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Measurement & Units

  • A1-01 MASSES - KILOGRAM AND POUND

    A1-01
    Compare the weights of one kilogram (SI unit of mass) to one pound (English system unit of force)
    This set of two brass masses (one lb and one kg) is suitable for passing around among the students, so they can get a hands-on feel for the difference between the units. This is valuable in introductory classes which may have students who have not encountered metric units, or whose introduction to them was only as an arithmetic exercise in making unit conversions. It is valuable for them to experience the masses themselves and begin to build a physical intuition for what they represent in terms of mass and force.
    A1

  • A1-02: MASSES - CHROME PLATED

    a1-02
    Show a collection of calibrated masses
    This is a collection of large masses, suitable for students to handle to get a feel for SI units of mass. Normally 1kg, 2kg, and 5kg masses are delivered; 20kg and 25kg available upon request. These are suitable for hands-on experience, but we recommend that the masses rest on a table for students to come up to and examine, rather than attempting to pass them around.
    ME1

  • A1-11 LENGTHS - METER AND YARD

    A1-11
    Compare the length of one meter (SI unit) to that of one yard (English unit)
    A meterstick and a yardstick, mounted in parallel on a stand. This is useful for introducing students familiar with English units to SI standards of length.
    A1

    meas

  • A1-12: METRIC TAPE

    a1-12
    Make measurements in the metric system
    Flexible 10-meter metric scale. The opposite side is scaled in feet and inches.

    Can be used for a variety of measurement purposes.
    A1

  • A1-21: METRONOME

    A1-21
    Means to show different intervals of time
    A typical mechanical metronome, beats between 40 and 208 clicks per minute. Useful for introducing the concept of time measurement.

    Invite students to speculate about the mechanism of changing the time base - why does moving a weight change the rate? This can be related to concepts of levers, moment of inertia, and mechanical harmonic oscillators.
    A1

  • A1-22: HOURGLASS

    A1-22
    Show an hourglass
    An hourglass was an early means of time measurement. The picture above shows our elementary version of the hourglass; many historical designs were more sophisticated and thereby able to time such diverse events as boiling an egg or measuring a one hour interval.

    This is primarily useful for introducing the concept of mesaurable time units, not for actually making measurements.
    A2

  • A1-31: VOLUME MEASURE DEMONSTRATION

    A1-31
    Illustrate metric volume units
    Two 1000 cc (1 liter) blocks are available, from which smaller units of volume (100cc, 10 cc and 1 cc) can be removed. Note that the smallest units are easily lost, so it is best to have students come to the lecture table to examine the models, rather than passing them around.

    This can also be useful to show in conjunction with discussions of estimation, eg "Fermi Problems."
    A1

  • A1-32: VOLUMES - SPHERICAL VS CYLINDRICAL

    A1-32
    Illustrate a volume perception paradox
    Water filling the graduated cylinder is poured into the apparently smaller spherical flask. While the spherical flask may appear to students to be much smaller than the tall cylinder, this enables them to see that it actually has the same volume.

    Invite students to make a prediction about how much of the cylinder will fit in the sphere, or how much it will overflow, before performing the experiment.
    A1

  • A2-32: HEIGHT MEASUREMENT BY TRIGONOMETRY

    A2-32
    Determine the height of a student using trigonometry
    Determine the height h of a student by measuring the distance x of the student from the protractor and the angle a of the top of the student from the floor: h = x tan a. Compare the experimental value with a direct measurement using the two-meter stick.
    A2

    g

  • B2-41: ROBERVAL BALANCE

    B2-41
    Demonstrate a paradox in equilibrium of forces and torques

    This unlikely-looking contraption is in neutral equilibrium when equal weights are placed onto the two outer arms, as shown, so it will remain at rest in any position. If a net weight is placed on either side, that side will go down.

    Ask your students what they think will happen when the system is released in the configuration photographed at the left above. Draw attention to the similarity between the Roberval balance and the simple pan balance.
    FS2

  • B4-21: DEFLECTION OF BEAM - OPTICAL LEVER

    B4-21
    Demonstrate the small deflection of an aluminum beam due to weighting between supports.
    A mirror serves as an optical lever for the laser beam, with its fixed support legs on a lab jack and its other legs on the aluminum beam. The aluminum beam deflects as weights are added, causing the laser beam to move along the scale at the rear of the photograph.
    OS1, F1, ME1, LS1

    b4-21a b4-21b

  • E2-02: MEASUREMENT OF RADIUS OF EARTH

    E2-02
    Demonstrate how the radius of the earth can be measured using trigonometry.

    A disc of radius R with two radial tabs, as shown, is mounted on the optical board and illuminated by a parallel beam of light, as if the earth were being illuminated by the sun. The equatorial tab must have its shadow along the horizontal diameter of the disc. Measure the length b of the upper tab, the length a of its shadow, and the distance S along the surface between the two tabs. By geometry: S/R=a/b, or R=bS/a. Compare the result of this calculation with the direct measurement of the radius R of the disc.

    E2, ofc

    e2-02

  • F2-11: HYDROMETER

    F2-11
    Measure the density of a liquid.
    If the hydrometer is immersed in a graduated cylinder filled with water, the reading on the scale (center photograph) should be C(W) = 1000, indicating that the scale is calibrated for water. If the hydrometer is put into the saline solution (photograph at right), the number C(L) at the level of the liquid is read. The density D(L) of the unknown liquid is given by: D(L)=C(L)*D(W)/1000,where D(W) is the density of water in kg/m^3. One can measure densities between 0.7 and 2.0 using this device.
    F2

    f2-11af2-11b

  • F2-41: DENSITY - SLOPE OF MASS VS VOLUME GRAPH

    F2-41
    Determine the density of water.
    Starting with the container empty, pour in water a small amount at a time and plot the total mass vs. the volume of water in the container. The slope of the graph is the mass density of water.

  • G1-55: INERTIA BALANCE

    G1-55
    Illustrate the measurement of inertial mass using SHM.
    A mass is placed on the platform and set into motion, executing SHM horizontally. The period of the oscillation T = (1/2 pi) SQRT ((M+m)/k), where M is the mass of the platform and m is the unknown mass. Making period measurements with and without the unknown mass m one can determine its inertial mass.
    G1, ME1

  • G2-06: FRAHM'S FREQUENCY METER

    G2-06
    Check the 60 Hz line voltage frequency.
    A set of reeds, all the same length, are weighted to resonate near 60 Hz. The reeds are driven by an electromagnet. Just plug the meter leads into the end of a power cord to check the line frequency. Use an oscillator for driving the meter at frequencies other than 60 Hz.

  • H1-11: MICROPHONE AND OSCILLOSCOPE

    H1-11
    Show the wave shape of various sounds.
    This setup can be used to look at the wave shape of the speaking voice, singing, whistling, playing musical instruments, musical synthesizers, oscillators with speakers, etc. The oscilloscope trace shown is that of a baritone voice singing the vowel "ee" with a frequency of about 160 Hz. The photographs from the oscilloscope above compare the sounds of a clarinet (top, resembling a square wave), a crumhorn (center, resembling a sawtooth wave), and a recorder (bottom, resembling a triangular wave).

    A variety of sound sources can be requested separately.
    H1, ME2, ME3

  • H1-31: SOUND LEVEL METER

    H1-31
    Demonstrate use of a sound level meter.
    Several loud sources can provided upon request, including musical instruments, noisy laboratory apparatus, and a portable audiotape machine with earphones. You can also invite students to bring up their own devices to test. It is surprisingly easy to get over 100dB in earphones. The sound level meter can viewed by a TV camera and displayed on the main screen.

  • I1-01: THERMOMETERS

    I1-01
    Show several types of thermometers.
    Several thermometers, as photographed above, just lie there reading the temperature. You must plug in the electronic one and turn it on.
    I1, I0

  • I2-07: THERMOPILE WITH DVM

    I2-07
    Observe infrared radiation.
    The output from a commercial thermopile is connected to a digital voltmeter where the voltage is proportional to the temperature observed: the hotter the object the higher the voltage. Use various sources: ice, boiling water, liquid nitrogen, the floor, people, etc. This is only qualitative; the system is not calibrated.
    N1, ME2, I2, PW1