RESEARCH METHODOLOGY

Home Experiments

Contents

1. Measurement of Pi
2. The Acceleration of Gravity
3. The Heating and Cooling of a Thermometer
4. The Binomial Distribution
5. Flow of Water through a Hole in a Bottle
6. The Density of Metal Objects

All the experiments below can be done easily by anyone without special equipment. You should do the experiments carefully in order to get the best possible results with the materials available. In each experiment you should:

1. Check your measurements by repetition.
2. Estimate the accuracy of your measurements.
3. Estimate the accuracy of the result calculated from your measurements.
4. Compare your result with the known value where possible.
   Does the known value lie within the band of error estimated for your result?
5. Repeat the experiment under varying conditions.
6. Write a report of your experiment in the form of a short research paper.

Measurement of Pi

• Measure the circumference and the diameter of a variety of circular objects (coins, cans, jar tops, plates, concrete drain pipes, etc.).
• Divide your measure of the circumference by your measure of the diameter. The quotent is a measure of pi.
• Repeat the measurements to get results as accurately as possible.
• Compare your result with the theoretical value 3.14159---.

The Acceleration of Gravity

• Make a pendulum by hanging a weight on a string from a fixed point of suspension.
• Measure the length L of the pendulum, and the periodic time T of the swings.
• Calculate the acceleration of gravity g from T and L.
• Compare your result with published values of g.

The acceleration of gravity varies over the surface of the Earth, so the value which you find in your experiment need not be the same as a value given in a textbook.

Heating and Cooling a Thermometer

• Put a thermometer in a refrigerator or an ice box.
• Wait until the thermometer is cold.
• Remove the thermometer and record its reading as a function of time.
• Determine the ambient temperature, and the time constant of the measurement.
• Repeat the experiment starting with the thermometer in warm water instead of in a refrigerator.

The Binomial Distribution

• Toss a coin a number of times and record the number of heads each time.
• Repeat the experiment several times.
• Compare your results with the binomial distribution for fair tossing.

Flow of Water through a Hole in a Bottle

• Make a small hole (diameter about one millimeter) in the bottom of a clear plastic water bottle.
• Fill the bottle with water and stand it upright so that the water can flow out. (The top of the bottle should be off.)
• Measure the depth of water in the bottle as a function of time.
• Fit a suitable curve to the results. The equation of the curve is a model of the system.
• Repeat the experiment with a larger hole in the bottom of the bottle.

The Density of Metal Objects

This experiment can be done in various ways. For example a ruler marked in centimeters and millimeters may be used as a standard of length, and the density of water is then used as a standard of mass. Another way is to assume that the weighing scale is accurate, and that you have a calibrated jug for measuring the volume of the water.

Part One: Calibration of the Apparatus

• Take a glass or a clear plastic cylinder which holds 1-2 liters of water.
• If necessary, attach a vertical strip of paper to the cylinder to measure changes in the depth of water in the cylinder, and measure the internal diameter of the cylinder with the ruler.
• Place the cylinder containing a small volume of water on a weighing scale (as used in the kitchen, or in the market).
• Make a note of the water level and the reading on the weighing scale.
• Add water to the cylinder in steps and repeat these operations.
• If you assume the density of water is 995 kg/m³ (correct at 30°C), then you can calibrate the weighing scale.
• Alternatively, if you assume the weighing scale is accurate, you can measure the density of the water.

Part Two: Density Measurement

• Start with the cylinder half full of water on the weighing scale.
• Put a metal object in the cylinder under the water.
• Record the change in the water level and the change in the reading on the weighing scale.
• Calculate the density of the metal from your results.
• Repeat the experiment with objects made of different metals: aluminum, iron, gold, etc.
• Identify the metals by comparing the densities you find with the known densities of different metals.

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By R. H. B. Exell, 2001. King Mongkut's University of Technology Thonburi.