Practical skills (Assessed in the Exam)

1. Planning:

⇒ Experimental design, including to solve problems:

• Experimental design in physics involves creating a controlled test to investigate a hypothesis or solve a problem. General outline for designing an experiment in physics:
• – Define the problem: Clearly articulate the question or issue to be addressed.
• – Research question: Formulate a specific question related to the problem.
• – Hypothesis: Propose a tentative explanation or solution.
• – Variables: Identify independent (manipulated), dependent (measured), and controlled variables.
• – Experimental design: Choose a suitable design (e.g., controlled experiment, comparative study).
• – Apparatus and materials: Select appropriate equipment and materials.
• – Procedure: Outline the step-by-step process for data collection.
• – Data analysis: Apply statistical methods to test hypotheses.
• – Interpretation: Draw conclusions based on results.
• – Practical application: Implement findings to solve the initial problem.
• Some common experimental designs in physics include:
• – Controlled experiment: Test the effect of an independent variable on a dependent variable.
• – Comparative study: Compare the effects of different variables or conditions.
• – Measuring physical quantities: Determine the value of a physical quantity (e.g., length, time, voltage).
• – Investigating relationships: Examine the relationship between two or more physical quantities.
• Experimental design in physics helps researchers:
• – Understand physical phenomena
• – Test theories and models
• – Develop new technologies
• – Improve measurement techniques
• – Solve practical problems
• Examples of experimental design in physics include:
• – Measuring the acceleration due to gravity (g)
• – Investigating the relationship between voltage and current (Ohm’s Law)
• – Testing the photoelectric effect (Einstein’s hypothesis)
• – Measuring the speed of light (c)
• – Investigating the properties of materials (e.g., conductivity, magnetism)
• By applying experimental design principles, physicists can develop innovative solutions to real-world problems and advance our understanding of the physical world.

2. Implementing:

• Using a wide range of practical apparatus in physics and techniques correctly requires:
• – Familiarity: Understand the apparatus and its components.
• – Calibration: Ensure the apparatus is properly calibrated.
• – Safety: Follow safety protocols and precautions.
• – Measurement techniques: Understand measurement techniques and units.
• – Data analysis: Know how to analyze and interpret data.
• – Troubleshooting: Identify and resolve issues with the apparatus.
• – Maintenance: Regularly maintain and clean the apparatus.
• – Standard operating procedures: Follow established procedures.
• – Quality control: Ensure accuracy and precision.
• – Practice: Regularly practice using the apparatus.
• Some common practical apparatus in physics include:

Table 1 Some apparatus which uses in different experiments

⇒ Data presentation:

• Data presentation in physics is crucial to communicate experimental or simulated results. Here are some key aspects:
• – Clarity: Present data in a clear and concise manner.
• – Accuracy: Ensure accuracy and precision in presenting data.
• – Units: Include appropriate units and labels.
• – Graphs: Use graphs to visualize data, such as:
• – Plots (e.g., position vs. time)
  – Histograms (e.g., energy distribution)
  – Scatter plots (e.g., correlation between variables)
• – Tables: Use tables to present data, such as:
• – Experimental results
  – Measured quantities
• – Figures: Include figures to illustrate:
• – Experimental setup
  – Data collection methods
  – Theoretical models
• – Captions: Provide clear and concise captions for figures and tables.
• – Analysis: Present data analysis, including:
• – Statistical analysis
  – Error analysis
  – Curve fitting
• – Comparison: Compare results to:
• – Theoretical predictions
  – Other experiments
  – Simulations
• – Conclusion: Summarize key findings and implications.
• Measurements should be given to appropriate units; prefixes help make understanding data easier.

Table 2 Prefixes and their meanings with symbols

• Some examples of practical techniques in physics include:
• – Measuring the acceleration due to gravity using a motion sensor
• Analyzing the spectrum of light using a spectrometer
• Measuring the electrical resistance of a material using a multimeter
• Observing microscopic structures using a microscope
• Measuring the temperature of a substance using a thermometer

⇒ Appropriate units for measurements:

• Units for measurements are standardized quantities used to express the magnitude of a physical quantity. Here are the definitions for some common units:

Table 3 Some specific units

3. Analyzing data:

⇒ Processing, analyzing and interpreting qualitative and quantitative experimental results

• Processing, analyzing, and interpreting experimental results in physics involves several steps:
• Qualitative Results:
• – Observations: Record observations during the experiment.
• – Patterns: Identify patterns or trends in the data.
• – Comparisons: Compare results with expected outcomes or theoretical predictions.
• – Anomalies: Note any unexpected results or anomalies.
• Quantitative Results:
• – Data collection: Collect numerical data during the experiment.
• – Data analysis: Apply statistical methods to analyze data.
• – Graphs: Plot data to visualize relationships and trends.
• – Fits: Perform curve fitting or regression analysis to model data.
• – Errors: Calculate uncertainties and errors in measurements.
• – Comparisons: Compare results with theoretical predictions or expected values.
• Interpretation:
• – Conclusion: Draw conclusions based on results.
• – Implications: Discuss implications of findings.
• – Limitations: Identify limitations of the experiment.
• – Recommendations: Suggest improvements or future experiments.
• – Theoretical framework: Relate results to theoretical concepts or models.
• – Validation: Validate results by comparing with previous studies or theoretical predictions.
• – For repeat results a mean of the repeats should be found
• [math] \text{mean} = \frac{\text{sum of results}}{\text{No. data points}} [/math]
• The mean value should be to the same number of significant figures as the data used to calculate it.
• Some common techniques used in physics to analyze and interpret experimental results include:
• – Statistical analysis (e.g., hypothesis testing, confidence intervals)
• – Data modeling (e.g., linear regression, curve fitting)
• – Error analysis (e.g., uncertainty propagation, error bars)
• – Graphical analysis (e.g., plots, histograms)
• – Signal processing (e.g., filtering, Fourier transforms)
• By following these steps and using appropriate techniques, physicists can extract valuable insights from experimental data and advance our understanding of the physical world.

4. Significant figures:

• The number of significant figures in a measured or calculated quantity indicates the number of digits that have a meaning and about which we can be certain.
• When recording data and calculating results, it is important to be consistent about the number of digits in a value that are known with certainty. This will depend on the resolution of the measuring instrument. One of the areas that causes confusion is the use of significant figures and decimal places.
• The use of a higher number of decimal places or significant figures will increase the accuracy of the experiment.
• Example:
• To how many significant figures and decimal places are the following numbers stated:
• [math] (a) \ 234.73 \quad (b) \ 54 \ 564.9 \quad (c) \ 12.3426 \quad (d) \ 4.762 \times 10^{20} [/math]
• Solution:
  (a) 5 significant figures and 2 decimal places
  (b) 6 significant figures and 1 decimal place
  (c) 6 significant figures and 4 decimal places
  (d) 4 significant figures and 3 decimal places – ignore the power term

⇒ Significant figures involving zeros:

• The first problem we encounter when dealing with significant figures occurs when the number has a zero digit.
• Example:
• To how many significant figures are the following numbers stated?
• [math] (a) \ 0.000438 \quad (d) \ 70 \ 457.4 \quad (b) \ 3.23 \times 10^{-6} \quad (e) \ 5.064 \ 06 \quad (c) \ 0.0760 [/math]
• Solution:
• (a) 3 significant figures – you start counting when you get to the ‘4’
• (b) 6 significant figures – the zero after the ‘7’ is significant because it is between other significant digits
• (c) 3 significant figures – ignore the power term
• (d) 6 significant figures
• (e) 3 significant figures

Table 4 Some examples for number of significant figures

⇒ Significant figures involving zeros, but with a nonzero digit at the end

• When a non-zero digit appears at the end of a value, this makes all the zero digits between the non-zero digits significant.
• ‘Zero values between non-zero numbers are significant.’
• – 20006 has 5 significant figures
• – 851 has 3 significant figures
• – 65008 has 5 significant figures
• – 9673 has 4 significant figures.

⇒ Significant figures involving zeros at the end of a number with a decimal point:

• In a number with a decimal point all the numbers to the left of the decimal point, regardless of whether they are zero or non-zero, are significant.
• For example:
• – 30 000 Ω is a resistance value that could have 1, 2, 3, 4 or 5 significant figures.
• – 30 000.0 Ω is a resistance value that is written to 6 significant figures. The decimal point makes all the zero values to the left of it significant. The zero after the decimal point shows that we are confident of the value to six significant figures.
• Using scientific notation makes it clear how many significant figures the values have been stated to.

⇒ The correct use of significant figures in calculated values:

• to determine the volume of a cube in an experiment relating to density calculations, you would be expected to measure the length of the side of the cube and then raise it to the power 3 to work out the volume.

Table 5 Some examples to calculate the volume of a cube

• In Table 5 note that both the measurements and calculated results are stated to the same number of significant figures.

5. Plotting and interpreting graphs:

• It is conventional to plot the independent variable (the one you change) on the x -axis and the dependent variable on the y -axis.
• When plotting graphs, it is important to consider the importance of the following factors.
• Choice of scale:
• – It needs to be big enough to accommodate all the collected values in as much of the graph paper as possible.
• – At least half of the graph grid should be occupied in both the x and y directions.
• – Scales should be clearly indicated and have suitable, sensible ranges that are easy to work with (for example, avoid using scales with multiples of 3).
• – The scales should increase outwards and upwards from the origin.
• – Each axis should be labelled with the quantity that is being plotted, along with the correct unit.
• Labelling the axes:
• – Label each axis with the name of the quantity and its unit.
• – For example, I/A means current in amperes Note that the solidus (/) is used to separate the quantity and the unit.
• Plotting of points:
• – Points should be plotted so that they all fit on the graph grid and not outside it.
• – All values should be plotted and the points must be precise to within half a small square.
• – Points must be clear, and not obscured by the line of best fit, and they need to be plotted so that they are thin.
• – There should be at least six ‘good’ points plotted on the graph, with major outliers identified.
• Line or curve of best fit:
• – There should be equal numbers of points above and below the line of best fit.
• – A clear plastic ruler will help you do this.
• – The line should not be forced to go through the origin, and the points plotted should not be joined up with a line that is too thick or joined up ‘dot-to-dot’ like a frequency polygon.
• – Outliers (anomalous values) that have not been subject to checking during the implementation stage, should be ignored if they are obviously wildly incorrect as they will have an unjustifiably large effect on the gradient of the line of best fit.
• Calculating the gradient:
• – The calculation needs to be shown, including the correct substitution of identified, accurately plotted from the axes into the equation that will be of the form
• [math] m = \frac{∆y}{∆x} [/math]
• – The triangle used to calculate the gradient should be drawn on the graph and it needs to be as large as possible – small triangles are not acceptable for working out a gradient.
• – When using the results from a table of values, the triangle that is used to obtain the gradient should have points that lie on the line of best fit.
• Determining the y -intercept:
• – The y -intercept is the y value obtained where the line crosses the y-axis – on the line x = 0.
• – You can apply your knowledge of the equation [math] y = mx + c [/math] if the best fit line does not cross the y-axis along the line x = 0.
• – Values should be read accurately from the graph, with the scale on the y -axis being interpreted correctly.

• Examples:

(1)
Two graphs are shown in Figure 6 (a and b). One of the graphs has been reasonably well drawn, the other has a number of significant errors. Identify:
(a) which of the two graphs is the better and explain why
(b) improvements you would make to graph 1
(c) improvements you would make to graph 2. 

(b) Graph 2

• Solutions:

1. Graph 2, despite not being perfect, is the better graph:
   • It has a line of best fit with points properly distributed above, below and on the line of best fit
   • It has more than enough ‘good’ points plotted
   • The axes are labelled and the spacing of the axes and graph size are appropriate.

   Graph 1 is deficient in the following:

   • There is no title – it is not possible to determine what the graph is showing, or even the context
   • There are no units or quantities are stated on the axes
   • There is no line of best fit – points are joined up ‘dot-to-dot’
   • The points plotted are too thick
   • There are not enough points plotted – there should be at least six
   • The points plotted are not spaced equally
   • No gradient shown and no gradient calculations are given.
2. Graph 2, despite being better than Graph 1 would benefit from:
• A title – e.g., ‘Graph to show how the extension of a spring varies as the mass added to it increases’
• Values on the x -axis could be shown to a higher number of significant figures, such as ‘2.000’ instead of ‘2’ for the first kilogram label.
• A gradient triangle shown that uses the maximum values e.g.
• [math] \text{gradient} = \frac{(120 – 0) \ \text{mm}}{(8 – 0) \ \text{kg}} [/math]
• which gives a value of [math] 15 mm \, kg^{-1}[/math].
• The experimenter could then argue that each kilogram causes an extension of 15 mm in their conclusion.
3. You could argue that force (N) would be a more suitable x-axis variable to plot, although this is open to debate. Error bars could be included if necessary and if you are familiar with their use.

(1)

The equation [math]V = E  \, – \,  Ir[/math]  is of the form [math] y = mx + c [/math] and so values can be plotted to give a straight line. A typical example of such a graph is shown in Figure 7.

Figure 2 Graph of V against I for the equation [math] V = E \, – \, Ir [/math]

From the shape of the graph and the equations provided determine values for E and r.
Solution:
E is the y -intercept, so is equal to 12.0 V; r is the gradient of the graph and corresponds to

[math]\frac{\Delta y}{\Delta x} \quad \text{or} \quad \frac{12}{1.5}
[/math]

Which gives a value of 8. The units are [math]VA^{-1}[/math], which is equivalent to ohms .

4. Evaluating experiments:

⇒Evaluation:

• Evaluation refers to the process of determining the value of a physical quantities and expression, often using mathematical methods and techniques.

⇒ Calculating percentage uncertainty of the apparatus used

• The percentage of uncertainty in any single reading taken using the equipment is found using:
• [math] \frac{\text{resolution or measurement error}}{\text{measured volume}} \times 100\% [/math]
• For example, if a voltmeter records a reading of 3.24 V and its resolution is 0.01 V, then the percentage uncertainty in the reading is [math] \frac{0.01}{3.24} \times 100\% = 0.3\% [/math]
• The final value would then be quoted as 3.24 ± 0.3%.
• Calculating percentage uncertainty of the apparatus used is a crucial step in physics experiments. Here’s a step-by-step guide:
1. Identify the apparatus: Determine which apparatus you want to calculate the percentage uncertainty for (e.g., ruler, voltmeter, etc.).
2. Find the uncertainty value: Look up or calculate the uncertainty value for the apparatus. This value is usually provided in the apparatus manual or can be calculated using calibration data.
3. Convert uncertainty value to percentage: Divide the uncertainty value by the apparatus’s measurement range (or full-scale range) and multiply by 100 to convert it to a percentage.
• Percentage uncertainty formula:
• [math] \text{Percentage uncertainty} = \frac{\text{resolution or measurement error}}{\text{measured volume}} \times 100\% [/math]
• Example:
• – Uncertainty value = 0.1 cm (for a ruler)
• – Measurement range = 10 cm (for a ruler)
• [math] \text{Percentage uncertainty} = \frac{0.1 \, \text{cm}}{10 \, \text{cm}} \times 100 = 1\% [/math]
• This means that the ruler has a 1% uncertainty in its measurements.
• Note:
• – Uncertainty values can be expressed as absolute (e.g., ±0.1 cm) or relative (e.g., ±1%).
  – Measurement range is the maximum value the apparatus can measure.
  – Percentage uncertainty represents the apparatus’s precision.
• By calculating percentage uncertainty, you can:
• – Evaluate the apparatus’s precision
  – Compare uncertainties between different apparatus
  – Propagate uncertainties in calculations
  – Determine the overall uncertainty of a measurement

⇒ Putting it all together to draw a conclusion

• Imagine that you are conducting an investigation into the behavior of elastic materials under the influence of tensile forces. This involves the calculation of a quantity called the Young modulus,
• Which is defined as
• [math]\frac{\text{Stress}}{\text{Strain}} \quad \text{or} \quad \frac{F \times l}{A \times e}[/math]
• Where:
• F is the tensile force in N,
• l is the original length of the wire in m,
• e is the extension of the wire in m and A is the cross-sectional area of the cylindrical wire in [math]m^2[/math].
• To determine the following percentage uncertainties:
• Uncertainty in F is 1% – based on the uncertainty in mass of the slotted masses used as loads
• Uncertainty in l is 0.1% – 1 mm in a 1 m length of wire.
• Uncertainty in e is 1% – based on the vernier scale on Searle’s apparatus, which measures to 0.05 mm.
• Uncertainty in the radius of wire is 1% – meaning that the percentage uncertainty in the calculated area is 2% (when you square a value, you double the percentage uncertainty associated with it).
• Because the [math] \text{Young’s modulus} = \frac{F \times l}{A \times e}[/math] and because you add uncertainties irrespective of whether you are multiplying or dividing, we end up with a total uncertainty of 1% + 0.1% + 1% + 2% = 4.1%, or 4% to 1 significant figure.
• This is the uncertainty from calculation, using the uncertainty values in the measurements. You can also determine the uncertainty from the difference between the gradients of line of best fit and the worst acceptable line.