Laboratory Overviews

Short descriptions of the experiments in the `round-robin' portion of Intermediate Laboratory are described below along with sources for more details about the theoretical background, methods, and procedures. At the end of each overview the number of students needed to perform the experiment is listed. If you have questions send me email at ggilfoyl@richmond.edu

1. Fundamental Forces: Coulomb's Law A torsion balance is used to make sensitive measurements of the properties of the electrostatic force or Coulomb's Law. Two spheres are charged with a high-voltage power supply and brought into proximity with each other. One sphere is attached to a post which is suspended from a wire and balanced so the post-sphere combination is horizontal. The apparatus rotates due to the electrostatic repulsion between the spheres and the amount of rotation is proportional to the electrostatic force. The experiment consists of three measurements: (1) the dependence of the force on the separation of the centers of the sphere, (2) the effect of charge on the size of the force, and (3) a determination of the Coulomb constant. For theoretical background consult any introductory physics text. For more details on the experimental procedure and analysis see the manual in the lab or download the manual entitled Coulomb Balance from the Pasco website. Remember to perform a full error analysis on your results. See Chapter 23 in Serway and Jewett or Chapter 25 in Knight for more background details. Two-person experiment.

2. Fundamental Particles I: The Charge of the Electron The effect of individual electrons is measured here using the eye-straining, Millikan oil drop method. Small drops of mineral oil (an internal lubricant) are ionized by alpha particles emitted by the radioactive decay of a small sample of 232-Th. These charged particles are falling between two metal plates and observed with a microscope. When a voltage is applied across those plates, the electrostatic force pushes the charges back up. The charges always move at a constant velocity due to the viscosity of the air and measurements of their terminal speeds with voltage on and off can be used to determine the charge on a single drop using Stoke's Law. The theoretical and historical background is covered in the Pasco manual (in the lab or on the Pasco website). You should perform a full statistical analysis on your results and also consider sources of systematic error in your final result. See Chapters 23 and 25 in Serway and Jewett or Chapter 25 in Knight and Chapter 3 in Rex and Thornton for more background details. Two-person experiment.

3. Fundamental Particles II: The Charge/Mass Ratio of the Electron Once you know the charge on the electron (see previous lab), then it is possible to 'weigh' an electron. A beam of electrons of known kinetic energy is produced from a hot filament and then injected into a region of constant magnetic field between two Helmholtz coils. The beam is bent into a circle whose radius depends on the charge and mass of the particle. This phenomenon forms the basis for a mass spectrometer. The square of the radius of the path of the electron beam is proportional to the ratio of the charge on the electron to its mass. See any introductory text for a description of the magnetic force on a moving, charged particle and how it is related to the workings of a mass spectrometer. See the manual in the lab (or download it from the Pasco website) for more details on the experimental procedure. You should also investigate how e/m changes (if at all) as the accelerating voltage is changed and as the magnet current is varied. You should perform a full error analysis on your results as usual. Combine your results (and their uncertainties) with the previous laboratory to extract the electron mass and compare it with the known value. The techniques here are still applicable in research today. See this. See Chapter 29 in Serway and Jewett or Chapter 32 in Knight for more background details. One-person experiment.

4. Fundamental Particles III: The Cloud Chamber It can be difficult to convince someone that our world is permeated with subatomic radiation. The cloud chamber is a device for visualizing and measuring the passage of charged, subatomic particles through a supersaturated alcohol vapor. When an alpha particle or beta particle interacts with the mixture, it ionizes it. The resulting ions act as condensation nuclei, around which a mist will form (because the mixture is on the point of condensation). The high energies of alpha and beta particles mean that a trail is left, due to many ions being produced along the path of the charged particle. These tracks have distinctive shapes. When any uniform magnetic field is applied across the cloud chamber, positively and negatively charged particles will curve in opposite directions, according to the Lorentz force law with two particles of opposite charge. Charles Wilson and Arthur Compton received the Nobel Prize in Physics in 1927 for their invention of the cloud chamber. There are more details here, here, and here.

5. Fundamental Constants I - Planck's constant At the start of the twentieth century one of the outstanding mysteries was the photoelectric effect where a light is incident on a metal surface and electrons ejected from the surface of the metal create a current that can be measured and its properties studied. Classical physics had no successful explanation for the photoelectric effect and it was not until Einstein's 'miraculous' of 1905 that the mystery was solved. The solution was one of the early triumphs of quantum mechanics and one of the sparks of the quantum revolution. In this laboratory you will measure the energies of the electrons that are ejected from a metal surface that has light of different wavelengths striking it. The dependence of these energies can be used to determine Planck's constant, one of nature's fundamental constants. A full accounting of the uncertainties in each of your measurements is expected. See Chapter 40 in Serway and Jewett with special emphasis on section 40.2 or Chapter 38 in Knight. The description of the use of the apparatus is in the notebook on the photoelectric effect or in the manual on the Pasco website. One-person experiment.

6. Fundamental Constants II - the gravitational constant G Understanding gravity is one of the great leaps forward made by Newton in the seventeenth century. The leap was not complete until Henry Cavendish was able to weigh the Earth using a torsion balance over a century later. You will be using an updated version of the torsion balance to measure the value of G. The torsion balance consists of a tungsten wire holding a carefully-balanced and suspended boom which has two small lead spheres on each end. The boom is free to rotate in the horizontal plane. A second, heavier boom holds two large lead spheres which also rotates in the horizontal plane using an axle attached to the frame of the balance and aligned with the axis of the suspended boom. By rotating the heavy boom from one side to the next you can get the suspended boom to oscillate back and forth. The oscillation is measured with a capacitive circuit and plotted with DataStudio. Once the suspended boom is oscillating put the heavy boom in one of the extreme positions and observe the decay of the oscillations. After four oscillations move the heavy boom to the opposite extreme and record four oscillations. The average position in each of these configurations will be used to determine the equilibrium angle for each configuration. You will also fit the oscillations to find the angular frequency of the torsion pendulum which is needed to calculate G. We will NOT be using the light lever to determine the angular calibration of the torsion balance. We will use the calibration posts described in the manual. See Chapter 13 in Serway and Jewett and especially section 13.2. More details can be found here or in Chapter 12 of Knight. Two-person experiment.

7. Fundamental Constants III - Boltzman's constant and Avogadro's number In the early days of the atomic theory one of the important unknown quantities was Avogadro's number (Avogadro died long before we measured his number). In developing the kinetic theory of gases one can calculate a new version of the well-known ideal gas law ( PV = nRT) (where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature). This new form is PV = nN_AkT where N_A is Avogadro's number and k is the Boltzman constant. Equating the two forms, one finds that R = N_Ak so a measurement of the Boltzman constant would determine Avogadro's number at the same time. At the time two different people proposed similar methods to measure k. In this laboratory you will use a variation of their proposed method. Using the Millikan oil drop apparatus (see Round-Robin lab 2 above), you will measure the fall time of a series of similarly-charged oil drops. This measured fall time varies from one trial to the next, because the falling oil drops are buffeted back and forth and up and down by the molecules of the air as they fall. Sometimes the buffeting speeds the oil drop (reducing the fall time) and sometimes it slows it down so that it takes longer. This is a form of Brownian motion. The two physicists showed that the variance of this fall time (not the average of the fall time, but the square of the standard deviation) could be calculated from the atomic theory and depends on the Boltzman constant. A reference on the method is here. The two physicists were Marian Smoluchowski from Poland and Albert Einstein. For experimental details see the notebook on the Millikan oil-drop experiment or get the manual from the Pasco website. Two-person experiment.

8. Fundamental Constants IV - Speed of Light Perhaps the most well-known of the constants of physics is the speed of light c. It plays a fundamental role in relativity, electromagnetism, cosmology, and nuclear and particle physics. It is still the subject of research at the frontiers of our understanding. A variety of methods have been used to measure it's value. In this experiment you will make a direct measurement of c using a laser that produces a variable, sinusoidal intensity oscillating a few million times per second. The light is reflected by a mirror and then detected by a photodiode that responds fast enough to detect that oscillation of the laser. A high speed oscilloscope is used to collect the signal from the photodiode. To learn how to use an oscilloscope follow the procedure here. Changing the distance from the laser to the mirror shifts the phase of the light curve enabling one to determine the speed of light. For experimental details see the notebook on this speed-of-light measurement or get the manual from the Pasco website. You can consider comparing the results of this measurement with the Foucault method described below. One-person experiment.

9. Fundamental Constants IV.B - Speed of Light (again) As described in the previous overview the most well-known of the constants of physics is the speed of light c which plays a fundamental role in a wide range of situations. In this experiment you will use the method of Foucault to measure it. More details on the technique are here. A rapidly rotating mirror is used to reflect the light and the displacement of the image measured to extract the speed. For experimental details see the notebook on this speed-of-light measurement or get the manual from the Pasco website. You can consider comparing the results of this measurement with the direct method described above. One-person experiment.

10. Resonance and Radio: The LRC Circuit Almost all physical systems oscillate in some form or fashion and when the system is driven by some outside force and the outside force oscillates with the same frequency, the amplitude of the oscillation can be wildly amplified. This occurs in electronic, mechanical, and even quantum mechanical systems. Our everyday radios depend on this phenomenon. In this experiment you will investigate a series LRC circuit through measurements of the voltage across the generator that drives the system, the resistor, the capacitor, and the inductor in the circuit. The computer will be used as a storage oscilloscope to make these measurements and to illustrate the phase relationships among the voltages across the circuit elements. To learn how to use an oscilloscope follow the procedure here. The primary goal is to illustrate the phase relationships of the different components and to determine the resonant frequency of the system. As usual, a full analysis of the uncertainties is expected. See Chapter 33 in Serway and Jewett or Chapter 35 in Knight for more background details. One-person experiment.

11. Geometric Optics Classical or geometric optics, sometimes called ray optics, is the branch of optics that describes light propagation in terms of rays. Rays are bent at the interface between two dissimilar media, and may be curved in a medium in which the refractive index is a function of position. The ray in geometric optics is perpendicular to the wavefront of the light. In this laboratory you can investigate a number of different phenomena related to the optics we used in the hydrogen emission line laboratory earlier in the course. The first topic is the study of prisms and diffraction gratings(see Experiment 2 in Pasco manual). Here, you will see how light is 'separated' by these devices. Next, you'll see how lenses work (Experiments 7 and 9 in the Pasco manual) and investigate how they effect different colors of light using different color lasers. Next, you pull these pieces together to investigate the workings of a telescope (Experiment 10 in the Pasco manual). There is an additional experiment to investigate the polarization of light using some polarizers, a point source, and a light sensor. In each part you should make a careful, quantitative comparison with theory and determine how well your data supports the models described in the manual and in the text you're using. As usual a full accounting of the uncertainties in each of your measurements is expected. See Chapters 35-36 in Serway and Jewett or Chapter 23 in Knight for more background details. One-person experiment.

12. Physical Optics - Diffraction Light acts as a wave under the appropriate circumstances so it exhibits diffraction; the bending and spreading of waves when they meet an obstruction. When light passes through some opening (like our eye) diffraction occurs around the edges of the opening. You will be using lasers and light-detecting phototransistors to study diffraction. The signal from the phototransistor can be recorded using Capstone. In particular, you will investigate three important aspects of diffraction. (1) Diffraction often occurs with other interference effects like multiple-slit interference described here and here. You will first investigate qualitatively how these two phenomena overlap with one another. (2) Diffraction limits our ability to see small objects. The theoretical description of the diffraction limit for openings of different shapes is often referred to as the Rayleigh criterion. You should pass laser light through differently-shaped openings and record the diffraction pattern with the phototransistor. These data can then be compared with the theoretical prediction. (3) Diffraction can be exploited to measure the size of objects that are too small to measure otherwise. A particle accelerator or electron microscope are prime examples of this technology. You should choose some small objects and shine the laser on them to produce a diffraction pattern. Measure the diffraction pattern with the phototransistor and extract the size of the objects. As usual a full accounting of uncertainties in your results is expected. See Chapters 37-38 in Serway and Jewett or Chapter 22 in Knight. One-person laboratory.

13. Microwave Optics Microwaves are a form of electromagnetic radiation that share all of the properties of visible light. They have wavelengths of the order of a meter versus light which has a wavelength that is a fraction of a micron. Microwaves exhibit their wave properties on scales that are convenient for use in our laboratory. In this investigation you will learn how waves interfere with one another in different configurations. In particular you should perform several of the experiments in the Pasco manual including the Introduction (1), Standing Waves (3) and Michelson interferometer (9) to measure the wavelength of the microwaves, Bragg diffraction (12) to determine the lattice structure of a 'crystal', and Double-Slit Interference (6). These microwave experiments are relevant to several of the other experiments here like Interferometry, Measuring Atomic Separations, and Physical Optics - Diffraction. See Chapters 37-38 in Serway and Jewett or Chapter 22 in Knight. One-person laboratory.

14. Interferometry This is a technique for measuring very small displacements (on the order of 0.1 microns) that we will use to measure some of the optical properties of different materials. A beam of light is divided somehow into two paths (e.g., using partially silvered mirrors) and then recombined so the light waves from the two parts are superposed (they add) and form an interference pattern. Small changes in one of the paths will alter the interference pattern in a systematic, measurable way. In this experiment you will use interferometry to (1) measure the wavelength of a laser light source, (2) determine the index of refraction of air (which differs from the value for a vacuum by only a few parts in 10,000), and (3) measure the index of refraction of glass. For more details see Chapter 37 in Serway and in particular sections 37.7 and 39.2 or you can see Chapter 22 in Knight. To get the best results use the large, blue, Jodon helium-neon laser. Eye protection should be worn at all times when the laser is turned on. One-person experiment.

15. The Adiabatic Gas Law Adiabatic processes are thermodynamic ones which occur without gain or loss of heat in the working fluid such as air or water. When combined with the First Law of Thermodynamics and the ideal gas law one can describe the what happens as gases compress and expand; an essential part of understanding many industrial applications like refrigerators. It can also be used to probe the quantum behavior of atoms and molecules. Gases made of different particles behave quantitatively differently when they undergo adiabatic changes. The goal in this laboratory is to test the adiabatic gas law with different gases and compare our results with the predictions of the ideal gas law. As usual, a full accounting of the uncertainties is expected. See Chapter 21 in Serway and Jewett or Chapter 18 in Knight for more background details. One-person experiment.

16. Measuring Atomic Separations One of the important methods for 'seeing' the structure of matter is the diffraction of electromagnetic (EM) radiation with a wavelength about the size of the interatomic distances - X-rays. The X-rays strike an ordered array of atoms and the scattered waves interfere with one another as they leave the material. The final pattern of X-rays reflects the internal arrangement of the atoms. This method was used by Watson, Crick, and Wilkins to unravel the structure of DNA (and win the Nobel Prize in 1953), In this laboratory you will use a beam of X-rays incident on different crystals to measure what is called Bragg scattering. The scattered radiation is detected as photons in a Geiger-Muller (GM) tube and the angular distribution is measured as a function of the angle between the beam and the scattered photons. You will do this by (1) aligning the instrument (section 12.0 in the Tel-X-Ometer manual), (2) calibrating the G-M tube (sections 13.0-14.0 in the manual), (3) testing it (sections D1.1-D1.2), (4) measuring the angular distributions of different crystals (sections D14 and D22-D23). Read sections 10-11 in the Tel-X-Ometer manual to introduce yourself to the use of the X-ray machine. A full accounting of the uncertainties in each of your measurements is expected. More background on diffraction is in Chapter 38 of Serway and Jewett with specific details about X-ray diffraction in Section 38.5. Look also in Chapter 24 in Knight. One-person experiment.

17. Dynamical Chaos in a Compound Pendulum Dynamical chaos is the phenomenon sometimes called the 'Butterfly Effect' where the evolution in time of a system is extremely sensitive to small changes in the initial conditions, e.g., a person steps on a butterfly in South America and causes a hurricane in the Atlantic Ocean. Small differences in the starting point are followed by diverging trajectories at later times. Weather, animal populations, electronic circuits, and many other physical systems exhibit this behavior. In this laboratory you will use an identical pair of compound pendula that exhibit simple harmonic motion under some initial conditions, but display richer, more complex, chaotic behavior under other initial conditions. You will use video analysis tools to measure the trajectories of the compound pendula and extract the Lyapunov exponent to test for the onset of chaos. An introduction to dynamical chaos is here with some references on the Lyapunov exponent [1, 2, 3, 4]. Two-person experiment.

18. Modeling Air Friction Falling balloons are used to investigate the velocity dependence of air friction and compare it with standard models presented in introductory physics texts. This is done by adding weights to a balloon and filming it as it falls. The resulting video is analyzed and the terminal velocity is measured from the motion of the falling balloon as a function of the force applied to the balloon by the hanging weights. Since the terminal velocity is constant, the net force is zero. The known force exerted by the weights can then be directly related to the velocity. This enables us to test different models of the friction due to air resistance. In particular, most texts present (without justification) forces that are either linearly or quadratically dependent on the velocity. In this project, you will test the validity of these textbook ideas. See Chapter 6 In Serway and Jewett or Chapter 5 in Knight for more details. Two-person experiment.

19. Fluid Flow and Bernoulli's Principle According to Bernoulli's Principle, the pressure in an incompressible moving fluid is lowest where the speed of the fluid is highest. This is the basic principle that keeps airplanes and birds in the air. It is essentially the application of the conservation of energy principle to flowing fluids. The qualitative behavior is that the pressure of a fluid is lower in regions where the flow velocity is high. In the high velocity flow, kinetic energy must increase at the expense of pressure energy. In this investigation you will use a Bernoulli cart. It consists of a vertical cylinder that can be rotated rapidly by pulling on a string. It is attached to a dynamics cart sitting on a track. When a fan blows air perpendicularly across the track, the cart moves along the track in a direction corresponding to the direction of rotation of the cylinder. If the cylinder is not rotating, the air-speed passing by the front and back of the cylinder is the same and the cart doesn't move. When the cylinder is spinning friction between the cylinder walls and the air causes the speed of the air on one side of the cart to become greater than the speed of the air on the other side. According to Bernoulli’s Principle, the faster moving air exerts less pressure on the cylinder than the slower moving air on the other side of the cart. This difference in pressure produces a net force which causes the cart to move forward along the track. In this lab you should investigate the quantitative aspects of Bernoulli's Principle. More details can be found in Chapter 15 in Knight, here, or in the manual (see notebook or Pasco website). One-person experiment.

20. Cosmic-Rays The Earth is constantly bombarded by high-energy, charged particles whose origin is still mysterious. These primary cosmic rays (mostly protons) strike the Earth's atmosphere creating a cascade of other particles that ends up being mostly muons by the time it reaches the ground. It is these muons that are the primary focus of this experiment along with the technology used to detect them. You will use a plastic scintillator to detect the passage of the muons, to measure the lifetime of muons that stop in the detector and decay into an electron and a neutrino, and to extract the ratio of positive to negative muons in the cosmic ray cascade. The first step is to learn how to use an oscilloscope by following the procedure here. Once that is complete set up the detector as described in the manual and use the Tektronix 2467B oscilloscope to see the waveform of the cosmic ray events after they are amplified. Trigger the scope on the discriminator output while viewing the discriminator signal and the analog signal simultaneously. Record what you see. The data acquisition software is available here. You need to unzip it and install it on your computer and leave your machine up and running so the software doesn't get deleted when you logoff. You can now measure the muon lifetime. Occasionally, a low-energy muon will stop in the plastic scintillator producing a signal. A 'long' time later (up to a few microseconds), the muon will decay into an electron and a neutrino. The passage of the energetic electron is detected like any charged particle producing a second signal. The time difference between these two signals is the lifetime for that particular muon. Collecting data on many such events will enable you to extract the lifetime. The sample of cosmic-ray muons you observe in your detector is actually a mixture of positive and negative particles. Use your observed lifetime to measure the ratio of positive to negative muons and to calculate the value of Fermi coupling constant (see the manual for details). See Chapter 46 In Serway and Jewett for more details. One-person experiment. More details on getting the computer to communicate with the data acquisition system are here and the software you need is here, and here.

21. Mechanical Equivalent of Heat Before the Industrial Revolution most thought of mechanical energy (the sum of the kinetic and potential energy of an object) and heat were separate entities. It was the work of James Prescott Joule in the mid-nineteenth century that showed the equivalence between these two quantities. This was an essential step in developing our current view of the conservation of energy. In this laboratory you will measure the transformation of mechanical energy into heat by performing mechanical work (turning a crank to hold up a bucket of sand) and measuring a temperature change (in the cylinder of the crank). See chapter 17 in Knight or Chap 17 in Serway and Jewett. One-person experiment.

22. Thermal Radiation (Leslie's Cube) To go along with the development of the equivalence of heat and mechanical energy (see above) is our understanding of thermal radiation. This understanding started in the early nineteenth century with the work of John Leslie who studied how different surfaces absorb radiation and change temperature. In this lab you will investigate how different materials absorb and emit radiation including the Stefan-Boltzman law which was an important part of the blackbody problem that lead to the development of quantum mechanics. In this laboratory you will use a specialized lamp to produce radiation along with a sensor for detecting it. You will also use a cube made with different materials on different faces of the cube to study the absorption and emission of radiation. See chapter 3 in Thornton and Rex. One-person experiment.

23. Electromagnetic Induction One of the simplest magnetic field problems encountered in introductory physics is the behavior of a current-carrying wire in a fixed magnetic field. In this laboratory, you will first map out the field of a permanent magnet using a Hall probe. You then insert a straight wire in the central region between the pole faces and turn on a current. The wire will be expelled from that central region and the forces of that repulsion and gravity will be in equilibrium. A simplified description of the effect is here and can be found in Chapter 22 of Serway and Jewett. More details are in Chapter 5 of the Griffith's electromagnetism text if you have had that course. By measuring the magnetic field you can go beyond the usual approximations made in introductory physics courses, i.e the field is constant in the region between the pole faces and then instantaneously drops to zero at the edges. You can also vary the current in the wire and the separation of the pole faces of the magnet. The same apparatus can also be used to detect the effects of diamagnetism and paramagnetism in different materials. One-person experiment.

24. Magnetic Force on a Current Loop All introductory physics texts cover magnetic force on a dipole, but there are few situations where we can study that experimentally. In this laboratory we use Helmholtz coils to produce a magnetic field and a Hall probe to measure the field in the region near the coils. This lab requires understanding how the coils produce the magnetic field and a precise knowledge of the position and orientation of the Hall probe in order to measure the field. Results include some that are often surprises to the investigator. See Chapter 32 in Knight. One-person experiment.