EXPERIMENT NOTES

I will work on this page on a weekly basis. This page will include quiz as well as lecture material. Please check back on Friday or Saturday.

MEANINGFUL MEASUREMENTS
    1. Associated with an instrument: The uncertainty associated with an instrument is determines by the size of the smallest division on the scale. One is allowed to imagine the smallest unit divided into ten. For example, if the smallest division is cm, one can divide it into 10 mm. Ex: 3.3m 0.1m

    NOTE:

    1. The uncertainty associated with an instrument can not be <10% the size of the smallest division.
    2. In an introductory lab, experimental uncertainties should be rounded to 1 significant figure.
    3. The last significant figure in any stated answer should be of the same order of magnitude (in same decimal position) as the uncertainty.
    • Definition – Interpolation: It is the process of estimating positions between the scale markings.
      1. Estimating Uncertainties in Repeatable Measurements: Imagine the following measurements are taken: 3.2s, 2.9s, 2.8s, 3.0s.

        2. The average time = best estimate = <t> = and the probable range is 2.8s – 3.2s

      2. Types of Error.
      1. Systematic Errors: Errors that affect all measurements in the same way and can be difficult to detect. Ex: A clock used for timing the measurements in b is running consistently 5% fast. One will not be able to determine this since all the measurements will be 5% fast.
      2. Random Errors: Experimental uncertainties that can be revealed by repeating the measurement. Ex: The reaction time of a person to stop a watch.
    • The Mean & Standard Deviation.

    a) Average = Mean (<x>,), Ex: 71, 72, 72, 73, 71.

    b) Standard Deviation = = an estimate of the average uncertainty of the measurements x1, …, xN.

    From the above example,

    • How To Agree When Measurements Agree.
      • If the uncertainties of 2 measurements overlap, we can not be sure that the 2 lengths are not identical (see diagram on your lab manual, pg 11)
      • We can be sure 2 lengths are not identical if and only if their uncertainties do not overlap (see diagram on your lab manual, pg 11)
    • Comparing Values.
    1. Percent Discrepancy: It is used to compare a given or theoretical value to an experimental value.

      2. ; Where T – theoretical value & E – experimental value.

    2. Percent Difference: It is used to compare experimental values.

    ; Where E1 is the first experimental value & E2 is the second one.
    • Combining Measurements & Uncertainties. See the example below.

    Rectangle’s height = 3.2m 0.2m & Rectangle’s Length = 4.3 m 0.2m. Find the area.

    1. What is the "highest reasonable area"? (3.2 + 0.2) (4.3 + 0.2) = 15.3 m2
    2. What is the "most reasonable area"? (3.2) (4.3) = 13.8 m2
    3. What is the "lowest reasonable area"? (3.2 – 0.2) (4.3 – 0.2) = 12.3 m2

    Therefore the area of the rectangle = 13.8 m2 1.5 m2
    • The Vernier Caliper. This will be explained in class.

    Moment of Inertia – Week 11

    Theory

    The tables below should be a great to the student in the understanding of angular motion. I will discuss their use in class.

    Mineral

    Kyanite

    Linear Angular

     1. Displacement     q
    2. Velocity
    3. Acceleration
    4.
    5. Force F = ma
    6. Kinetic Energy
    7. Momentum p =mv
    8. Work
    9. Power