Physics Measurements: Base & Derived Quantities

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Questions and Answers

Which of the following is an example of a base quantity?

  • Velocity
  • Length (correct)
  • Volume
  • Density

Derived quantities cannot be expressed in terms of base quantities.

False (B)

What is the SI unit for the base quantity of mass?

kilogram

The prefix 'milli' represents a factor of ______.

<p>0.001</p>
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Match each prefix with its corresponding power of ten:

<p>kilo = 10^3 mega = 10^6 giga = 10^9 tera = 10^12</p>
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Which of the following instruments is most suitable for measuring the length of a football field?

<p>Trundle wheel (A)</p>
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The precision of a measuring instrument refers to its ability to provide the same reading over multiple measurements.

<p>False (B)</p>
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Explain how using set squares can improve the accuracy of length measurement with a meter rule.

<p>Set squares ensure the line of sight is perpendicular to the scale, reducing parallax error.</p>
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A ______ error occurs when the eye is not correctly aligned with the measurement scale.

<p>parallax</p>
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Match the type of error with its description:

<p>Parallax error = Error due to the observer's eye position. Zero error = Error due to an incorrect zero point on the measuring instrument.</p>
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To minimize parallax error when reading a liquid in a measuring cylinder, where should the observer's eye be positioned?

<p>At the same level as the bottom of the meniscus (B)</p>
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Zero error in a measuring instrument can be corrected by simply resetting the instrument to zero before taking measurements.

<p>False (B)</p>
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Describe a method to accurately measure the thickness of a single sheet of paper using a ruler.

<p>Measure the thickness of a stack of sheets and divide by the number of sheets.</p>
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The volume of a liquid is typically measured using a measuring ______.

<p>cylinder</p>
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Match each method to the type of solid volume it is best suited for:

<p>Cubic formula = Regular solids Displacement method = Irregular solids</p>
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When measuring the volume of an irregular object using the displacement method, what should you do if the object floats?

<p>Use a sinker to fully submerge the object and adjust the calculation. (A)</p>
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Bubbles in a liquid will not affect the accuracy of volume measurement in a measuring cylinder.

<p>False (B)</p>
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Explain why it is important to ensure a measuring cylinder is resting on a flat, horizontal surface when taking a measurement.

<p>To ensure the liquid level is uniform and the scale is aligned correctly.</p>
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The time for one complete oscillation of a pendulum is called its ______.

<p>period</p>
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Match the time measurement instrument with its principle of operation:

<p>Pendulum clock = Periodic swing of a pendulum Digital stopwatch = Electronic timing circuits</p>
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Which of the following can affect the period of a simple pendulum?

<p>The length of the pendulum (D)</p>
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A simple pendulum completes one oscillation when it moves from its starting point to the opposite extreme and back to the starting point.

<p>True (A)</p>
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Explain how calibrating a pendulum clock involves adjusting the length of the pendulum.

<p>Adjusting the length alters the period of the pendulum to match a known time standard.</p>
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The quantity of space an object occupies is referred to as its ______.

<p>volume</p>
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Which of the following is a derived unit?

<p>Newton (N) (B)</p>
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The standard form of a number always has one non-zero digit to the left of the decimal point.

<p>True (A)</p>
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Convert 0.000045 meters to standard form.

<p>$4.5 \times 10^{-5}$ m</p>
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The prefix 'nano' represents a factor of 10 to the power of ______.

<p>-9</p>
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Match the prefix with its numerical value:

<p>Mega (M) = 1,000,000 Kilo (k) = 1,000 Centi (c) = 0.01 Milli (m) = 0.001</p>
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What is the purpose of using prefixes when measuring physical quantities?

<p>To express very large or very small quantities in a more manageable way (B)</p>
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Density is a base quantity.

<p>False (B)</p>
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If a student measures the dimension of a cube as 3cm, what is its volume?

<p>27 cm^3</p>
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The formula for density is density = mass / ______.

<p>volume</p>
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Match each quantity with its appropriate instrument for measurement:

<p>Length = Ruler, Vernier Caliper Volume = Measuring Cylinder Time = Stopwatch Temperature = Thermometer</p>
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The abbreviation for micro is:

<p>µ (C)</p>
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The most accurate way to read a measuring cylinder is from above the meniscus.

<p>False (B)</p>
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What do the prefixes like kilo, mega and giga represent with respect to a unit?

<p>They represent multiples of the unit.</p>
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Zero error on a measuring instrument means that when it should read zero, it shows a ______ reading.

<p>non-zero</p>
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Match the following instruments with their function :

<p>Meter rule = Measuring length Stopwatch = Measuring time</p>
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What should typically be done to reduce random errors when measuring?

<p>Take multiple readings and calculate average (D)</p>
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Flashcards

What is measurement?

Method to determine physical quantities.

What are physical quantities?

Quantity that can be measured, consisting of a magnitude and a unit.

What are base quantities?

Quantities that cannot be defined by other physical quantities; they are fundamental.

What are derived quantities?

Quantities derived from base quantities, using formulas.

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What are prefixes (in measurement)?

Used to express very large or small physical quantities.

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What is standard form (scientific notation)?

A way of writing numbers as a single digit multiplied by a power of 10.

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What is precision (or resolution)?

The smallest unit a measuring instrument can measure.

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What is parallax error?

Error in reading due to the eye not being perpendicular to the measuring instrument's scale.

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What is zero error?

Error due to the instrument not starting at zero, leading to consistent offsets in measurements.

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How is volume measured for regular solids?

Volume measured using cubic meters (m³) and cubic centimeters (cm³).

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How to find the volume of a small solid that sinks?

Amount of space occupied by irregular small solids

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How to find the volume of a small solid that floats?

Amount of space occupied by irregular small solids

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What can be used to tell time?

Events that repeat at regular intervals or periods.

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What is the Period of a Simple Pendulum?

Time taken for one full back-and-forth swing.

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How can pendulum clocks be calibrated?

Adjusting the length of the pendulum.

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Study Notes

  • Chapter 1 is about the measurement of physical quantities

What you will learn

  • The difference between base and derived quantities
  • Skills relating to prefixes and standard form
  • Equipment for measuring length, volume, and time

Measurement

  • Measurement determines physical quantities

Physical Quantities

  • A measurable quantity
  • Consists of a magnitude and a unit

Base Quantities

  • Quantities that cannot be defined in terms of other physical quantities

  • Base quantities and their SI units:

    • Length (meter, m)
    • Mass (kilogram, kg)
    • Time (second, s)
    • Temperature (Kelvin, K)
    • Current (Ampere, A)

Derived Quantities

  • Quantities that are derived from base quantities
    • Volume = Length x Width x Height = m³
    • Density = Mass ÷ Volume = kg m⁻³
    • Velocity = Displacement ÷ Time = m s⁻¹
    • Acceleration = Velocity ÷ Time = m s⁻²
    • Force = Mass x Acceleration = kg m s⁻²

Prefixes

  • Used to express very large or very small physical quantities
Prefix Value Standard Form Symbol
Tera 1 000 000 000 000 10¹² T
Giga 1 000 000 000 10⁹ G
Mega 1 000 000 10⁶ M
Kilo 1 000 10³ k
deci 0.1 10⁻¹ d
centi 0.01 10⁻² c
milli 0.001 10⁻³ m
micro 0.000 001 10⁻⁶ μ
nano 0.000 000 001 10⁻⁹ n
pico 0.000 000 000 001 10⁻¹² p

Standard Form

  • Expressing numbers where an integer (1 to 9) is multiplied by a power of 10
    • Positive power signifies a large number (e.g., 4.3 x 10⁶ = 4 300 000)
    • Negative power signifies a small number (e.g., 2.1 x 10⁻³ = 0.021)

Measuring Length

  • Ancient instruments include: foot step, rope, hand span, and arm length
  • Modern instruments include: ruler, measuring tape, screw gauge, and vernier caliper
  • Rulers are suitable for measuring small distances, accurate to the nearest mm
  • Tape measures are used for measuring distances of a few meters
  • Trundle wheels are used for measuring even larger distances

Precision or Resolution

  • The smallest unit a measuring instrument can measure.
  • Can measure a sheet of paper by measuring multiple sheets and taking the average

Using Set Squares

  • Set squares are used to align objects to improve accuracy of reading
  • Measurements should be repeated by rotating the sphere

Avoiding Errors in Measurement

  • Parallax Error: Occurs when the eye is not perpendicular to the scale

  • Zero Error: Caused by an incorrect zero point position or instrument calibration

  • Ways to avoid error:

    • Perpendicular eye position relative to the rule
    • Using a different point on the ruler if the zero mark is worn
    • Taking several readings and calculating the average

Measuring Volume

  • Volume of a regular solid is measured in cubic meters (m³) or cubic centimeters (cm³)
  • Use the formulas to calculate them

Measuring Volume of Irregular Solids

  • Volume can be determined using displacement method
    • By immersing the solid objects in a liquid and measuring the volume of fluid displaced.
  • For small solids that sink, the volume is the difference between the final and initial liquid levels
  • A similar principle can be used for solids that float, using a sinker to fully submerge them

Measuring Volume of Liquids

  1. Pour into a measuring cylinder
  2. Read the volume directly
  3. Cylinder should be on a flat surface
  4. Ensure any bubbles are removed

Measuring Time

  • Instruments used to measure time include:
    • Pendulum clock
    • Wall clock
    • Digital stopwatch
    • Analog stopwatch
  • Events that repeat at regular intervals or periods can be used to tell time
  • Measured in hours (h), minutes (min), and seconds (s)

Simple Pendulum

  • Period of a pendulum is the time taken for one complete oscillation
  • One complete oscillation = complete to-and-fro motion
  • Period is dependent on its length
  • Pendulum clocks are calibrated by adjusting the length

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