Arts and Science 2D06 - 2019/20
Independent Term Projects


The laboratory component of ArtSci 2D06 this year consists of two independent term projects. In total these count for 21% of the course grade. This is subdivided as follows:

  • Writeup for Term I project: 8 %

  • Writeup for Term II project: 8 %

  • Class presentation (one to be done in either term): 5 %

Given below is a long list of options for project ideas which you can choose from. You will do two of these: one in Term I and another one in Term II (the project lists are conveniently separated by term).

Rather than selecting from the lists below, you can devise your own project. See me or your TA if you have other ideas.

In addition, you will take one of your two term projects and prepare a class presentation for it. Choose which one, and schedule a time for your presentation, by meeting with me. The presentation should be 10 minutes long, plus a 5 minute period afterward for questions and general discussion with the class. Use any approach you like, but don't build it around PowerPoint or video presentations.

The ground rules for the projects are quite simple:

  • Find one partner (i.e. no teams of 3).

  • Select a term project from the list on the course website and let me know your choice. Failure to let me know your project selection will result in a 50 percent reduction of your report mark for that term. Develop an outline for how you want to do it. Then see your assigned TA to discuss the experimental approach you want to take. Failure to meet with your TA to discuss your experimental approach will result in 50 percent of your report mark for that term.

  • Each project on the list can be done by at most two teams. That is, you can do the same project that some other team is working on, but remember, you will be graded on how distinctive and interesting your approach is.

  • Design and carry out the experiment.

  • Prepare a writeup as a team and hand it in by the deadline that you have been assigned.

Doing Your Experiment:

You will see that the outlines for the suggested projects (given below) are very much less detailed, formalized, or constrained than in a typical "lab manual". Often they are nothing more than a suggestion. You will need to work out your own method and put together your own apparatus where necessary (and the simpler the better). Most of the projects are also open-ended and can be pursued in a variety of ways. All of them will work; but it's up to you to make them work.

Experiments are about measurement -- an oscillation period, a fluid flow rate, a falling time -- whatever it is you are aiming for. Your emphasis should be on running a simple experiment to get a series of measurements, and not on trying to build something complicated. The end point is the measured data, not the apparatus. (To put it another way -- this is supposed to be physics, not engineering!)

What pitfalls and warnings should you be aware of? Read more about these in the attached file (below), but here are a few brief things:

Probably the most common problem that people run into with these independent projects is to not give themselves enough lead time to do it. Your experimental setup probably won't quite work the way you wanted it to when you designed it on paper. Things will go wrong. One working session between you and your partner won't be enough; plan for more. This is very typical of real-world experiments! Give yourself enough time to change things around, use trial and error, and finally get something that works the way you imagined it would.

Probably the second most common problem is to plan the experiment but then run the whole measurements not quite knowing exactly how you are going to analyze the numbers afterward. Don't say to yourselves "We'll just collect all our data now and figure it all out later". This is almost guaranteed to get you into trouble -- and if you are discovering this the night before your writeup is due, you're sunk. It's better to do one trial run of the experiment, then take the measurements and go all the way to the end of the calculations you need to do afterward. Things will come up that you didn't predict, and you can then go back and fix it. (And of course you will also understand your experiment a whole lot better.)

For a few suggested projects, safety may be an issue. Be aware of the risks ahead of time and plan your experiment accordingly. Make sure that neither you nor innocent bystanders will get hurt, and that no property damage occurs.

Writing It Up:

Your writeup does not need to be in any specific format -- organize it how you wish. However:

  • It should be no more than about 8 pages in length (not including graphs or illustrations).

  • It should carefully document any resources from other texts, the published literature, the Internet etc. that you used in developing your experiment.

  • It should document which of you did what parts of the work.

  • It should contain photos of your apparatus and your experiment in action.

You can find lots more instructions, suggestions, and help for the writeups in these extra documents. Here they are:

CLICK HERE TO GET THE MANUAL

CLICK HERE TO GET MORE INFO ON MEASUREMENT UNCERTAINTIES

CLICK HERE FOR A SAMPLE LAB REPORT

The due date for your written report in Term I is Wednesday, November 20 before 5 PM in Alan's office. If you hand in your writeup on November 19 or before, you will get a 1-mark bonus (out of a total mark of 20). Reports handed in after November 21 will have a per-day 2-mark penalty applied.

The due date for your written report in Term II is Wednesday, March 25 before 5 PM. If you hand in your writeup on March 24 or before, you will get a 1-mark bonus (out of a total mark of 20). Reports handed in after March 26 will have a per-day 2-mark penalty applied.

Evaluation of your Writeup and Presentation:

Your written reports will be marked on these criteria:

  • Originality of approach and quality of experimental design.

  • How deeply you investigated the question and understood the physics involved.

  • Quality of your measurements, data.

  • Quality of the writeup (completeness, polish, readability, organization, and documentation of your procedure).

  • Inclusion of sample calculations and error analysis (where appropriate -- this may differ from one project to another).

Your class presentation will be marked on these criteria:

  • Description of the necessary background (explain the background physics and experimental setup).

  • Concise summary of results and appropriate "style" (Is it best to use the blackboard or overhead projector with a mini-lecture? Run a sample experiment in real time in front of the class? Skit format?)

  • Energy, enthusiasm, class involvement, originality.

  • Confidence of delivery (Can everyone hear you? Did you practice beforehand? Are both you and your partner participating equally?)

  • Timing and selection of material (stay within time limits and pick what you want to say ...)

Now here are the project lists!

Projects For Term I:

I.1. Measure the center of mass and center of percussion of a baseball bat.

I.2. Measure how fast you can throw a baseball, perhaps by more than one method. Compare this to the figure for top athletes.

I.3. Measure the value of g (the acceleration due to gravity) by three different methods including (a) dropping a ball over a large height and timing it (is air resistance negligible?) (b) a simple pendulum (c) one other method of your choice. Which is most accurate and/or precise?

I.4. Measure two or three types of balls in vertical free fall (tennis balls, beachballs, etc.) over the same distance and find out how important air resistance is for each of them. Do any of them reach terminal velocity over (say) a 10-meter drop?

I.5. Use the linear model of fluid drag (p.129 of Giancoli text) to derive the equation of motion y(t) of a moderately big, light ball such as a child's play ball, for which air resistance is fairly important. Do this by dropping it over a reasonably large height and timing its fall (which will be longer than the ideal falling time for a pure projectile). Find the frictional constant b in the equation.

I.6. If you drop a ball onto a hard surface, it will lose some energy on each bounce and the time interval between bounces gets shorter and shorter. The coefficient of restitution R is defined as the ratio of the ball's speed just after the bounce to its speed just before the bounce. Take a hard ball or two, roll them horizontally off a table onto a hard floor, and measure R from either the times between bounces or the distance between bounces.

I.7. Many of the winter sports dear to Canadians rely on low coefficients of friction for their operation (skates and pucks on ice, curling stones and sliders, skis, sleds, snowboards ...). What are the values of the coefficients of kinetic friction in these situations, and how low can they become in practice? Would even lower values make the sport better, or worse?

I.8. What is the coefficient of static friction for various types of shoes on pavement and floor tiles (men's and women's dress shoes, sneakers, hiking shoes ...)? Do they really differ by large amounts? What about their values on icy or watery surfaces?

I.9. Measure the coefficient of rolling friction for a few simple rolling objects on a hard surface. For a discussion of the basic theory of rolling friction, see pp. 224-225 of the text by Benson, University Physics .

I.10. In theory the coefficient of kinetic friction mu_k between two particular surfaces does not depend on the weight of the sliding object. But is this really true? For something simple like a book on a table, test this out. Measure mu_k for a range of weights (stack progressively more weight on the book and see what happens).

I.11. If you drop an opened coffee filter it reaches ``terminal velocity'' almost immediately. A simple model for air resistance (air friction) is that the air drag force varies as F_d = C v^n, i.e. proportional to a simple exponent of the velocity of the object. Find the value of the exponent n by dropping one filter and measuring its speed, then two filters nested together, then three, etc. Knowing n, then find the ``drag coefficient'' C.

I.12. Measure the acceleration experienced by a falling steel ball when it lands on a deformable surface such as soft wood, by the depth of the dent it makes in the surface. How does this depend on the height you drop it from? How does the acceleration depend on the size/weight of the ball?

I.14. Use billiard balls on a pool table to illustrate and test a certain theorem involving conservation of momentum: in elastic collisions where a ball at rest is struck by another one, the two will go off in separate directions that are precisely at right angles to each other. Is this true experimentally?

I.15. If you gently slide a piece of toast off the edge of a table, does it always land jelly side down? Does it depend on the height of the table? Is the average result different if it's plain, un-jellied toast?

I.16. The center of mass of a completely full pop can is obviously halfway up from the bottom. So is the center of mass of a completely empty one. But a partially full can must have a center of mass below the halfway point. At what water level does it have its lowest center of mass, thus its most stable point?

I.17. The "packing fraction" of small objects packed into a container is (volume taken up by the objects) divided by (volume of container). Use marbles and two or three different types of containers to derive the packing fraction of the marbles. How can you make it as high as possible? Does it depend on the relative size of the marble and container? What is the theoretical maximum?

I.18. In the Roadrunner cartoons, we often see Wile E. Coyote being tricked into walking off a cliff, but he begins falling only after he notices that he's standing on thin air, in flagrant violation of Newton's laws. In contrast to this kind of ``roadrunner physics'', find several examples in the media of good, accurate physics and discuss carefully which physics laws are being demonstrated. "Media" could include movies, cartoons, comic strips, TV shows ... pick one type.

I.19. Find the center of mass of various individual people including both men and women.

I.20. Many kinds of toys provide good illustrations of Newtonian mechanics or other physics principles. Pick some, analyze them, and devise measurements that will show these principles.

I.21. Recall the "Newton's cradle" demonstration with 6 steel balls suspended from strings and swinging back and forth in collision. It demonstrates conservation of momentum in elastic collisions. Run a modified version of this experiment in which you get together a few people on roller blades. Have all but one of them stand together (in close contact). Then have the remaining person coast into them at reasonable speed (not so fast as to injure anyone!!). Remember, everyone is on roller blades (with their wheels pointing parallel to the direction of motion so that they are all free to "roll" easily). What happens to the person at the other end of the chain? How close to elastic is this chain of collisions?

I.22. This is a demonstration of Newton's Third Law. Both you and your partner should be on rollerblades for this one. On a smooth level surface (such as on a hard indoor floor), stand close together. Then, one of you pushes the other. What happens to each of you? Do you go off at speeds inversely proportional to your masses? What if both of you push the other at the same time? Does it change the result?

Projects For Term II:

II.1. Make a physical pendulum from a stick 1 meter long or more; measure how its period of oscillation depends on the distance from the center of the stick to the pivot point, and compare the results with the theoretically expected relation.

II.2. How does the period of a simple pendulum actually depend on the amplitude A of its swing? Find this out for the full range of amplitudes from A=0 degrees up to 90 degrees and compare with theory, in a descriptive way.

II.3. Use a simple harmonic oscillator such as a simple pendulum or spring system to measure its damping constant b (the coefficient describing the rate of energy loss to air resistance or friction; see section 14.7 of the text.

II.4. Real springs have mass. If you hang a mass from one, and measure the k-value from the oscillation period, this should actually depend on the mass. Try this for a real spring and a range of hanging masses. Plot up the trend of k versus m and interpret.

II.5. The domino effect: Push over the first domino in a long row, and they will all fall over in a `wave' going down the row. How does the wave speed depend on (a) the height of the dominos and (b) the spacing between them? Can you make any comments about how the speed would be theoretically expected to vary with these?

II.6. What is the tensile strength of a human hair? Does it depend on the type of hair (blonde, dark, red - ?) What is the stress (force per unit cross-sectional area) at its breaking point (see Chapter 12.5 for background)? Thus, how much hair would have to be braided together to form a ``rope'' strong enough to easily support one person's weight?

II.7. The moment of inertia of a rolling object is generally expressed as I = k M R^2 where M is its total mass and R its radius. The factor k depends on the way the object is built. Take various kinds of rolling objects (such as a solid or hollow sphere, ring, solid cylinder, etc.) and measure their k-values by rolling them down a ramp. Is there a tilt angle (or range of angles) of the ramp for which this experiment "works" the best?

II.8. Take a juice can and puncture a small hole in the side very near the bottom. Fill it with water, set it on the edge of a table, and notice where the stream of water lands on the floor. How does the point of impact of the stream (its horizontal ``range'') depend on time as the water in the can runs out?

II.9. Fill a cylindrical container with water, puncture a small hole in the bottom, and then find the flow rate (amount of water per unit time) by measuring how fast the water level drops, dy/dt. Does it behave in agreement with theory (Torricelli's theorem)?

II.10. In the story of Archimedes and the golden crown, he is said to have measured volumes directly from the water overflow of the crown immersed in a container. How accurate would this method have actually been? Find out the true precision of this method by using simple solids whose geometric volumes you know before immersing them.

II.11. In a simple pendulum, is it possible that a lot of the air friction as it swings back and forth is from the string, not the heavy ball itself?. Test this by setting up a simple pendulum, first with extremely thin string and then with thick string. How different is the "exponential decay" in the motion, assuming that you start both of them off in the same way?

II.12. Make two identical simple pendulums and hang them about 10 cm apart from a horizontal stretched string. Set one of them oscillating and notice how the energy gets transferred to the second one, and back again. How long does this take (does it depend on the tension of the horizontal string)? Change the length of one pendulum slightly and measure what fraction of the original SHM energy gets transferred, as a function of the length difference. See the text for a discussion of `resonant frequencies'.

II.13. You and your partner find the volume of your own bodies, by fairly carefully measuring your mean density and mass.

II.14. It's possible to demonstrate the Equivalence Principle from general relativity fairly simply. Take a large ball (like a basketball or soccer ball) to a swimming pool with a diving board. Get your partner to climb up to the diving board with the ball, and then jump off while releasing the ball at the same moment. Meanwhile, you videotape this and record it. Where does the ball stay relative to the diver? [This project should be done only by experienced divers and swimmers.]

II.15. A stream of water from a faucet becomes narrower as it falls (see the illustration on page 355 of the text). Why? Measure this effect from a real faucet over the biggest height difference you can, plotting up the stream width versus ''drop height''. Once the water has fallen far enough, the stream breaks up into droplets, so you need to stick to the "laminar flow" region. Compare the measured amount of narrowing with the predicted amount for an ideal fluid from Bernoulli's principle.

II.16. Some types of heavy atoms (such as uranium, plutonium, and various others) spontaneously fall apart through the phenomenon of radioactive decay. Each such element has a characteristic half-life which is the time over which half of the initial population of atoms will decay. Then in the next half-life, half the remainder will decay, and so forth. The number remaining never reaches zero, but is an exponentially declining number with time. The phenomenon was defined for atomic nuclei, but it can be applied to lots of other situations that are governed by statistical rules. Find the half-life of a coin denomination of your choice (from any country) - that is, the time over which half of them will randomly go out of circulation. Does the "half-life" idea apply accurately to the results, or does it behave according to a different model?

II.17. An old trick to measure human reaction time is this: take a ruler, hang it loosely between your fingers, and then ask someone else to hold their finger and thumb around the ruler near the bottom end (so that they are almost but not quite touching it). Then, at some random moment, let go of the ruler. Your friend is then supposed to catch it by closing his/her finger and thumb as quickly as they can. You can convert the drop distance to a time, which is then the reaction time. Try this out for various people and make sure you have a statistically decent sample. Are there significant differences between people?

II.18. An experiment done by Newton himself went like this: take a hollow ball and make a simple pendulum out of it. Measure the "exponential decay" of its motion as it experiences air resistance. Now, fill up the ball with water or weights, and repeat the experiment. Now it is more massive, so it should take longer to slow down (it has exactly the same surface area as before, so experiences just the same force of air drag, but that force is now acting on a heavier weight). So, the deceleration due to air resistance should be inversely proportional to the pendulum weight. Make a simple pendulum of this type and test out if this is true.

II.19. Design and carry out an experiment to determine the speed of light using marshmallows and a microwave oven. Try it also with cheese slices (on toast, say) instead of marshmallows.