behave like a single resistor of resistance Rs=R1+R2+... . Resistors in parallel behave like a single resistor of resistance Rp, where 1/Rp=1/R1+1/R2+... . You will be given a number of 100kW resistors and be asked to create combinations of resistors that equal other values. Your instructor will show you how to solder these resistors together to make these combinations. Before you begin, how would you make a combination resistor of 200kW, 300kW, 400kW resistance? How would you make a combination of 50kW, 33kW, 25kW? Draw a diagram of how you think you would make such a combination, then make the combination and measure its resistance (Measure the individual resistors before you begin, since they are unlikely to be exactly 100kW.). As a final step, can you make a 120kW resistor using just five resistors? Do so, and verify its resistance.
KIRCHHOFF
Put two lightbulbs in series, measure current through, and the voltage across each bulb. Repeat for two bulbs in parallel, then with 2 parallel bulbs in series with another bulb, measuring the current through, and the voltage across each bulb. Compare your results to what Kirchhoff would predict.
POWER DISSIPATION
Calculate the power dissipated by a lightbulb by measuring the current through it and the voltage across it. Do the same for two bulbs in series, then for two bulbs in parallel. At $0.10/kW.hr, calculate how expensive it would be to keep a single light bulb on for 5min.
RC CIRCUITS
You will be given a capacitor (approx. 200-300mF), an analog ammeter, an analog voltmeter, a resistor and some wire. Measure the capacitance and the resistance first to check how well they match the 'specs'. Use the lab power supply to charge up the capacitor (without the resistor). Measure the voltage across the capacitor by briefly touching the meter leads to it. Being careful not to discharge the capacitor, short it out through the resistor while recording the voltage across it and the current through it every minute or so until the current is only about 1% of its original value. Compare the following measured quantities to what you would calculate them to be from theory: the initial current, the time constant (It takes 4.6 time constants to decay to 1% of the original value.), the original charge on the capacitor. (To calculate the original charge, multiply each current reading by 60s, and add up all these products. For more accuracy, subtract off half of the first product.)
PLOTTING THE MAGNETIC FIELD
Given a large piece of paper, a bar magnet, and some compasses, plot the magnetic field in the vicinity of a bar magnet. In your notebook, you will describe some of the differences between this plot and what the electric field near two oppositely-charged charges looks like. Notice, the direction of the lines in this plot tells you the direction of the field at any point in space, and the closeness of neighboring lines tells you something about the magnitude of the field. (What, exactly?)
USING FARADAY COIL TO MEASURE A.C. FIELDS
You will use some Faraday coils to convert AC magnetic fields to AC voltages. There will be a calibrated AC electromagnet for you to calibrate your coil with. Measure the fields around the lab and try to locate sources of 60Hz magnetic fields. Compare to the levels reported in literature on the alleged physiological effects of low-level AC magnetic fields, typically tens of milligauss or a few microtesla.
TRANFORMERS
You will investigate what a transformer can do to voltages that are put across one of its coils. Hook up the secondary to an AC voltmeter (which can also measure DC voltages). Connect a 9V battery to the primary coils. What is the final voltage at the secondary, after any transient signals have died down? Are there any transient signals? What causes them? Now connect a variac (a variable AC voltage source) to the primary coils. Measure the secondary voltage at three different voltages -- say 25, 50, 100V. How do the ratios of secondary to primary voltages compare? Turn the variac down to zero, connect it to the secondary coils in place of the meter, and put the meter across the primary. Dial the variac to supply the same voltages to the secondary as the meter read at the secondary before. What voltages does the meter read at the primary? Could you set the variac to get 200V at the primary?
AC IMPEDANCES
You will be given an inductor and a capacitor. First use an ohmmeter to verify which is which. Write down the DC resistance of each. Now, hook up a circuit to measure the current through and voltage across each when wired to 110V from an electrical socket. Calculate the 60Hz impedance for each, and calculate the capacitance and inductance. You can easily verify the capacitance by using a digital capacitance meter. Notice that a real inductor behaves like an ideal inductor in series with a resistor: take that into account when calculating the inductance.
SCAVENGER HUNT FOR ELECTRICAL COMPONENTS
Given a few clues, you should be able to 'cannibalize' a printed circuit board to locate, desolder, and test the following components: resistor (what is its resistance?), capacitor (ditto), transformer, diode, transistor. Each group will be given a circuit board and a checklist of parts to find. (Some circuit boards may not have all these components, but do look for each.) Each lab partner should sketch each part, and record the basis by which it was identified. One lab partner should include the group's specimens taped to the handed-in report.
E=MC2?
Use a spreadsheet to calculate your relativistic kinetic energy in Joules as a function of velocity for v=0 to 25m/s (55mph). Compare to the classical expression for the kinetic energy on the same graph. Now plot relativistic and classical kinetic energy vs velocity for v=0 to c (in steps of 0.1c). Comment on the two graphs. For what values of v will the two agree to within 10%?
BLACKBODIES
Given a lightbulb and a variable voltage source, measure the power dissipated (from current and voltage values) as a function of voltage for every 20V to 120V. Measure the power emitted (or a fraction thereof) by using a thermal sensor. Use an optical pyrometer to measure the temperature (in oC) of the filament at 120V. Set the voltage to give you about half the power dissipation. What is the ratio of this temperature (in K) to the 120V temperature? What should it be?
SPECTROSCOPY
Borrow a diffraction grating from your instructor. Use it to identify discrete and continuous light sources. Try a normal lightbulb, a fluorescent bulb, 'bluish' and 'yellowish' streetlamps or stadium lights, the Moon, the stars. When you find a discrete source, write down each color that you see, describing the relative intensities of each -- 'very bright', 'bright', 'much weaker', 'very faint', for example. At our next meeting, we will compare these spectra to the spectra to the spectra of other gas discharge lamps, and try to identify the discrete sources. In your report, describe the difference between what you observe for a continuous and for a discrete source.
HYDROGEN SPECTRUM
Using the fiberboard spectrometers, we will measure the wavelengths of the hydrogen Balmer series. First we will use a sodium lamp (589.3nm) to calibrate the instrument. Place a piece of paper under the rotating telescope of your spectrometer. Point it at the sodium source. Keeping the base fixed, rotate the telescope until the bright yellow band is at the cross-hairs inside the telescope. Mark on your paper the position of the notch at the telescope base. Rotate the telescope back to center, then rotate it in the opposite direction, and repeat. The distance between the two marks is proportional to the wavelength. Measure this distance and find the conversion factor. Now replace the sodium lamp with a hydrogen lamp, mark the position of all the visible lines on both sides of the center, and calculate their wavelengths. Compare to the theoretical values for these, the Balmer lines.
BINDING ENERGY
From the table your instructor hands out, calculate the mass defect and the binding energy for the 7Li atom. Calculate how much energy is either released or absorbed in the reaction: 3H+4He-->7Li, and whether the reaction gives off or absorbs energy. (Would one build a lithium fission bomb or a hydrogen/helium fusion bomb?)
MEASURING THE RADIOACTIVITY OF A SMOKE DETECTOR
In this lab, you will estimate the total amount of americium inside a smoke detector. From a portion of a 'table of the nuclides', identify which isotope of americium is likely to be inside the smoke detector. (Think about what the active lifespan of a working smoke detector has to be.) Next, open up the detector and locate the source. Put it under a Geiger counter and verify that it is radioactive. Find out how many counts you can detect in one minute. Since the radiation consists of pretty wimpy beta particles, most of which don't make it through the window of the detector, a more reliable value for the activity of the source is what is printed on the cover that surrounds the source. (1Bq=1count/sec) Use this value to determine how many decays would occur in two half-lives. This is approximately the number of americium nuclei inside. Using the atomic mass you got from knowing which isotope it is, calculate how many grams of americium are in the smoke detector.
HOW FAR BELOW THE WATER'S SURFACE DOES AN IMAGE APPEAR?
Mark the apparent rays that light from an object in a water-filled tank appear to travel in the water. Following these backwards gives one the apparent position of the object. Draw a ray diagram of the system and calculate where the virtual image should appear, given the index of refraction of the water.
MAKING A LENS FROM A BLOCK OF ICE, OR HOT MELT PLASTIC, OR...
Use the overhead lights or the windows as near-infinite sources to determine whether different shapes of lenses are converging or diverging, and to measure any positive focal lengths. Compare the net focal length of two converging lenses to their separate focal lengths.
MEASURING YOUR EYES
(1) If you hold your thumb as far in front of your eyes as possible, you can focus on a region the size of your thumbnail, but everything outside this region is blurred. This is the region of highest visual acuity in your eye. Measure its size, given that your eye is about one inch in diameter. (2) Mark an 'O' on a piece of paper with a '+' two inches from it on the left and on the right. Staring at the 'O', with one eye closed, can you hold the paper at a distance from your eyes such that one of the '+'s disappears? Repeat with you other eye closed. Measure the distance, and calculate how far, and in which direction, your blindspot is from the region of visual acuity. (3) Sketch the back of your eyeball -- the region of visual acuity and the location of the blindspot -- to size in your notebook.
BILLIARDS -- A GALLILEAN RELATIVITY SIMULATION
Two billiard balls approach -- at a selectable impact parameter -- and head off in different directions. The program prints out the initial and final velocities, momentum components, and kinetic energy. One can then review the same collision as viewed by other observers, all moving with constant velocity relative to the original observer.
NUCLEAR DECAY SIMULATION
Your instructor will supply you with a simulation program DECAY1 in which an array of 'nuclei' is displayed on the screen, and these decay through a few generations. The program displays a plot of the number of each species of nucleus vs time. Some of these appear as 'dying exponentials', but some don't. Which do and which don't, and why?