General

Question 1

Absolute Uncertainties

Answer 1

Uncertainty in Measurements:

• Represents the interval within which a value lies, with a given level of confidence.
• Calculated as: (Range of measurements ÷ 2) or (Biggest - Smallest).

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Percentage Uncertainty in Apparatus:

• Depends on the resolution or smallest scale division of the measuring instrument.

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Analogue Instruments:

• Readings must be rounded to the nearest scale division.
• Uncertainty in a reading: ± half the smallest division.
• Uncertainty in a measurement: At least ±1 smallest division.

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Repeated Data:

• Uncertainty: ±½ (largest - smallest value).

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Digital Readings:

• Uncertainty: ± the last significant digit (unless otherwise stated).

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Natural Log Uncertainty:

• Absolute uncertainty in ln(x) = (uncertainty in x) ÷ x.

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Gradient Uncertainty:

• (Gradient of line of best fit - Gradient of line of worst fit) ÷ Gradient of line of best fit.

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Absolute Uncertainties (Δ):

• Have the same units as the measured quantity.

Question 2

Anomalies

Answer 2

Anomalies in Data:

• Data points that don’t fit the pattern of the data.
• Determine the cause of an anomalous result before removing it.

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Identifying Anomalies:

• Experimental errors (operator errors or ‘one-off’ errors) can produce anomalies.
• Anomalies should be identified during evaluation before drawing conclusions.
• Look for results on a graph that don’t fit the trend or differ significantly from replicates.
• A result is often considered anomalous if it differs from the mean by more than 10%.

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Improving Reliability:

• Repeat experiments several times to make data more reliable.
• Remove anomalies to allow more valid conclusions to be drawn.

Question 3

Percentage Uncertainties

Answer 3

Percentage Uncertainty:

• The uncertainty of a measurement, expressed as a percentage of the recorded value.
• Formula: 𝑧 = 𝑥 ± 𝑦 → 𝛿𝑧 = 𝛿𝑥 + 𝛿𝑦

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Adding/Subtracting Data:

• Add together the absolute uncertainties.

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• Add the percentage or fractional uncertainties.

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• Multiply the percentage uncertainty by the power.

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• Percentage uncertainties have no units.
• The uncertainty in constants (e.g. π) is zero.

Question 4

Precision, Accuracy, Limitations

Answer 4

Precision:

• A measure of how close a measurement is to the mean value.
• Indicates the magnitude of random errors, not closeness to the true value.

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Limitations:

• Any design flaw or fault that affects the accuracy of an experiment.
• Identify and correct limitations to ensure valid results.

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Accuracy:

• How close a reading/measurement is to its true value.
• Affected by systematic errors.
• Use appropriate methods and equipment to ensure high accuracy.
  
  • Example: Use a micrometer or vernier callipers for small measurements instead of a metre ruler.

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Precision, Accuracy & Error Margins:

• Precision:
  
  • Reflected in the number of decimal places recorded.
• Accuracy:
  
  • Improved by repeating measurements and calculating the mean.
• Uncertainty:
  
  • An estimate of the difference between a measurement and the true value.

Question 5

Repeatable

Answer 5

The same experimenter can repeat a measurement using the same method and equipment and obtain the same value.

Question 6

Reproducible

Answer 6

The ability to achieve consistent results when an experiment is repeated by different experimenters using various methods or equipment.

Question 7

Resolution

Answer 7

Resolution:

• The smallest change in a quantity that causes a visible change in the reading recorded by a measuring instrument.
• Every instrument is limited by its resolution.

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Key Points:

• In imaging, resolution is the ability to distinguish two structures as separate entities rather than one fuzzy image.
• The smaller the change an instrument can measure, the greater its resolution.
  
  • Example: A digital thermometer (resolution: 0.1°C) has a higher resolution than a mercury thermometer (resolution: 1°C).

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Importance of Resolution:

• When using measuring instruments, it is crucial to know what each division on the scale represents.
• Resolution determines the precision of measurements.

Question 8

Resolution of Forces

Answer 8

The splitting of a force into its horizontal and vertical components.

Question 9

Scalar Quantities

Answer 9

• A quantity that only has a magnitude, without an associated direction.
• Examples include speed, distance, and temperature.

Question 10

SI Units + prefixes

Answer 10

SI Base Units:

• The standard units used in equations:
  
  • Metres (m)
  • Kilograms (kg)
  • Candela (cd)
  • Seconds (s)
  • Amps (A)
  • Kelvin (K)
  • Moles (mol)

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Metric Prefixes:

• Tera (T): ( 10^{12} )
• Giga (G): ( 10^9 )
• Mega (M): ( 10^6 )
• Kilo (k): ( 10^3 )
• Milli (m): ( 10^{-3} )
• Micro (μ): ( 10^{-6} )
• Nano (n): ( 10^{-9} )
• Pico (p): ( 10^{-12} )
• Femto (f): ( 10^{-15} )

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Volume Conversions:

• cm³ is the same as millilitre (ml).
• dm³ is the same as litre (l).

Question 11

Type of Errors

Answer 11

Systematic Error:

• Causes all readings to differ from the true value by a fixed amount.
• Cannot be corrected by repeat readings; instead, a different technique or apparatus should be used.
• Arises from faulty instruments or flawed experimental methods.
• Repeated consistently every time the instrument is used or the method is followed.
• Reduce systematic errors by:
  
  • Recalibrating instruments or using different instruments.
  • Making corrections or adjustments to the technique.

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Random Error:

• Causes unpredictable fluctuations in readings due to uncontrollable factors (e.g., environmental conditions).
• Affects precision, causing a wider spread of results about the mean value.
• Reduce random error by:
  
  • Repeating measurements and calculating an average.

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Zero Error:

• A type of systematic error where an instrument gives a reading when the true reading is zero.
• Introduces a fixed error that must be accounted for in results.

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Parallax Error:

• Occurs when a scale reading is not read directly (e.g., at an angle).
• Minimised by ensuring the line of sight is perpendicular to the scale (e.g., at eye level).
• Fixed by using a mirror behind the needle; align the needle with its mirror image for accurate readings.
• Examples of where parallax error is common:
  
  • Determining the volume of liquid.
  • Aligning two objects.
  • Reading the temperature from a thermometer.

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Margin of Error:

• Most apparatus has a margin of error used in percentage error calculations.
• A high percentage error may require:
  
  • Improvements to the apparatus or experimental procedure.
  • Rejection of conclusions or further testing.

Question 12

Triangle of Forces

Answer 12

• A method of finding the resultant force of two forces.
• The two forces are joined tip to tail, and the resultant is the vector that completes the triangle.

Question 13

Vector Quantities

Answer 13

• A quantity that has both a magnitude and an associated direction.
• Examples include velocity, displacement, and acceleration.

Question 14

Type of equipment

Answer 14

Vernier Scales:

• Used on calipers and micrometers for accurate measurements.
• Involves reading from a fixed scale and a moving scale to interpolate between the smallest divisions on the main scale.
• Allows readings to a greater number of decimal places.

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Micrometer Screw Gauge:

• Used to measure small widths, thicknesses, or diameters (e.g., diameter of a copper wire).
• Resolution: 0.01 mm.
• Components:
  
  • Main scale (on the sleeve/barrel).
  • Thimble scale (rotating scale on the thimble).
• Procedure:
  
  • Clamp the spindle and anvil around the object using the ratchet.
  • Avoid overtightening to prevent deformation or zero errors.
• Reading:
  
  • Record where the thimble scale aligns with the main scale.
  • Always record to 2 decimal places (e.g., 1.40 mm, not 1.4 mm).

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Vernier Calipers:

• Used to measure lengths, diameters, thicknesses, or depths (e.g., length of a screw or depth of a hole).
• Resolution: Typically 0.1 mm, but some can measure 0.02 mm - 0.05 mm.
• Procedure:
  
  • Clamp the upper or lower jaws around the object.
  • Use the locking screw to hold the sliding vernier scale in place.
• Reading:
  
  • Record where the vernier scale aligns with the main scale.
  • Always record to at least 1 decimal place (e.g., 12.1 mm, not 12 mm).

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Comparison of Micrometer and Vernier Calipers:

• Micrometer:
  
  • Smaller measuring range.
  • Better accuracy (due to higher resolution).
  • Slower to use (requires rotating the thimble).
• Vernier Calipers:
  
  • Larger measuring range.
  • Quicker to use.
  • More suitable for taking many measurements.

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Other Measuring Instruments:

• Oscilloscope: Displays waves and measures their frequencies.
• Top-pan Balance: Measures the mass of an object.
• Laser: Provides a monochromatic source of light.

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Experimental Planning:

• State the necessary measurements to be taken.
• Choose the most suitable equipment based on resolution and purpose.
• Explain how the desired quantity can be determined from the measurements.

Question 15

Significant figures

Answer 15

Significant Figures (s.f.) Rules:

• Copy the s.f. of the raw data that has the least number of s.f. (or use 3 s.f. to be safe).
• Zeros that come before all non-zero digits are not significant.

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Mean Value Calculations:

• When calculating the mean value of measurements, it is acceptable to increase the number of significant figures by 1.

Question 16

How to answer 6 markers

Answer 16

1. Break down the question:
   
   • Identify the aim and hypothesis.
2. Identify variables:
   
   • Independent variable: What you change.
   • Dependent variable: What you measure.
   • Control variables: What you keep constant.
3. Equipment + measurements:
   
   • Choose appropriate apparatus for accuracy and precision.
   • Plan how measurements will be taken.
4. Accuracy and errors:
   
   • Consider systematic and random errors.
   • Plan to minimise errors (e.g., repeat readings, calibrate equipment).
5. Safety/controls:
   
   • Identify health and safety risks and how to mitigate them.
   • Ensure controlled conditions for reliable results.
6. Formulas:
   
   • Write down any relevant equations or formulas.
7. Data analysis:
   
   • Use y = mx + c for linear relationships.
   • Plan how to process and present data (e.g., graphs, tables).

(Identifying health and safety issues)

Question 17

If they Introduce a new equation

Answer 17

Homogeneity of Physical Equations:

• An important skill is to check the homogeneity of physical equations using SI base units.
• The units on both sides of the equation must be the same.

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Steps to Check Homogeneity:

1. Check the units on both sides of the equation.
2. Determine if they are equal.
3. If they do not match, the equation needs to be adjusted.

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Key Point:

• Always work in SI units when checking homogeneity.

Question 18

Coplanar forces

Answer 18

• Act in the same plane

Question 19

The Four Fundamental Forces of Nature

Answer 19

• Gravity: The weakest force, but acts over infinite distances. It’s responsible for the attraction between objects with mass.
• Electromagnetism: Governs the interaction between charged particles. It’s responsible for electricity, magnetism, and light
• Strong Nuclear Force: The strongest force, but acts over very short distances. It holds the nucleus of an atom together.
• Weak Nuclear Force: A short-range force involved in certain types of radioactive decay.

Question 20

Inertia

Answer 20

• Tendency for an object’s motion to stay constant if there’s no resultant force

Question 21

Squared Or Cubic Conversions

Answer 21

Cube or square the conversion factor too

• E.g. 1 mm³ = 1 / (1000)³ = 1 × 10^-9 m³
• E.g. 1 cm³ = 1 / (100)³ = 1 × 10^-6 m³

Question 22

Presenting & Interpreting Results

Answer 22

Quantitative vs. Qualitative Data:

• Quantitative data: Uses numerical values.
• Qualitative data: Observed but not measured numerically (e.g., colour).

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Recording Data:

• Use a sensible range of values, stated to an appropriate number of significant figures or decimal places (usually matching the resolution of the instrument).
• Table headings: Include both the quantity and unit.

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Organising Data in Tables:

• First column: Independent variable.
• Second column: Dependent variable.
• Repeat readings: Include columns for repeats and a mean value.
• Processed data: Add columns for calculations after the raw data.

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Plotting Data on Graphs:

• Plot all readings, including suspected anomalies, for easy identification.
• For repeat readings, plot the mean value.

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Types of Data and Graphs:

1. Discrete data:
   
   • Only specific values (e.g., whole numbers like the number of students).
   • Display on a scatter graph or bar chart.
2. Continuous data:
   
   • Can take any value on a scale (e.g., voltage in a circuit).
   • Display on a line graph or scatter graph.
3. Categorical data:
   
   • Values sorted into categories (e.g., types of material).
   • Display on a pie chart or bar chart.
4. Ordered data:
   
   • Data in ordered categories (e.g., low, medium, high).
   • Display on a bar chart.

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Graph Skills:

• Aim to find relationships between variables by translating information between graphical, numerical, and algebraic forms.
• Example: Plotting displacement vs. time and calculating instantaneous velocity from the tangent to the curve.

Question 23

Graphs

Answer 23

Graph Plotting Guidelines:

1. Axes:
   
   • Independent variable: Plotted on the x-axis.
   • Dependent variable: Plotted on the y-axis.
2. Plotting Points:
   
   • Plot all values, precise to within half a small square.
   • Use a sharp pencil for thin, clear points.
   • Ensure points are not obscured by the line of best fit.
3. Number of Points:
   
   • Include at least six points.
   • Identify and mark any major outliers.
4. Line of Best Fit:
   
   • Use a clear plastic ruler to draw the line.
   • Ensure equal numbers of points above and below the line.
   • Do not force the line to pass through the origin.
   • Avoid thick lines or dot-to-dot connections.
5. Anomalous Values:
   
   • Ignore obviously incorrect points that were not identified earlier.
6. Graph Scale:
   
   • Cover over 75% of the graph space.
   • Axes do not need to start at 0, except for reading the y-intercept.
   • Use suitable scales (e.g., steps of 1, 2, 5, or multiples of 10).
7. Gradient Calculation:
   
   • Draw a gradient triangle covering at least 75% of the data points.
8. Axis Labels:
   
   • Include units and, if necessary, powers of ten (e.g., ( t / \times 10^2 \, \text{s} )).

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Error Bars:

• Represent the uncertainty in a measurement.
• Drawn above and below (or side to side) for each point.
• Usually plotted vertically for y-values but can also be horizontal for x-values.

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Determining Uncertainties from Graphs:

1. Lines of Best Fit:
   
   • Best fit: Passes as close as possible to all points.
   • Worst fit: Steepest or shallowest line within all error bars.
2. Percentage Uncertainty in Gradient:
   
   • Use the formula:
     Change ÷ Original × 100
3. Percentage Uncertainty in Y-Intercept:
   
   • Use the formula:
     Change ÷ Original × 100

Question 24

Methods to Increase Accuracy

Answer 24

Increasing Accuracy:

• Repeat measurements and use mean values to improve accuracy.
• Reduce systematic errors by recalibrating instruments or adjusting techniques.

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Reducing Uncertainty:

• Timing over multiple oscillations.
• Using a fiducial marker.
• Using a set square or plumb line.
• Taking multiples of measurements (e.g., oscillations).

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Reducing Uncertainty in Periodic Time Measurements:

• Measure many oscillations to calculate the average time for one oscillation.
• Increase the total time measured for multiple swings.
• Ideal method: Measure the time for 10 (or more) oscillations and divide by 10 to find the time period of one oscillation.

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Fiducial Marker:

• A reference point (e.g., for timing a pendulum).
• Improves accuracy by:
  
  • Timing when the pendulum passes the marker.
  • Sighting the pendulum at its highest speed (lowest point).

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Set Squares & Plumb Lines:

• Set square: Used to check if:
  
  • An object is vertical.
  • Two objects are at right angles.
  • Two lines are parallel.
• Plumb line: Used to check vertical alignment.

Question 25

Percentage difference

Answer 25

• Indicates how close the experimental value is to the accepted value.
• Not the same as percentage uncertainty.
• Defined by the equation:
  Percentage difference = |(Experimental value - Accepted value) ÷ Accepted value| × 100
• The smaller the percentage difference, the more accurate the results.

Question 26

Scale Drawing (Vectors)

Answer 26

Scale Drawing for Vectors:

• Used to calculate the resultant vector when two vectors are not at right angles.

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Steps for Scale Drawing:

1. Link vectors head-to-tail (if not already).
2. Draw the resultant vector using the triangle or parallelogram method.
3. Measure the length of the resultant vector using a ruler.
4. Measure the angle of the resultant vector (e.g., from North for bearings) using a protractor.

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Scale Conversion:

• A scale (e.g., 1 cm = 1 km) is often provided.
• Convert the measured length back to the required units.
  
  • Example: For a scale of 1 cm = 2 km, a 5 cm resultant vector equals 10 km.

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Triangle Method:

1. Link vectors head-to-tail.
2. The resultant vector is the line connecting the tail of the first vector to the head of the second vector.

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Parallelogram Method:

1. Link vectors tail-to-tail.
2. Complete the parallelogram.
3. The resultant vector is the diagonal of the parallelogram.

Question 27

Analogue Vs Digital

Answer 27

Analogue Instruments:

• Cheaper but have lower accuracy and resolution.
• More sensitive, making it difficult to read fluctuating values.
• Range and resolution:
  
  • Example: 0 - 10 A range with 1 A resolution.
• Zero errors:
  
  • Check the marker is at zero before use; subtract any offset from measurements.
• Parallax error:
  
  • Read the meter from a position directly perpendicular to the scale.

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Digital Instruments:

• More expensive but have greater accuracy and resolution.
• Display measured values as digits, making them easy to use and precise.
• Range and resolution:
  
  • Example: Wider range with 0.01 A resolution.
• Zero errors:
  
  • Ensure the reading is zero before starting, or subtract the “zero” value from results.
• Auto-range function:
  
  • Automatically adjusts to display very low or very high values, saving time.

Question 28

Interpolation

Answer 28

• Used when a pointer on an analogue meter falls between two scale markings.
• The process of estimating unknown values that fall between known values.
  
  • Example: If a straight line passes through two known points, the midpoint can be estimated.
• Calibration is crucial to ensure accurate interpolation.

Question 29

Lightgates, Data Loggers, Video Techniques

Answer 29

Stopwatch:

• Used to measure time intervals with a resolution of up to 0.01 s.
• Digital stopwatches are preferred for:
  
  • Easier readability.
  • Lap tracking.
• Disadvantages:
  
  • Human reaction time (~0.25 s).
  • Mechanism delays (older stopwatches).
  • Accidental button presses.
  • Consistent timing errors (starting too early/late).
• Solution: Take repeat readings to improve accuracy.

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Light Gates:

• Accurate method to measure time for objects passing through a set distance.
• Consist of an infrared transmitter and receiver.
• When an object obstructs the beam:
  
  • A timer starts or stops.
• Speed calculation:
  
  • speed = distance ÷ time
• Advantages:
  
  • Removes human reaction time errors.
  • Can be connected to digital timers or dataloggers for data analysis.

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Data Loggers:

• Electronic devices that automatically record data over time (e.g., temperature, pressure, voltage).
• Benefits:
  
  • Higher accuracy than manual methods.
  • Reduces human error (e.g., reaction time, subjectivity).
  • Can record data over long periods (e.g., hourly temperature readings).
  • Can capture very short intervals beyond human capability.
  • Reduces safety risks in extreme conditions (e.g., boiling water).
• Data processing:
  
  • Data can be inputted into a computer for tables, graphs, and gradient calculations.

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Computer Modelling:

• Used alongside data loggers to process experimental data.
• Benefits:
  
  • Generates graphs and charts from data tables.
  • Predicts future outcomes by speeding up time in simulations.
  • Exports data for scientific reports.