Standard Units and Measurements
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Standard Units and Measurements

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Questions and Answers

What is the standard unit of measurement for length in the International System of Measurements (SI)?

  • Foot
  • Yard
  • Inch
  • Meter (correct)

    • What was the definition of a meter prior to its redefinition in 1983?

  • The length of a specific atomic strand
  • Distance traveled by sound in air
  • The height of an average adult male
  • 1 650 763.73 wavelengths of orange-red light from a krypton-86 lamp (correct)

    • How is the second defined in the International System of Measurements?

  • The duration of light travel for a specific distance
  • The time taken for an electron to orbit a nucleus
  • The time of one oscillation of the cesium-133 atom (correct)
  • The time it takes for Earth to complete one rotation

    • Why was the metric system created?

    <p>To improve accuracy and convenience in measurements</p> Signup and view all the answers

    What is the mass equivalent of one kilogram in grams?

    <p>1000 grams</p> Signup and view all the answers

    What is ‘Le Grand K’?

    <p>The actual kilogram standard cylinder</p> Signup and view all the answers

    What is a conversion factor used for?

    <p>To express quantities in different units</p> Signup and view all the answers

    Which of the following physical quantities is NOT one of the three fundamental quantities considered?

    <p>Temperature</p> Signup and view all the answers

    What is the diameter of the aorta in meters?

    <p>0.018 m</p> Signup and view all the answers

    How many meters are in 2.1 miles?

    <p>3,360 m</p> Signup and view all the answers

    What is the mass of a liter of water?

    <p>1 kilogram</p> Signup and view all the answers

    What is the equivalent of 120 km/h in m/s?

    <p>33.33 m/s</p> Signup and view all the answers

    What is the diameter of a proton in meters?

    <p>$2 imes 10^{-15}$ m</p> Signup and view all the answers

    What type of error is associated with variations in measured data due to limitations of the measuring device?

    <p>Random errors</p> Signup and view all the answers

    If the length of a football field is 102 m, how many centimeters is this?

    <p>10,200 cm</p> Signup and view all the answers

    What is a normal adult’s arm span or height in meters?

    <p>Almost 2 meters</p> Signup and view all the answers

    What does systematic error imply in measurements?

    <p>Errors are reproducibly inaccurate.</p> Signup and view all the answers

    What is the time between normal heartbeats in seconds?

    <p>0.8 s</p> Signup and view all the answers

    In the context of the basketball analogy, what does accuracy represent?

    <p>Proximity of a shot to the basket.</p> Signup and view all the answers

    What is a recommended method to reduce random errors in measurements?

    <p>Performing multiple measurements and averaging.</p> Signup and view all the answers

    How can you best describe the nature of systematic errors?

    <p>They occur consistently in the same direction.</p> Signup and view all the answers

    What measurement did the student report incorrectly in the test tube scenario?

    <p>15 g</p> Signup and view all the answers

    Which of the following best defines an error in measurement?

    <p>Uncertainty between the measured value and the standard value.</p> Signup and view all the answers

    What conclusion can be drawn from the scenario of the temperature measurements made by the student?

    <p>There was high precision but low accuracy.</p> Signup and view all the answers

    What can be done to reduce the impact of systematic errors identified due to instrument calibration?

    <p>Apply a correction factor to compensate for the error.</p> Signup and view all the answers

    What is an example of a systematic error that can occur when measuring free fall?

    <p>Failure to account for air resistance during measurements.</p> Signup and view all the answers

    Which of the following best describes a personal error that can affect experimental measurements?

    <p>Carelessness or bias from the experimenter.</p> Signup and view all the answers

    What does a large variance in a set of measurements indicate?

    <p>Numbers in the set are far from each other and the mean.</p> Signup and view all the answers

    What type of error could occur due to misalignment of the observer's eye with the measurement scale?

    <p>Parallax error affecting the reading.</p> Signup and view all the answers

    Which factor does NOT contribute to environmental errors during measurements?

    <p>Poor measurement technique.</p> Signup and view all the answers

    Why is it important to discuss all aspects that could affect an experiment before measuring?

    <p>To identify potential sources of systematic error and mitigate them.</p> Signup and view all the answers

    What is one method to reduce random error in physical measurements?

    <p>Take the average of several measurements over a range.</p> Signup and view all the answers

    What does a variance of zero mean for a set of numbers?

    <p>All values are identical.</p> Signup and view all the answers

    Why can't the variance be negative?

    <p>It results from squaring a number.</p> Signup and view all the answers

    What is the correct formula used to compute variance?

    <p>s2 = Σ(xi – x)^2/n</p> Signup and view all the answers

    How is the mean of the width values calculated from the given data?

    <p>By adding all values and dividing by their amount.</p> Signup and view all the answers

    What is the purpose of squaring the differences from the mean when calculating variance?

    <p>To avoid negative values.</p> Signup and view all the answers

    What is the summed value of the squared differences from the mean for the given data?

    <p>0.05508</p> Signup and view all the answers

    What concluding value of variance is calculated from the provided observations?

    <p>0.01377</p> Signup and view all the answers

    In the example, how many observations were taken to measure the width of the paper?

    <p>5</p> Signup and view all the answers

    Study Notes

    Standard Units

    • Previously people used non-standard units like cubits to measure length which could vary
    • The metric system was introduced to provide consistent standard units
    • Meter, kilogram, and second are standard units for length, mass, and time respectively
    • The SI system (International System of Units) is the modern version of the metric system

    Defining the Meter

    • Originally defined as 1 650 763.73 wavelengths of the orange-red light emitted by a krypton-86 lamp
    • Currently defined as the distance light travels in a vacuum in 1/299 792 458 of a second

    Defining the Kilogram

    • Standard kilogram is a platinum-iridium cylinder kept in France, called 'Le Grand K'
    • Its mass was originally chosen to be close to the mass of 1 liter of pure water at 4°C
    • One kilogram (kg) is equal to 1000 grams (g)

    Defining the Second

    • Defined as 9 192 631 770 times the period of one oscillation of the cesium – 133 atom

    Unit Conversion

    • Unit conversion can be done using conversion factors, which are equivalence statements expressed as ratios equal to 1
    • For example: 1 inch = 2.54 cm, 1 km = 1000 m, 1 h = 3600 s
    • Unit analysis helps choose the appropriate conversion factor to cancel unwanted units

    Accuracy vs Precision

    • Accuracy refers to how close a measurement is to the true value
    • Precision refers to how close repeated measurements are to each other
    • A good measurement is both accurate and precise

    Random Errors

    • Variations in measured data due to limitations of the measuring device
    • Can be reduced by statistical analysis like averaging multiple measurements

    Systematic Errors

    • Reproducible inaccurate data that are consistently in the same direction
    • Can be caused by a calibration issue in the measuring device
    • Can be reduced by applying a correction factor

    Sources of Error in Experiments

    • Inadequate definition of measurement conditions
    • Exclusion of relevant factors
    • Environmental factors
    • Limited scale of the instrument
    • Calibration errors
    • Variations in the physical measurement
    • Parallax - misalignment of the eye
    • Personal errors

    Variance

    • A statistical measure of how spread out data points are from the mean
    • Large variance signifies widely spread data points
    • Small variance signifies data points close to the mean
    • Variance cannot be negative
    • Can be calculated using the formula: s^2 = Σ(xi - x)^2 / (n-1)

    Variance Example

    • To find the variance of a set of measurements, calculate the mean, subtract each individual measurement from the mean, square the differences, sum the squared differences, and divide by (n-1), where n is the number of measurements.

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    Lecture Notes (Prelim to Midterm) PDF

    Description

    Explore the significance of standard units in measurement, including the metric system and defining the meter, kilogram, and second. Understand how these units were historically defined and how they are utilized in modern science. This quiz will also cover unit conversion techniques.

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