Archive for the ‘class xii physics project’ Category

Using a Laser Pointer to Measure the Data Track Spacing on CDs and DVDs

September 1, 2008

Objective

The objective of this project is to learn how to use a diffraction pattern to measure the pitch (spacing) of the data tracks on CDs and DVDs.

Introduction

CDs and DVDs are everywhere these days. In fact, you probably receive one free in the mail every month or two as an advertisement for an Internet service provider. CDs and DVDs store huge amounts of binary data (patterns of 0’s and 1’s) which your player can “read” with a laser, lenses, light detector, and some sophisticated electronics.

CDs and DVDs are both multi-layered disks, made mostly of plastic. The layer that contains the data (DVDs can have more than one data layer) consists of a series of tiny pits, arranged in a spiral, tracking from the center of the disk to the edge. The data layer is coated with a thin layer of aluminum or silver, making it highly reflective.

How small are the pits? Well, their diameter is 500 nanometers (nm). How small is that? A millimeter (mm), which you can see with your unaided eye, is one-thousandth of a meter. Imagine how much you have to shrink a meter to get down to the size of a millimeter. Now imagine shrinking a millimeter by the same amount. That takes you down to a micrometer (μm), or one-thousandth of a millimeter. You have to shrink a micrometer one thousand times more to get down to the size of a nanometer. A typical human hair is about 100 μm wide. The pits on a CD are 0.5 μm wide. So you could fit 200 pits across the width of a typical human hair! The diameter of the pits is also similar to the wavelengths of visible light (400 to 700 nm).

On the CD, the pits have some blank space (“land”) on either side of them. This means that the adjacent data tracks of the spiral are regularly spaced (something like 3 times the pit diameter). This regular spacing of the spiral tracks, slightly larger than the wavelengths of visible light, produces the shimmering colors you see when you tilt a CD back and forth under a light. The colors result from diffraction of the white light source by the CD.

What is diffraction? That is a bit harder to describe, so we’ll start with a related concept that is easier to understand: interference. Interference is what happens when waves collide with each other. If the peak of the first wave meets the peak of the second wave, the peaks add together to form a higher peak. If the trough of the first wave meets the trough of the second wave, the troughs add together to form a lower trough. If the peak of the first wave meets the trough of the second wave, the peak is made smaller. And if the peak of the first wave is the same size as the trough of the second wave, they can actually cancel each other out, adding to zero at the point of interference. You can see a demonstration of interference with the Ripple Tank Applet link in the Bibliography.

The first screen shot shows the results of a single wave source (choose “Setup: Single Source” from the first drop-down list and “Color Scheme 2″ from the fourth drop-down list). To avoid the complications of ripples reflected from the walls of the tank, click on the “Clear Walls” button (simulates an infinitely large tank, so reflections are eliminated):

Applet Screen Shot 1

The second screen shot shows the results of two wave sources (choose “Setup: Two Sources” from the first drop-down list):

Applet Screen Shot 2

The diagonal black lines are regions of destructive interference (where peaks of one wave met troughs of the other). If you run the applet yourself, you’ll see that, though the waves keep moving, these regions are a steady feature. This is a simple example of patterns that can form when waves interfere in well-defined ways.

There are many more simulations you can try with the Ripple Tank Applet to give you a better understanding of interference and diffraction. Take some time to explore with it.

When there are a large number of wave sources, or an array of obstacles that a wave interacts with, the result is usually described as “diffraction” rather than “interference”, but it is basically the same fundamental process at work.

So, how can you use diffraction to measure the data track spacing on a CD or DVD? The diffraction pattern from a bright, monochromatic source (e.g., a laser pointer) interacting with a regular structure can be described by a fairly simple equation:

d(sin θm – sin θi ) = mλ (Equation 1)

  • In this equation, d is the spacing of the structure (in this case, the data tracks).
  • θm is the angle of the mth diffracted ray, and θi is the angle of the incident (incoming) light. Both angles (θm and θi) are measured from the normal, a line perpendicular to the diffracting surface at the point of incidence (where the light strikes the CD).
  • m is the order of the diffracted ray. The reflected ray (when θm = θi) has order 0 (zero). Rays farther from the normal than the reflected beam have order 1, +2, +3, etc. Rays closer to the normal have order −1, −2, −3, etc. In certain cases, for example very small d, some or all of the negative m orders may actually be diffracted through such a large angle that they are on the same side of the normal as the incident light. When the diffracted beam is on the same side of the normal as the incident light, the angle for the diffracted beam is negative.
  • λ is the wavelength of the light.

The Experimental Procedure section will show you how to produce and measure a diffraction pattern with a CD and laser pointer. It will also show you how to use the equation to calculate the track spacing.

Terms, Concepts and Questions to Start Background Research

To do this project, you should do research that enables you to understand the following terms and concepts:

  • CD, CD-ROM
  • DVD
  • interference
  • diffraction

Questions:

  • DVDs can hold from 7 to 25 times the amount of data on a CD, depending on the DVD format. Do you think the DVD data track spacing will be greater, lesser, or the same as the CD data track spacing? If greater or lesser, how much?

Bibliography

Materials and Equipment

  • laser pointer (with known wavelength)
  • CD
  • DVD
  • protractor
  • index card
  • several pieces of thin cardboard (cereal box, or similar)
  • sturdy box, preferably wooden
  • stack of books
  • black marker
  • calculator with trigonometry functions (sin, cos, tan)
  • digital camera and tripod (optional)

Experimental Procedure

Laser Pointer Safety

Adult supervision recommended. Even low-power lasers can cause permanent eye damage. Please carefully review and follow the Laser Safety Guide.

Procedure 1

  1. The image above shows the experimental setup. It’s a good idea to work near the edge of a table, with good lighting. Here are the important features of the setup, in order of construction:
    1. Place the CD, label-side down, near the center of the workspace.
    2. Put a piece of cardboard to the right of the CD, and another piece of cardboard behind the CD. Both pieces should be about the same thickness as the CD. You will be placing the box on top of all this. The cardboard prevents the box from wobbling.
    3. If you want, put a piece of paper or tissue over the back half of the CD, to prevent scratching.
    4. For measuring the angles, you will attach the protractor to the index card, flush at the bottom. Use a stack of two cardboard spacers at the points indicated, so that the laser pointer can shine down between the index card and the protractor.
    5. Tape the index card to the side of the box (we used a wooden box for holding magazines). The index card and protractor should be flush with the bottom of the box.
    6. Carefully place the box over the CD and cardboard pieces. You want the index card lined up along the diameter of the CD, parallel to the front of the table. The center of the protractor should be lined up midway between the center and the rim of the CD.
    7. A stack of books makes a convenient elbow rest for the person holding the laser pointer. Rest your fingers against the box as shown to help hold the laser pointer steady.
    8. Before you turn on the laser pointer, make sure that no one is in the path of the diffracted beams (the plane of the index card, extended out on both sides and above).
    9. Direct the laser pointer beam down the face of the index card, and align the beam with the center of the protractor. You may have to fiddle slightly before you see a diffraction pattern like the one in the photo. Make your adjustments carefully, keeping the beam as close to parallel with the card as possible.
  2. Making measurements
    1. When the incident and diffracted beams are clearly visible, mark their locations with the marker, or take a digital photo for later analysis. If you are using a marker, start with a fresh index card for each measurement. If you are using a digital camera, make sure that the camera is aligned parallel to the index card, with the frame horizontally centered on the protractor. As a test, it’s a good idea to take a picture of an index card marked with three lines at known angles. Measure the angles with your favorite photo editing program to confirm that your camera is aligned properly.

      Procedure 2
    2. The image above shows how to mark and measure the angles. If you are using a marker, mark the beam locations with dots, and label them. If you are using digital photos, use a photo editing program to draw lines over the beams, starting from the center of the protractor. Remember that angles are measured from the normal (black line in the illustration). For example, θi, the angle of the incident beam, is 20 degrees in the image above. You measure from the normal (90° on the protractor) to the incident beam (70° on the protractor). The angle for the diffracted beam of order m=1 is about +48 degrees. You measure from the normal (90° on the protractor) to the diffracted beam (about 138° on the protractor). This angle is positive because the diffracted beam is on the opposite side of the normal from the incident beam. The angle for the diffracted beam of order m=−1 is about −7 degrees. This angle is negative because the diffracted beam is on the same side of the normal as the incident beam. What is the angle for diffracted beam of order m=−2? Is it positive or negative?

      [Note: Did you notice the small problem with this setup? Examine the protractor closely, and you will see that the positions for 0 and 180 degrees are not flush with the CD. Because of this, the angles measured with this setup will be slightly underestimated. If you do the calculations with the angles given above, you’ll see that the calculated values for data track spacing are reasonable nevertheless. However, a protractor that has 0 and 180 degrees flush with its edge is a better choice.]

    3. Repeat the procedure at least five times. If you are using a marker, remember to start with a fresh index card for each measurement. It is OK to vary the angle of the incident beam with each trial.
    4. Do five trials with a DVD for comparison.
  3. Calculating d, the data track spacing.
    1. Make separate tables for your CD and DVD data, similar to the one below. You’ll fill in the first five columns from your measurements, and you will calculate values for the last four columns. For some angles of the laser pointer, you may not see all of the diffraction orders. In that case, just leave the column corresponding to the missing order blank.

      Trial θi θ+1 θ+2 θ−1 θ−2 d, m=1
      (nm)
      d, m=2
      (nm)
      d, m=−1
      (nm)
      d, m=−2
      (nm)
      1
      2
      3
      etc.

    2. Here is the formula for calculating d:
      d = m × λ / (sin θm − sin θi ) (Equation 2)
    3. Calculate d for each of the non-zero order diffracted rays (i.e., m = +1, +2, −1, −2). For example, for m = −1, and a laser pointer with a wavelength of 655 nm, the formula would be:
      d = (−1) × 655 / (sin θ−1 − sin θi )

      Since we entered the wavelength in units of nm, our answer is also in nm. (To convert to μm, multiply your answer by 1 μm/1000 nm.)

    4. Note: make sure that your calculator is set for entering angles in degrees.
    5. If your laser pointer specifies its wavelength as a range of numbers, use the center of the range as the value for λ. Inexpensive red laser pointers are generally in the 635 – 670 nm range. Green laser pointers are 532 nm.
    6. Calculate the average value for each d column, and, separately, for all of the values of d.

Variations

  • If you measure d for 3 different CDs or DVDs, how do the values compare?
  • How sensitive is the value to the placement of the index card relative to the disk? In other words, if your measurement is not along a diameter of the disk, but instead is along a chord, do you get a different value for the track spacing?
  • If you have a green laser pointer available, do you get the same value for d? (Remember to change λ when you calculate d!)
  • When you calculate the d, for your data table, you are performing the same operations over and over. This is a good chance to add some computer science to your project. Here are two possible ways to go:
    1. Learn how to use JavaScript to create your own data-track spacing calculator using Equation 2, above.
    2. Learn how to use a spreadsheet program (e.g., Microsoft’s Excel or WordPerfect’s QuattroPro). A spreadsheet is basically a huge, blank data table that you can fill in any way you like. You can even program it to do the calculations for you, automatically. Note: if you program the spreadsheet to do the calculations, check the documentation for the spreadsheet’s “sin()” function. It may be expecting angles specified in radians, so you may need to convert your angles from degrees to radians.

Investigating the ‘Mpemba Effect': Can Hot Water Freeze Faster than Cold Water?

September 1, 2008

Objective

The goal of this project is to investigate the question, “Can hot water freeze faster than cold water?” Thorough background research, a precise formulation of the hypothesis, and careful experimental design are especially important for the success of this experiment.

Introduction

It may seem counterintuitive, but folk wisdom and a body of published evidence agree that, under some conditions, warmer water can freeze faster than colder water (for an excellent review on the subject, see Jeng, 2005).

This phenomenon has been known for a long time, but was rediscovered by a Tanzanian high school student, Erasto Mpemba, in the 1960s. He and his classmates were making ice cream, using a recipe that included boiled milk. The students were supposed to wait for the mixture to cool before putting it in the freezer. The remaining space in the freezer was running out, and Mpemba noticed one of his classmates put his mixture in without boiling the milk. To save time and make sure that he got a spot in the freezer, Mpemba put his mixture in while it was still hot. He was surprised to find later that his ice cream froze first (Meng, 2005).

When Mpemba later asked his teacher for an explanation of how his hotter ice cream mixture could freeze before a cooler one, the teacher teased him, “Well all I can say is that is Mpemba physics and not the universal physics” (quote in Jeng, 2005). Mpemba followed his curiosity and did more experiments with both water and milk, which confirmed his initial findings. He sought out an explanation for his findings from a visiting university professor, Dr. Osborne. Work in Dr. Osborne’s lab confirmed the results, and Mpemba and Osborne described their experiments in a published paper (Mpemba and Osborne, 1969).

How can it be that hot water freezes faster than colder water? Somehow, the hot water must be able to lose its heat faster than the cold water. In order to understand how this could happen, you will need to do some background research on heat and heat transfer. Here is a quick summary, so that you can be familiar with the terms you will encounter. Heat is a measure of the average molecular motion of matter. Heat can be transferred from one piece of matter to another by four different methods:

  • conduction,
  • convection,
  • evaporation, and
  • radiation.

Conduction is heat transfer by direct molecular interactions, without mass movement of matter. For example, when you pour hot water into a cup, the cup soon feels warm. The water molecules colliding with the inside surface of the cup transfer energy to the cup, warming it up.

Convection is heat transfer by mass movement. You’ve probably heard the saying that “hot air rises.” This happens because it is less dense than colder air. As the hot air rises, it creates currents of air flow. These circulating currents serve to transfer heat, and are an example of convection.

Evaporation is another method of heat transfer. When molecules of a liquid vaporize, they escape from the liquid into the atmosphere. This transition requires energy, since a molecule in the vapor phase has more energy than a molecule in the liquid phase. Thus, as molecules evaporate from a liquid, they take away energy from the liquid, cooling it.

Radiation is the final way to transfer heat. For most objects you encounter every day, this would be infrared radiation: light beyond the visible spectrum. Incandescent objects—like light bulb filaments, molten metal or the sun— radiate at visible wavelengths as well.

In addition to researching heat and heat transfer, you should also study previous experiments on this phenomenon. The review article by Monwhea Jeng (Jeng, 2005) is a great place to start. The Jeng article has an excellent discussion on formulating a testable hypothesis for this experiment.

Another excellent article, if you can find it at your local library, is by Jearl Walker, in the September, 1997 issue of Scientific American (Walker, 1977). Walker measured the time taken for various water samples to cool down to the freezing point (0°C), not the time for them to actually freeze. He measured the temperature of the water using a thermocouple, which could be placed at various depths in the beaker. Whether you use a thermocouple or a thermometer, it is important that the sensing portion of the device (thermocouple itself, or the bulb of the thermometer) be immersed in the water in order to get accurate readings. Walker used identical Pyrex beakers for his water samples, since they could go from the stove to the freezer without breaking. He used a metal plate over the stove burner to distribute the heat evenly to the beakers as they were heating. He heated the beakers slowly, and he also kept the beakers covered while heating, so that water that evaporated during heating would be returned to the beaker. Walker notes that “You cannot obtain accurate readings by first heating some water in a teakettle, pouring the water into a beaker already in the freezer and then taking a temperature reading. The water has cooled too much by then” (Walker, 1997, 246). Walker also reported that the air temperature in his freezer was between −8 and −15°C. He advises, “To maintain a consistent air temperature be sure to keep the freezer door shut as much as possible” (Walker, 1977, 246). For further details on his experimental procedure and findings, see the original Scientific American article.

The graph in Figure 1 shows some of Walker’s data. The x-axis shows the time it took for the sample to reach 0°C (in minutes). The y-axis shows the initial temperature of the sample (in °C). The graph shows data from six separate experiments (a–f), each with a different symbol:

  1. 50 ml water in small beaker, non-frost-free refrigerator (black squares),
  2. 50 ml water in large beaker, non-frost-free refrigerator (red circles),
  3. 50 ml water in large beaker, frost-free refrigerator (green triangles),
  4. 100 ml water in large beaker, thermocouple near bottom (blue triangles),
  5. 100 ml water in large beaker, covered with plastic wrap, thermocouple near bottom (light blue diamonds),
  6. 100 ml in large beaker, thermocouple near top (magenta triangles).

Under some conditions (b, d, f), he found that samples that were initially hotter reached 0°C faster than samples that were initially cooler, confirming Mpemba’s results. Under other conditions (a, e), hotter samples took as long or longer than cooler samples to reach 0°C. The results for experiment c are equivocal–it’s difficult to say whether the time differences are significant or not.

Redrawing of results from Walker, 1977.
Figure 1. Some of Walker’s results (Walker, 1977). For details, see text.

This project is an excellent illustration that thorough background research, a clear formulation of your hypothesis, and careful experimental design are crucial to the success of an experiment.

Terms, Concepts and Questions to Start Background Research

To do this project, you should do research that enables you to understand the following terms and concepts:

  • Mpemba effect,
  • heat and heat transfer,
    • conduction,
    • convection,
    • evaporation,
    • radiation;
  • phase change.

More advanced students may also want to study:

  • supercooling,
  • nucleation sites for initialization of crystal formation.

Questions

  • How does your freezer work to make things colder?
  • What are some of the mechanisms that have been proposed to explain the Mpemba effect?
  • How would you design an experiment to test one of the proposed explanations?

Bibliography

  • For a news-type article on the subject, see:
    Ball, P., “Does Hot Water Freeze First?” Physics World April, 2006 [accessed March 19, 2007] http://physicsweb.org/articles/world/19/4/4.
  • This review by Monwhea Jeng should be considered essential reading for this project:
    Jeng, M., 2005. “Hot Water Can Freeze Faster Than Cold?!?” PhysicsarXiv:physics/0512262, v1 (29 Dec 2005) [accessed March 20, 2007] http://arxiv.org/PS_cache/physics/pdf/0512/0512262v1.pdf.
  • This Scientific American article has data from actual experiments and includes details of the experimental methods used. It is highly recommended :
    Walker, J. 1977. “The Amateur Scientist: Hot Water Freezes Faster Than Cold Water. Why Does It Do So?” Scientific American 237 (3): 246–257.
  • CEC, 2006. “How Does a Refrigerator Work?” California Energy Commission [accessed March 19, 2007] http://www.energyquest.ca.gov/how_it_works/refrigerator.html.
  • This is the article that renewed interest in the phenomenon, and gave it the name “the Mpemba effect:”
    Mpemba, E.B. and D.G. Osborne, 1969. “Cool?” Physics Education 4:172–175.
  • For contrary views, see this article and the references in it:
    Nave, C.R., 2006. “Hot Water Freezing,” HyperPhysics, Department of Physics and Astronomy, Georgia State University [accessed March 19, 2007] http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/freezhot.html#c1.
  • It’s always a good idea to understand your experimental apparatus. If you use a freezer for your experiment, you should know how it works:
    HowStuffWorks, Inc., 2007. “How Does a Frost-Free Refrigerator Work?” HowStuffWorks.com [accessed March 19, 2007] http://home.howstuffworks.com/question144.htm.
  • CBSE Blog: http://cbse-sample-papers.blogspot.com

Materials and Equipment

  • identical Pyrex beakers for holding water,
  • metal plate for stove burner to distribute heat evenly,
  • cover for the beaker during heating,
  • two thermometers,
  • freezer (or other means for cooling water below freezing point),
  • stove (or other means of heating the water),
  • hot mitt,
  • gram scale,
  • clock or timer.

Experimental Procedure

  1. Do your background research so that you are knowledgeable about the terms, concepts and questions, above. You should also do as much research as possible on previous experiments related to this phenomenon. The articles by Jeng and Walker (Jeng, 2005; Walker, 1977) are highly recommended.
  2. Choose 4 or more initial temperatures to test, and follow the same standard procedure for each initial temperature. For example:
    1. Measure a chosen volume of water (e.g., 50 ml) into a Pyrex beaker.
    2. Cover the beaker so that water vapor will be captured and returned.
    3. Heat the water to the desired initial temperature.
    4. Quickly weigh the beaker and water and then place in the freezer.
    5. Monitor the temperature at regular intervals, and record how long it takes for the temperature to reach 0°C.
    6. Weigh the beaker and water at the end of the experiment to see how much water evaporated while it was in the freezer. (You can let the beaker warm up, so that there is no condensation on it, but keep it covered so that water does not evaporate.)
    7. Repeat the experiment at least three times for each chosen initial temperature.

Variations

There are many possible explanations for the Mpemba effect which you could choose to explore. You can think of your own variation on this experiment, or explore one or more of these variables:

  • the method used for freezing, (e.g.: freezer compartment of your refrigerator, rock salt and ice bath, dry ice and alcohol bath, walk-in freezer, outdoors in sub-freezing weather),
  • the method used for controlling evaporation, (e.g.: either covering the containers, or adding a layer of oil on top of the water should reduce evaporation),
  • container material, size, and shape,
  • endpoint of the experiment: wait for freezing solid instead of reaching 0°C.

Science Projects {Physics}~Simple Harmonic Motion in a Spring-Mass System*

September 1, 2008

Objective

In this science fair project you will investigate the mathematical relationship between the period (the number of seconds per bounce) of a spring and the load (mass) carried by the spring. Based on the data you collect, you will be able to derive the spring constant, as described in Hooke’s Law, as well as the effective mass of the spring.

Introduction

This project requires very simple materials to explore the physics of periodic motion. All you need is a mini Slinky® and some weights, such as small fishing sinkers. The period of the Slinky is the time it takes to go through one down-and-up cycle when it is hung vertically from one end. The spring with the weight is a simple harmonic oscillator, which is a system that follows Hooke’s law. Hooke’s law states that when the simple harmonic oscillator is displaced from its equilibrium position, it experiences a restoring force, F, proportional to the displacement, x, where k is a positive constant:

Hooke’s Law: F = -kx

Physics Science Project simple harmonic oscillator

As you add weights to the spring, the period (or cycle time) changes. In this project, you will determine how adding more mass to the spring changes the period, T, and then graph this data to determine the spring constant, k, and the equivalent mass, me, of the spring. The equation that relates period to mass, M, is shown below:

Physics Science Project equation 1

<!–Equation 1: M = k (T2/4 2)–>

  • M is the load on the spring in kilograms (kg).
  • k is the spring constant in units of Newtons/meter (N/m).
  • T is the period in seconds (sec).

In an ideal spring-mass system, the load on the spring would just be the added weight. But real springs contribute some of their own weight to the load. That is why the Slinky bounces even when there is no weight added. So the equation can be modified to look like this:

Physics Science Project equation 2

<!–Equation 2: M = m + me = k (T2/4 2)–>

In this equation, the total mass pulling down on the spring is actually comprised of two masses, the added weight, m, plus a fraction of the mass of the spring, which we will call the mass equivalent of the spring, me. Rearranging equation 2, will give you the form of the equation you will use later for graphing, so:

Physics Science Project equation 3

<!–Equation 3: m = k (T2/4 2) – me–>

Based on this equation, if you graph the added mass, m vs. Physics Science Project equation , you will be able to find the spring constant, k, and the mass equivalent, me, of the spring.

Terms, Concepts and Questions to Start Background Research

To do this project, you should do research that enables you to understand the following terms and concepts:

  • Simple harmonic oscillator
  • Hooke’s law
  • Simple harmonic motion
  • Physics of springs
  • Spring constant

Questions

  • How does adding mass change the period of a spring?

Bibliography

Materials and Equipment

To do this project, you will need the following materials and equipment:

  • Mini Slinky
  • Weights to hang from the spring. Here are some tips:
    • Fishing sinkers work well since they have holes in them for attaching to the spring. You could also use hex nuts, or AAA batteries attached to the wire with tape.
    • You will need five identical items to get a spread of data for the graph. The total weight should be around 35 g, or approximately 1 ounce.
    • Depending on the weights you choose, you might need fine wire or string to attach the weights to the spring.
  • A scale for measuring actual mass of weights used, accurate to +/- 1 gram. Use an electronic kitchen scale, a scale from your school lab, or a postal scale.
  • Stopwatch, or clock with a second hand
  • Lab notebook
  • Graph paper

Experimental Procedure

  1. Do your background research so that you are knowledgeable about the terms, concepts, and questions above. Be sure to record your data in your lab notebook as you go along.
  2. Measure the mass of one of your weights, using the scale. If your scale does not measure small weights, you can weigh all five of your weights and divide by five. Then measure the mass of the spring.
  3. Perform the following steps to collect your data:
    1. Hold one end of the spring in your hand and let it bounce gently down and then back up.
    2. Count the number of cycles the spring makes in 60 sec with no weight hanging from it.
    3. Hang one weight from the spring (using a fine wire or string, if needed).
    4. Count the number of cycles the spring goes through in 60 sec with the weight attached.
    5. Perform at least three trials for each weight.
    6. Repeat steps c-e for a series of different weights.
  4. Keep track of your results in a data table like this one. Try using the program Microsoft Excel to make the tables and perform the calculations when you work through this project. Each of the tables below has some example data to help you with your calculations.
    Load (mass added to spring)
    (g)
    Number of cycles per 60 sec Average
    Trial #1 Trial #2 Trial #3
    0
    6
    12
    18
    24 48 49 47 48
    30 41 41 41 41
  5. Make another table like the one below to convert your raw data into numbers that can be used to determine the spring constant and spring’s effective mass.
    A B C D E
    Added mass (kg) Average # cycles in 60 sec
    (1/min)
    f, the frequency, or cycles per second
    (1/sec)
    T, the period of spring, or the time for each cycle (sec) (sec 2)
    Convert to kilograms From the table above Divide “Average # cycles in 60 sec” in column B by 60 Reciprocal of cycles per second in column C (divide 1 by the numbers in column C) Multiply value in column D by itself and divide by 4(pi)2
    0.007 48 0.8 1.25 0.0396
    0.028 41 0.68 1.46 0.05395
  6. Make a graph with “Added mass,” m, in kilograms, on the y-axis, and , in sec2, on the x-axis. Use kilograms rather than grams so that the value of k is in units of N/m, which is equivalent to kg/sec2. Usually you are instructed to graph the independent variable (mass in this case) on the x-axis and the measured parameter () on the y-axis. You should ignore this rule in this project since graphing m on the y-axis will let you read me from the y-intercept.

    This graph of m vs. has the same terms found in Equation 3:

    Physics Science Project equation 3

    <!–Equation 3: m = k (T2/4 2) – me–>

    Let’s look at the equation. It has a form similar to the equation of a straight line: y = ax + b, where a is the slope and b is the y-intercept. In fact, Equation 3 is an equation for a straight line, with slope equal to k, the spring constant, and y-intercept equal to the negative value of me. In other words, there is a linear relationship between m and (), so a graph of m vs. () will be a straight line with slope k and y-intercept -me. The reason you calculated was to be able to read the values of k and me from the graph of m vs. .

    Physics Science Project graph

    How do you determine the slope of the line you have drawn? The slope is measured as change in m, divided by the change in , over the same range.

    slope = k = Δm/Δ()

    Δm/ Δ() can be read as “delta m over delta “, with the Greek letter for delta, Δ, indicating “change of.” Make another table like the one below to find the slope. Pick points that are near the ends of the graph, rather than adjacent points.

    Added mass (kg) (sec2) Δy (kg) Δx (sec2) Δy/ Δx
    (kg/sec2)
    Subtract one y value from another, larger y value Subtract one x value from another, larger x value This is the spring constant, k, in units of N/m (kg/sec2)
    0 0.02 0.027 – 0 = 0.027 0.05-0.02 = 0.03 0.027/.03 = 0.900
    0.027 0.05

    Once you have determined the value of the spring constant, k, from the slope of the line, you’re ready to determine the effective mass of the spring. To do this, extend the straight line until it intersects the vertical y-axis. The line will intersect the y-axis at -me (negative me). Based on theoretical considerations, the absolute value of me should be around one-third of the mass of the spring.

Science Projects {Physics}~Distance and Constant Acceleration

September 1, 2008

Objective

The objective of this project is to determine the relation between elapsed time and distance traveled when a moving object is under constant acceleration.

Introduction

You know from experience that when you ride your bike down a hill, it’s easy to go fast. Gravity is giving you an extra push, so you don’t have to do all the work with the pedals. You also know from experience that the longer the hill, the faster you go. The longer you feel that push from gravity, the faster it makes you go. Finally, you also know that the steeper the hill, the faster you go.

The maximum steepness is a sheer vertical drop—free fall—when gravity gives the biggest push of all. You wouldn’t want to try that on your bicycle!

In free fall, with every passing second, gravity accelerates the object (increases its velocity) by 9.8 meters (32 feet) per second. So after one second, the object would be falling at 9.8 m/s (32 ft/s). After two seconds, the object would be falling at 19.5 m/s (64 ft/s). After three seconds, the object would be falling at 29 m/s (96 ft/s), and so on.

Measuring the speed of objects in free fall is not easy, because they fall so quickly. There is another way to make measurements of objects in motion under constant acceleration: use an inclined plane. An inclined plane is simply a ramp. You’re making a hill with a constant, known slope. With a more shallow slope, the acceleration due to gravity is small, and the object will move at a speed that is more easily measured.

This project will help you make some scientific measurements of the “push” from gravity, using a marble rolling down an inclined plane, with a metronome for measuring time.

Terms, Concepts and Questions to Start Background Research

To do this project, you should do research that enables you to understand the following terms and concepts:

  • velocity,
  • acceleration,
  • inclined plane,
  • mass,
  • gravity.

Questions

  • What is the formula for velocity as a function of time when an object is subject to constant acceleration?
  • What is the formula for distance traveled as a function of time when an object is subject to constant accleration?

Bibliography

Materials and Equipment

To do this experiment you will need the following materials and equipment:

  • inclined plane:
    • you’ll need a flat board, about 2 m long (longer is better unless you are using a video camera);
    • cut a groove straight down the middle to guide the rolling marble, or
    • glue a straight piece of wood along the length of the board to act as a guide;
    • mark a starting line across one end;
    • you will also need some wood blocks (about 2.5 cm thickness) to raise up one end of the board.
  • tape measure (for measuring height and length of inclined plane),
  • marble,
  • metronome,
  • helper,
  • pencil.

Experimental Procedure

In this experiment, the goal is to measure the distance the marble travels in equal time intervals as it rolls down an inclined plane.

  1. Set up your inclined plane on a single block, so that it has a low slope. If the slope is too high, the marble will roll too fast, and it will be too hard to make accurate measurements.
  2. Hold a marble in place at the starting line.
  3. Use a metronome to keep track of equal time intervals.
    1. You can set the number of beats per minute that the metronome will sound.
    2. 60 beats per minute would give you one tick every second.
    3. 120 beats per minute gives you two ticks every second, or one tick every half-second.
    4. We suggest that you start with one tick every second.
  4. In time with a tick, release the marble, being careful not to give it a push as you let go.
  5. Have your helper mark where the marble is at the first tick after release.
  6. Measure and record the distance (cm) from the starting line.
  7. Repeat this 10 times.
  8. Next your helper will mark where the marble is at the second tick.
  9. Measure and record the distance (cm) from the starting line.
  10. Repeat this 10 times.
  11. Keep repeating the process for each successive tick, making 10 measurements for each tick, until the tick when the ball goes past the end of the inclined plane.
  12. Calculate the average and standard deviation for the distance the marble has traveled at the end of each tick.
  13. Graph the average distance traveled (y-axis) vs. time, in terms of the number of ticks (x-axis).
  14. Graph the average distance traveled (y-axis) vs. time squared. Compare the two graphs.
  15. Another way to see the relationship between time and distance traveled with constant acceleration is is to use the distance traveled during the first “tick” as the distance unit instead of centimeters. How many of these distance units has the ball traveled by the second tick? By the third tick? By the fourth tick? By the fifth tick?

Variations

  • Does the mass of the marble affect its acceleration? Try the experiment with marbles of different masses. Or, even better, compare a steel marble (e.g., a pinball or a large ball bearing) with a glass marble of the same diameter. Use a gram balance to weigh each marble (you can always weigh them at the post office if you don’t have a gram balance available at home or school). Is the acceleration the same or different for the marbles with different masses?
  • For another method of measuring distance traveled and velocity of an object rolling down an inclined plane, see the Science Buddies project, Distance and Speed of Rolling Objects Measured from Video Recordings.
  • Use your measurements to calculate the approximate velocity of the marble at each tick. As an example, to calculate the average velocity at the second metronome tick, take the distance the marble has traveled by the second tick, and subtract the distance the marble traveled by the previous tick. Divide the result by the amount of time per tick. Repeat this calculation for several successive time points to see how velocity changes as the marble rolls down the ramp. Make a graph of velocity (y-axis) vs. time (x-axis). Does this graph look more like the distance vs. time or the distance vs. time squared graph?
  • One reason a marble was chosen for this experiment was to minimize the frictional forces which counteract the acceleration of gravity. Try repeating the experiment with other rolling objects (e.g., a toy car with the same mass as the marble) or different surface treatments (e.g., smooth, waxed surface, vs. rough, sandpapered surface). Can you detect a decrease in acceleration due to increased friction?
  • For more advanced students:
    • If you have studied trigonometry, you should be able to derive a formula that describes the acceleration, a, of the marble as function of the angle, θ, of the inclined plane (see Henderson, 2004).
    • If you have studied calculus, you should be able to explain both velocity and acceleration as the first and second derivatives, respectively, of distance traveled with respect to time. Conversely, you should be able to explain velocity and distance traveled at a given time as the first and second integrals, respectively, of acceleration with respect to time.

Science Projects {Physics}~Going the Distance: Launch Angles & Projectile Trajectory

September 1, 2008

Objective

The goal of this project is to determine which launch angle results in the greatest distance for a projectile.

Introduction

This project is about projectile motion, specifically, how the launch angle affects the distance that a projectile will travel. You’ll build a spring-powered mechanical launcher using pieces of PVC pipe, a wood frame, and fastening hardware, so this is a project for someone who is handy with tools.

Before you start designing and building your launcher, you should do some background research on the physics of projectile motion. The Bibliography section has some good resources to get you started. Think about the forces that act on a projectile in flight, and make a prediction about the launch angle that will result in the longest flights. The student-written “Water Balloons” site (Terrence and Jason, 1996) has a great balloon-launching simulation that you can use to make some preliminary tests.

To test your hypothesis in the real world, you’ll want a launcher that will make it easy to change the launch angle while keeping the other variables (e.g., projectile mass, force used to launch the projectile) constant. The instructions below will assist you with your design. Remember to have an adult present when you do the test launches to make sure that they are done safely. Then it’s bomb’s away and may the best launch angle win!

Terms, Concepts and Questions to Start Background Research

To do this project, you should do research that enables you to understand the following terms and concepts:

  • Mass
  • Velocity
  • Range
  • Launch angle
  • Gravity
  • Projectile motion

Questions

  • What forces act on a projectile in flight?

Bibliography

Materials and Equipment

To do this experiment you will need the following materials and equipment:

  • 1-1/2 in diameter PVC pipe (main body of launcher), 75 cm length
  • 1 in diameter PVC pipe (launcher barrel), 45 cm length
  • Wooden dowel, 77 cm length, diameter to fit inside plastic sleeve
  • 9/16″ ball bearings (projectile)
  • 2 U-bolts with nuts and washers for attaching launcher to launch frame
  • Spring (fits over dowel, provide driving force, 20 Newtons)
  • Large washer (attach to dowel to push against spring, must fit inside launcher barrel)
  • Wood screws (to hold washer in place)
  • Copper sleeve (to keep launcher barrel fixed inside main body)
  • Plastic sleeve (to keep dowel from wobbling in barrel)
  • Pipe cap with hole (allows ball bearing to be launched, but holds dowel inside the barrel)
  • 1 in × 4 in lumber for launcher frame (approx. 8 ft required)
  • Hinge and wood screws for mounting
  • PVC cement
  • Tools:
    • Drill and bits
    • Saw
    • PVC pipe cutter
    • Screw driver
    • Tape measure
    • Protractor

Experimental Procedure

Safety Notes:

  • The apparatus described for this experiment should only be operated with adult supervision.
  • Injury is possible if adequate safety precautions are not followed.
  • Make sure no one is near the projectile’s path!
  • Test fire with only partial spring compression, and build up gradually to full power to make sure that you have sufficient space.
  1. Do your background research so that you are knowledgeable about the terms, concepts, and questions, above.
  2. The illustration below shows an example of the kind of launcher you can build for this project.
    projectile launcher made from PVC pipe with wood frame
    The projectile launcher is made from PVC pipe mounted on a wood frame. The frame is hinged at the base so that the launch angle can be easily adjusted.
    1. The launcher is made from PVC tubing. An outer tube (1-1/2 in diameter) is attached to the wood frame using two U-bolts. (Note: it should also be possible to omit the outer tube and attach the barrel directly to the frame.)
    2. The barrel of the launcher is the inner tube of PVC (1 in diameter). It fits inside the outer tube, held snugly in place with some short lengths of copper sleeve.
    3. A wooden dowel is placed inside the barrel, with a large washer attached near the midpoint, and a spring around the dowel below the washer. A string is firmly attached to the dowel in order to pull against the spring to “cock” the launcher.
    4. The lower end of the outer tube is covered with a PVC cap, cemented in place. The cap is drilled so that the dowel passes through, but not the spring (see detail photo, below).
      projectile launcher made from PVC pipe with wood frame
      Detail view of the base end of the projectile launcher. A PVC cap holds the spring in place inside the barrel. The dowel passes through a hole in the cap. The string is used to pull the dowel back against the spring to “cock” the launcher.
    5. The launcher frame can be fashioned from 1 in × 4 in lumber and a hinge.
    6. Prop the frame open with short pieces of 1 × 4 to achieve different launch angles.
  3. Be safe when using the launcher!
    1. The apparatus described for this experiment should only be operated with adult supervision.
    2. Injury is possible if adequate safety precautions are not followed.
    3. Make sure no one is near the projectile’s path!
    4. Test fire with only partial spring compression, and build up gradually to full power to make sure that you have sufficient space.
  4. Measure the distance that the ball bearing travels for several different angles, e.g. 15°, 30°, 40°, 45°, 50°, and 60°.
    1. Use at least 10 trials for each angle.
    2. Use the same spring compression for every shot, i.e., pull the dowel back the same distance each time.
    3. Use the same projectile for each test.
  5. Calculate the average distance traveled for each angle.
  6. More advanced students should also calculate the standard deviation of the distance traveled for each angle.
  7. Which launch angle resulted in the greatest distance traveled?

Variations

  • You could extend the experiment by testing additional launch angles.
  • How does the mass of the projectile affect the distance it will travel, when the same force and launch angle are used? Design an experiment to find out.

Science Projects {Physics}~Measuring the Surface Tension of Water

September 1, 2008

Objective

The goal of this project is to use a homemade single-beam balance to directly measure the surface tension of a liquid.

Introduction

You’ve seen examples of surface tension in action: water striders walking on water, soap bubbles, or perhaps water creeping up inside a thin tube. What, exactly, is surface tension?

Surface tension is defined as the amount of energy required to increase the surface area of a liquid by a unit amount. So the units can be expressed in joules per square meter (J/m2). You can also think of it as a force per unit length, pulling on an object (Mellendorf, 2002). In this case, the units would be in newtons/meter (N/m). Since the forces are so small, you often see surface tension expressed in millinewtons per meter (mN/m — 1 mN is 1/1000 N). It’s a good exercise to do the dimensional analysis and prove that both ways of expressing surface tension—J/m2 and N/m—are equivalent. If you need a refresher on your units of energy and force, there is a good reference in the Bibliography.

The force arises from the mutual attraction between the molecules of the liquid. Do background research on the chemistry of water to learn more about its intermolecular attractions. In particular, you should study up on hydrogen bonding.

In this experiment, you will be making and using a single beam balance to measure the force exerted by surface tension on a needle, floating on the surface of the water. The needle will be attached to your balance, and you will measure how much force is required to pull the needle out of the water. The surface tension of the water is providing the resistance. From your measurements, you will be able to calculate the surface tension of water.

Terms, Concepts and Questions to Start Background Research

To do this project, you should do research that enables you to understand the following terms and concepts:

  • surface tension,
  • water molecules,
  • hydrogen bonding of water molecules,
  • detergent,
  • force.

Questions:

  • Considering what you have learned about hydrogen bonding in your background research:
    • will adding detergent to water increase or decrease the surface tension?
    • will adding rubbing alcohol to water increase or decrease the surface tension?

Bibliography

Materials and Equipment

To construct a homemade single-beam balance (see Figure 1 in the Experimental Procedure section), you will need the following:

  • a beam (e.g., drinking straw, piece of stiff cardboard, wooden or plastic ruler),
  • a fulcrum (e.g., a pin or nail),
  • 2 supports of equal height (e.g., two books arranged back-to-back with a small space between them, two cans, two wood blocks),
  • pan for weights (you can make this from foil),
  • needle (or 5 cm length of straightened paper clip wire),
  • thread (for attaching pan and needle to balance),
  • small bit of modeling clay to counterbalance the empty pan.

You will also need:

  • a small bowl,
  • water,
  • liquid detergent,
  • plus any other liquids whose surface tension you would like to measure (e.g., rubbing alcohol, cooking oil).

Finally, you will need:

  • weights (common pins, drops of water from an eyedropper),
  • and a way to calibrate them (self-service scale at post office, 10 ml graduated cylinder).

Experimental Procedure

  1. Do your background research.
  2. Gather the materials and find a good place to work.
    Diagram of a simple single-beam balance
    Figure 1: Diagram of a simple single-beam balance
  3. Constructing the balance (refer to Figure 1).
    1. Take your time and work carefully. You’ll get better results.
    2. First construct the beam.
      1. There are many choices for materials. You just need something stiff enough to support a few grams at each end.
      2. You’ll need to mark the center point for the fulcrum. Depending on your choice of material, either drill a hole for the fulcrum (e.g., for wood), or simply push it through (e.g., pin through a drinking straw). The beam needs to rotate freely about the fulcrum.
      3. You’ll also need to make holes at each end of the beam, equidistant from the center. Attach loops of thread through the holes (paper clips, or ornament hangers could also work), as shown.
      4. Push the fulcrum through the center hole of the beam, and place it on the supports.
    3. Next construct the pan.
      1. This can be a simple box or dish folded from aluminum foil. (It’s square in the diagram only because it was easier to draw.)
      2. If you make a round pan, three strings will work fine for supporting it.
    4. Tie a thread to the center of your needle or paperclip wire. Adjust the thread so that the needle or wire hangs horizontally.
  4. Measuring surface tension.
    1. Hang the pan from one end of the beam and the needle from the other. Use a small piece of modeling clay as a counterbalance (as shown in Figure 1) to balance the needle and empty pan.
    2. Place your container of water so that the needle (or wire), still hanging horizontally, is submerged in the water.
    3. You will add small amounts of weight to the pan, and measure the force needed to pull the needle (or wire) free from the surface of the water.
    4. It will not take much weight, so you need to add it in small increments. Here are two different methods you could try.
      1. Use common pins as your weights, adding them one at a time. Calibrate them by weighing a bunch of pins on a postal scale, and dividing by the number of pins to get the weight per pin.
      2. Use drops of water from an eyedropper or plastic transfer pipette. You can calibrate the water drops by counting how many drops are needed to make, say, 5 ml. Each ml of water weighs 1 g, so with your count you can calculate how much each drop weighs.
      3. Try both methods and see how your results compare!
    5. Repeat the measurement (steps 1–3) at least 5 times (more is better), to assure consistent results. If something goes wrong (e.g., you accidentally tap the pan and pull the needle out of the water), repeat the trial from the beginning.
    6. Average your results.
    7. The force you will be measuring can be expressed by the equation:
      F = 2sd, where
      • F is the force, in newtons (N),
      • the factor of 2 is because the film of water pulled up by the needle (or wire) has 2 surfaces,
      • s is the surface tension per unit length, in units of newtons/meter (N/m), and
      • d is the length of the needle (or wire), in units of meters (m).
    8. To convert grams to the force, F, you have to account for gravity pulling down on the mass in the pan. Do this by multiplying the mass (in grams) by 9.83×10-3 N/g (for more information, see the link on “Gravitational Force” in the Bibliography).
    9. You can rearrange the equation above to solve for s, the surface tension of water. Measure the length of the needle (or wire), and you’ll have all the information you need to calculate the surface tension of water.
    10. How do you know that you are measuring surface tension, and not an attractive force between the needle (or wire) and the water? Here’s a good tip from Robert Gardner’s book (Gardner, 2004). Surface tension is the cohesive force between water molecules. Observe the needle (or wire) carefully after it is pulled out of the water. If it remains wet, then it must be the water that pulled apart, and this is the force (surface tension) that you measured. If it is dry, then the adhesive force between the water and the needle broke first, and this is what you measured, not surface tension.

Variations

  • Add a drop of liquid dish detergent to the water in your dish, mix it by stirring gently (you don’t want a lot of bubbles), and measure the surface tension again. Do you think it will be higher or lower than for plain tap water?
  • Try measuring the surface tension of other liquids, (e.g., rubbing alcohol, cooking oil). Remember note 2j, in the Experimental Procedure section.

Science Projects {Physics}~How Does Color Affect Heating by Absorption of Light?

September 1, 2008

Objective

The goal of this project is to see how the color of an object affects how much heat it absorbs when exposed to incandescent light.

Introduction

Light is an example of an electromagnetic wave. Electromagnetic waves can travel through the vacuum of interstellar space. They do not depend on an external medium—unlike a mechanical wave such as a sound wave which must travel through air, water, or some solid medium. Electromagnetic waves cover a huge range of frequencies, from high-frequency gamma rays and x-rays, to ultraviolet light, visible light, and infrared light, and on into microwaves and radio waves. As the frequency decreases, so does the energy. The wavelength of an electromagnetic wave is inversely proportional to its frequency. So waves with high frequency have short wavelengths, and waves with low frequency have long wavelengths.

Electromagnetic waves interact with materials in different ways, depending on the nature of the material and the frequency of the electromagnetic wave. Light is the range of electromagnetic waves that are visible (Figure 1). For humans, the range of visible wavelengths is from 400 to 700 nm (1 nm = 1 ×10−9 m).

the visible spectrum
Figure 1. The visible spectrum. X-rays, light, and radio waves are examples of electromagnetic waves. Light is the part of the electromagnetic spectrum that we can detect with our eyes. At the blue end of the visible spectrum, the wavelength of light is shorter (about 400 nm). At the red end of the spectrum, the wavelength of light is longer (about 700 nm) (Illustration from Abrisa Glass & Coatings, 2005).

This range of wavelengths is called the visible spectrum of light. When you see a rainbow in the sky, or white light that has been refracted through a prism, or diffracted by the regular surface of a CD, you are seeing a spectrum of colors. The different colors are related to the different wavelengths of light. Violet light is at the short-wavelength end of the visible spectrum (400 nm), and red light is at the long-wavelength end of the visible spectrum (700 nm), with the rainbow of colors in between.

We perceive different colors because our visual system has evolved to make use of the spectral information in reflected light. When light interacts with an object, the light can be absorbed by the object, reflected by the object, or transmitted by the object.

For example, when you look at yourself in the mirror, the light that you are seeing has been relected by the mirror, transmitted through the air, through your cornea, through the lens of your eye, and through two layers of cells in your retina before it is absorbed by light-sensitive pigments in your photoreceptor cells. The energy from the absorbed light starts a cascade of chemical reactions in your photoreceptors that ultimately leads to your percpeption: seeing yourself in the mirror.

Objects in the world have different colors depending on which parts of the visible spectrum they absorb, and which parts of the visible spectrum they reflect. Red objects reflect long wavelengths of light (and absorb shorter wavelengths), while blue objects reflect short wavelengths of light (and absorb longer wavelengths). Black objects absorb all visible wavelengths about equally, and white objects reflect all visible wavelengths about equally.

Light that is absorbed by an object is usually converted into heat energy. The goal of this project is to measure how much heat is produced by the absorption of light by different colors. You’ll use an incandescent light (a heat lamp), and water-filled jars wrapped with different colors of construction paper. By measuring how much the temperature of the water increases, you’ll have a measure of how much light was absorbed by each color.

Before you get started, study Figure 2 below and then try to predict what your results will be. The graph compares the spectrum of sunlight with the spectrum of an incandescent bulb. You can see that sunlight has much more energy (brightness) in the range of visible wavelengths (gray shaded region), while the incandescent bulb has more energy in the red and infrared (invisible, longer-wavelength electromagnetic radiation) region of the spectrum.

spectrum of sunlight vs. spectrum of an incandescent light
Figure 2. A comparison of the spectrum of sunlight vs. the spectrum of an incandescent bulb (Schroeder, 2003). The x-axis shows the wavelength (in microns), and the y-axis shows the relative energy (brightness) at each wavelength. The gray region corresponds to the visible region of the spectrum (0.4–0.7 μm = 400–700 nm).

Terms, Concepts and Questions to Start Background Research

To do this project, you should do research that enables you to understand the following terms and concepts:

  • electromagnetic spectrum,
  • visible light,
  • ultraviolet light,
  • infrared light,
  • absorption of light,
  • reflection of light.

Questions

  • How does an incandescent light bulb work?
  • What wavelength is the peak output for an incandescent bulb?

Bibliography

Materials and Equipment

To do this experiment you will need the following materials and equipment:

  • 6–8 identical glass jars, 1 quart size, with lids,
  • 6–8 sheets of colored construction paper (different colors),
  • scissors,
  • tape,
  • water,
  • thermometer,
  • modeling clay,
  • heat lamp,
  • timer or clock,
  • drill and bit for making holes in jar lids.

Experimental Procedure

  1. Drill a hole slightly larger than the diameter of your thermometer in the lid of one jar. (In this project you’ll be testing the jars one at a time, so you can use the same lid with each jar.)
  2. Tightly wrap each jar with a different color of construction paper.
  3. Carefully fill each jar with water.
    1. Keep the construction paper dry.
    2. You need to have the same starting temperature for each jar. The easiest way to do this is to have all of the jars at room temperature. Fill them with water that is about the same temperature the day before you want to start your experiment. Cover the jars and leave them to equilibrate to room temperature overnight.
  4. Cover the jar to be tested with the lid with the drilled hole.
  5. Put the thermometer in through the hole so that its bulb is completely immersed in the water. Use the clay to seal the hole and hold the thermometer in place. The rest of the thermometer will be out of the jar, and you should still be able to take readings with it. Keep the thermometer at the same height with respect to the jar lid for all of the tests.
  6. Note the starting temperature for each jar.
  7. Next, set up your heat lamp in a convenient location, so that it can shine directly at the side of a jar placed between 15–30 cm away. (Decide on an exact distance, and use it for all of the tests.)
  8. Set the jar to be tested at the correct distance, centered in front of the heat lamp.
  9. Leave the jar in front of the lamp for a set amount of time (e.g., 30 min), and check the temperature of the jar when that time has elapsed.
    1. Be sure to make the time interval long enough so that there is a measurable increase in temperature.
    2. Be sure to use the same time interval for each jar.
  10. Repeat until all of the jars have been tested.
  11. You should do at least three separate trials for each color, with each trial starting with water at room temperature. (It may take more than one day to do your measurements, so plan ahead!)
  12. Analyze your results.
    1. What was the average increase in temperature for each color?
    2. Make a bar graph to show your results, ordering the colors from lowest to highest temperature increase.
    3. How does the arrangement of the colors in your bar graph compare to the spectrum of incandescent light?

Variations

  • Compare temperatures of the jars when exposed to sunlight instead of incandescent light. You’ll need a separate thermometer for each jar, and a location where all of the jars receive the same amount of sunlight for a defined time period. As in the experiment described above, you should conduct at least three separate trials. How does the spectrum of sunlight compare to the spectrum of incandescent light? Are the results of your experiment the same or different with sunlight compared to incandescent light?

Science Projects {Physics}~The Joly Photometer: Measuring Light Intensity Using the Inverse Square Law

September 1, 2008

Objective

The goal of this project is to measure the relative intensity of different light bulbs, using a simple photometer that you can build yourself.

Introduction

Intro image

As you move away from a light source, the light gets dimmer. No doubt you’ve noticed this with reading lamps, streetlights, and so on. The diagram at right shows what is happening with a picture. At the center, the yellow star represents a point source of light. Imagine the light from the star spreading out into empty space in all directions. Now imagine the light that falls on a square at some arbitrary distance from the star (d = 1, yellow square). Move away, doubling the distance from the star (d = 2). The light from the original square has now “spread out” over an area of 4 (= 22) squares. Thus, at twice the original distance, the intensity of the light passing through a single square will be 1/4 of the original intensity. Going out still further, tripling the original distance (d = 3), and the light from the original square now covers an area of 9 (= 32) squares. Thus, at three times the original distance, the intensity of the light passing through a single square will be 1/9 of the original intensity. This is what is meant by the “Inverse Square Law.” As you move away from a point light source, the intensity of the light is proportional to 1/d2, the inverse square of the distance. Because the same geometry applies to many other physical phenomena (sound, gravity, electrostatic interactions), the inverse square law has significance for many problems in physics.

In this project you’ll build a simple photometer, invented by the Irish scientist, John Joly. As you’ll see, the design of the photometer is based on the inverse square law. In the Joly photometer, two equal-sized blocks of paraffin wax are separated by a layer of aluminum foil. The wax blocks are mounted in a box with windows cut out on the left, front, and right sides, as shown in Figure 1.

mount the wax blocks in a small cardboard box with windows cut in the left, front, and right sides
Figure 1. Diagram of a Joly photometer. Inside the box are two equal-sized blocks of paraffin wax, separated by a sheet of aluminum foil.

The photometer is positioned between two light sources (see Figure 2). The two light sources and the center of the photometer should all be at the same height. Light from the first source illuminates the left-hand paraffin block. Light from the second source illuminates the right-hand paraffin block. To insure uniform illumination, the distance from each light source to the photometer should be relatively large compared to the size of the wax block. Also, there should be no other light sources in the room. The experimenter views the photometer through the front window and moves it back and forth between the two light sources until both blocks appear equally bright. The photometer should be moved along an imaginary straight line connecting the two light sources.

schematic diagram of Joly photometer experimental setup
Figure 2. schematic diagram of Joly photometer experimental setup. See text for details.

When the two wax blocks are equally illuminated, the relationship between the intensities of the two light sources is determined by the inverse square law. Here is the relationship in the form of an equation:

inverse square law relation between the intensities of the two light sources

You can build your own Joly photometer and use it to measure the relative intensity of different light bulbs. Using the wattage of each bulb, you can also compare how efficient different bulbs are at producing light.

Terms, Concepts and Questions to Start Background Research

To do this project, you should do research that enables you to understand the following terms and concepts:

  • inverse square law,
  • incandescent light bulbs,
  • compact fluorescent light bulbs,
  • photometer.

Questions

  • How do incandescent light bulbs work?
  • How do incandescent light bulbs wear out?
  • How do compact fluorescent light bulbs work?
  • How do incandescent light bulbs wear out?
  • Which type of bulb lasts longer?
  • Which type of bulb is more efficient at producing light?

Bibliography

Materials and Equipment

To do this experiment you will need the following materials and equipment:

  • 1 lb. box of paraffin wax (contains 4 slabs),
  • sharp knife for cutting wax,
  • aluminum foil,
  • small cardboard box,
  • scissors,
  • two identical light fixtures (e.g., clamp-on work lamp),
  • measuring tape,
  • various light bulbs to test.

Experimental Procedure

Building the Photometer

  1. You should be able to find one-pound boxes of paraffin wax at your local grocery or hardware store. Each box contains four slabs of paraffin wax.
  2. Cut one slab of the wax in half with a sharp knife. Work carefully so that you don’t chip or break the slab.
    cutting the wax slab in half
  3. Cut a piece of aluminum foil to the same size as your two blocks of wax, and place it in between them.
    aluminum foil goes in between the two blocks of wax
  4. Use tape and small pieces of cardboard to mount the wax blocks inside a small cardboard box, with windows cut on three sides, as in the diagram below.
    mount the wax blocks in a small cardboard box with windows cut in the left, front, and right sides

Experimental Setup

  1. The illustration below is a schematic diagram of the experimental setup.
    schematic diagram of Joly photometer experimental setup
  2. Place the photometer in between two light sources.
    1. Each wax block is illuminated by only one of the sources. The aluminum foil prevents light from passing between the blocks.
    2. The light sources and the photometer should be at the same height.
    3. The photometer should be positioned on the straight line between the two sources.
    4. The two light sources should be the only sources of light in the room. No bright sunlight!
    5. To insure uniformity of illumination at the photometer, the distance from the photometer to the nearest light source should be large compared to the size of the wax block.
  3. Move the photometer back and forth between the two light sources until the the two wax blocks are equally bright.

Analyzing Your Results

  1. When the wax blocks are equally illuminated, the inverse square law says that the intensities of the two light sources are related by the following equation:
    inverse square law relation between the intensities of the two light sources
  2. Choose one light bulb as your standard, for example, a 60 W soft white bulb. Call this light I1. The intensity of the second light is then given by:
    calculating the relative intensity of the second light source
  3. Measure the distance from each light source to the aluminum foil layer of the Joly photometer.
  4. Calculate the relative intensity of each bulb compared to your standard bulb. (Your standard bulb will have an intensity of 1.0. You can check this by using two identical bulbs. It’s a good way to show that your photometer works as expected.)
  5. To calculate the efficiency of each bulb, divide the relative intensity by the bulb wattage.

Variations

  • Compare the output of incandescent vs. compact fluorescent bulbs. Using your measurements, can you figure out how to compare the cost of using each type of bulb in order to provide an equal amount of light? Your cost comparision should include the cost to purchase each bulb, the cost of electricity for each bulb, and the lifetime of each bulb.
  • Compare the output of “long-life” bulbs vs. normal incandescent bulbs. Many long-life bulbs are designed to run at higher voltage (e.g., 130 V) than is normally supplied from the wall socket (115 V in the U.S.). When run at normal house voltage, these bulbs do not get as hot as they would at 130 V, which means that they last longer. You can use your photoometer to find out what effect the lower voltage has on the light output for these bulbs. Are they more or less efficient than normal bulbs?

Solid Motor Rocket Propulsion

September 1, 2008

Objective

The objective of this project is to measure changes in a rocket’s performance based on differences in the rocket’s motor.

Introduction

Intro image

Model rockets utilize small, commercially-manufactured rocket engines to enable speeds of up to several hundred miles per hour, while reaching altitudes as high as several thousand feet. By following the National Association of Rocketry, Model Rocket Safety Code, you can experiment with the aerodynamics of these rockets with almost complete safety. And, there are many possible experiments you can undertake (see “Variations” below).

Model rockets can make for an extremely fun and exciting science fair project!

Terms, Concepts and Questions to Start Background Research

To do an experiment in this area, you should do research that enables you to understand the following terms and concepts:

  • The four forces in flight: weight, thrust, drag, and lift
  • Key concepts having to do with rocket engines: combustion chamber, propellant, nozzle, F=ma, specific impulse, total impulse
  • The equation for thrust (advanced students)

In addition, study the Model Rocket Safety Code and the proper means to construct a rocket.

Bibliography

Be sure to study the model rocketry sections (among others) of NASA’s Beginner’s Guide to Aeronautics. This excellent NASA Web site includes a rocket simulator called RocketModeler as well as a nozzle simulator. http://www.grc.nasa.gov/WWW/K-12/airplane/guided.htm

Stine, G. Harry, and Stine, Bill. Handbook of Model Rocketry, 7th Edition. John Wiley & Sons, 2004. This book is the bible of model rocketry, containing a wealth of information on rocket design, construction, and competition.

This is an excellent introduction to model rocket motors: http://www.lunar.org/docs/handbook/motors.shtml

You can find a wealth of general information at these sites:

Altitude tracking is important for many experiments in rocketry. These links contain excellent information about how to measure your rocket’s altitude:

Materials and Equipment

Model rocketry supplies can be purchased at many hobby stores. Two of the primary manufacturers are:

Experimental Procedure

The National Association of Rocketry offers these tips for experimentation(1):

  • Plan to do at least three flights of identical rockets with identical engines for each variable that you want to test. There is a lot of “scatter” in the data from rocket-based experiments, and you will get much better results if you use the average of three or more flights for a data point rather than a single flight. This scatter is the result of a combination of experimental error (such as in measuring altitude), weather-based variations (such as in measuring parachute flight duration), and/or slight differences in the construction of the rocket or the motor. If you understand statistics, having multiple data averaged into a single point gives you the opportunity to impress the judges with an analysis of standard deviations and confidence intervals in your data.
  • Measuring a rocket’s maximum altitude accurately is not easy, but is generally the best way to show conclusively how differences in rocket characteristics affect performance. Altitude measurement should be done using data from at least two trackers who look at the flight from different directions but about the same distance, and who communicate by radio to make their measurements at the same moment in the rocket’s trajectory. This is generally either at the exact highest point or “apogee” or (this is easier) at the moment of parachute ejection. Using the more complex tripod-mounted trackers that measure both horizontal “azimuth” angle as well as vertical “elevation” angle gives far more accurate results than simple hand-held elevation-only trackers.
  • Measuring a rocket’s flight duration is fairly easy, but the data is generally only useful for demonstrating differences in the performance of recovery systems (such as parachutes of various sizes) rather than the rocket….
  • Make sure that you vary only one variable between flights. The height a rocket reaches depends on the engine type and delay time; the smoothness of the surface finish on the rocket; the weight of the rocket; and the shape/size/alignment of the rocket and all its parts (fins, launch lug, nose, etc.). How long it stays up depends on how high it goes, plus on the type and size of the recovery system, the weather conditions, and whether the recovery device deploys fully and properly. If your hypothesis is that rockets with one shape of nose go higher than with another shape, for example, make sure the rockets you test are identical in design, liftoff weight, and surface finish and fly them in the same weather conditions off the same launcher. Make sure that the nose cone difference is the only difference. And use identical motors (preferably from the same pack or with the same date-of-manufacture code on the casing) in all your tests of the two different rockets.

Variations

The National Association of Rocketry suggests these possible experiments dealing with propulsion(1):

  • Rocket engine average thrust vs altitude. What difference does it make in tracked altitude performance if the same rocket is flown with two engines of very different average thrust levels (like the Estes A3 or A8) but the same total impulse and liftoff weight?
  • Multi-staging vs single staging. Which goes higher, a two-stage design with a B motor in each stage, or a single-stage model with a C motor having the same total impulse as the combined total of the two B motors?
  • Rocket weight vs altitude. How much difference does the weight of a rocket (with variable weights in its payload compartment) make in how high it goes with a given engine?

Science Projects {Physics}~How the Strength of a Magnet Varies with Temperature*

September 1, 2008

Objective

The objective of this experiment is to determine whether the temperature of a magnet affects its strength.

Introduction

Magnetic fields are produced by electric currents. This could be the familiar electric current flowing in a wire, that you can measure with an ammeter. Or it could be a less familiar, microscopic current associated with electrons in atomic orbits (Nave, 2005a). Certain materials, called ferromagnetic materials, have unpaired electrons in their outermost atomic orbits that can become magnetically aligned over large distances (relative to the atomic scale). These regions of alignment are called magnetic domains.

An electric current flowing in a straight wire creates a magnetic field around the wire. The blue lines in Figure 1, below, show the orientation of such a magnetic field. Notice the “right hand” rule for determining the orientation: when the thumb of the right hand is pointing in the direction of the current, the fingers of the right hand curl in the direction of the magnetic field. You can see the effect of this magnetic field by bringing the wire close to the needle of a magnetic compass when the current is flowing. You can even make an electric current detector based on this principle (see Using a Magnet as an Electrical Current Detector.)

magnetic field produced by electric current in a straight wire
Figure 1. The illustration shows the magnetic field produced by electric current in a straight wire. When the thumb of the right hand is pointing in the direction of the current, the fingers of the right hand curl in the direction of the magnetic field (Nave, 2005f).

A current flowing through a coil of wire (the coil is also called a solenoid) creates a stronger magnetic field than the same current flowing through a straight wire. The magnetic field is strongest at the center of the coil. Each loop in the coil contributes additional strength to the magnetic field. The more loops, the stronger the field.

magnetic field produced by electric current in a coil of wire
Figure 2. The illustration shows the magnetic field produced by electric current in a coil of wire (solenoid). When the fingers of the right hand curl in the direction of the current flow, the thumb of the right hand curl points in the direction of the magnetic field (i.e. thumb points toward magnetic North pole of the solenoid). (Nave, 2005g)

The magnetic field of a solenoid can be increased even further by placing a bar or rod of ferromagnetic material within the coil (diamagnetic and paramagnetic materials will also work, but will not retain a magnetic field when the current is turned off). The magnetic field from the coil strongly aligns all of the magnetic domains in the ferromagnetic material, creating a much stronger magnetic field than either the coil or the ferromagnetic material would have alone.

Permanent magnets are made from ferromagnetic materials. Ferromagnetic materials can “remember” their magnetic history. If a ferromagnetic material is exposed to a strong magnetic field, the magnetic domains within the material will retain at least some of the alignment induced by the external magnetic field.

When the temperature of a material is increased, what is happening on the atomic scale is an increase in the random motion of the atoms of which the material is made. You might think that random motion of atoms could affect the alignment of magnetic domains, so that increasing the temperature of a magnet would tend to decrease its strength. In fact, each ferromagnetic material has a Curie tmperature (named after Pierre Curie), above which it can no longer be magnetized. For soft iron, the Curie temperature is over 1,300°C! Your oven at home might get as hot as 260°C, so obviously 1,300°C is out of the question for a science fair experiment. But what happens to the strength of a magnet over a more approachable range of temperatures, for example from the temperature of dry ice (about −78°C) to the temperature of boiling water (+100°C)? This project shows you how to find out.

Terms, Concepts and Questions to Start Background Research

To do this project, you should do research that enables you to understand the following terms and concepts:

  • magnetic force,
  • magnetic domain,
  • ferromagnetism,
  • ferromagnetic materials,
  • temperature.

More advanced students may also want to study:

  • diamagnetic materials,
  • paramagnetic materials.

Questions

  • Are some magnetic materials more temperature-dependent than others?

Bibliography

Materials and Equipment

To do this experiment you will need the following materials and equipment:

  • safety glasses,
  • 5–10 permanent iron magnets of equal size and strength,
  • thermometer (minimum range 0–100°C),
  • tongs for holding magnets (preferably plastic, for minimizing heat transfer),
  • dry ice (frozen CO2),
  • water ice,
  • insulated containers to hold ice and dry ice,
  • thick insulated gloves for handling dry ice,
  • small pot,
  • water,
  • stove or hot plate for heating water,
  • 2 large plastic bowls,
  • at least one box of standard #1 paper clips,
    • if you have a really strong magnet, you may need more than one box,
    • test the magnet at room temperature first, and make sure that there are plenty of paper clips left over (see Experimental Procedure, below),
    • alternatives to paper clips: small steel BBs or nails.

Experimental Procedure

Note: this experiment is designed for testing the temperature dependence of permanent magnets not electromagnets.

  1. You will test each magnet at four different temperatures:
    1. −75°C, the temperature of dry ice (don’t try to use the thermometer for this one!),
    2. 0°C, the temperature of a water ice bath,
    3. 20°C, room temperature,
    4. 100°C, the temperature of boiling water.
  2. Wear safety glasses when heating, cooling, and transfering the magnets. Always use tongs for handling magnets at extreme temperatures.
  3. Before measuring each magnet’s strength at a given temperature, allow the magnet to equilibrate to the test temperature for at least 15 minutes.
  4. To test magnetic strength, follow these steps:
    1. Use the tongs to place a magnet into a bowl filled with paper clips (or steel BB’s).
    2. See how many clips (or BB’s) the magnet can lift out.
    3. Set the magnet and paper clips (or BB’s) down in an empty plastic bowl.
    4. Wait until they are safe to touch before counting the number of paper clips (or BB’s).
    5. Record the number in your lab notebook for each magnet and temperature tested.
    6. It’s a good idea to practice handling the magnets with tongs at room temperature first until you get the hang of it. Make sure your results are reproducible at room temperature before trying the experiment at extreme temperatures.
  5. For each temperature, calculate the average number of objects each magnet picked up.
  6. Make a graph of magnetic strength, as measured by number of objects lifted (y-axis), vs. temperature (x-axis).
  7. Does magnetic strength increase, decrease, or stay the same over the temperature range you tested?

Variations

  • Compare the temperature dependence of magnets made of different materials (e.g., neodymium vs. iron). Do background research to find the Curie temperature and normal operating temperature range for each type of magnet you test. If necessary, adjust the temperature range for the experiment in order not to exceed the safe operating temperature range for the magnets you test.


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