Experiment to determine the value of g

Write up your experiment Usual write up Aim Diagram, labelled identifying the apparatus Method, describing the steps you took and the reasons for your decisions Results Graph and calculations Conclusion Evaluation, how close are your points to the line of best fit, any anomalies, considering percentage error from the accepted value of g, systematic and random errors, areas which could be improved

Calculations Find the gradient of your line. This will be equal to 0.5g. Hence calculate your experimental value of g. How close is your reading to the accepted value of g? Percentage error from the accepted value of g can be calculated as Percentage error= difference between accepted value and experimental value x 100% accepted value

What is an error? You need to identify the sources of errors in your experiment and describe the steps you took to minimize errors No matter how careful we try to be when planning an experiment, there will always be occasions where errors occur in the collection of data and subsequent calculation process A systematic error is an error that does not happen by chance but instead is introduced by an inaccuracy in the apparatus or its use by the person conducting the investigation. This type of error tends to shift all measurements in the same direction. Random errors in experimental measurements are caused by unknown and unpredictable changes during the experiment. A better result can be obtained by finding the mean of the results in several readings.

Uncertainty from your gradient The absolute uncertainty of a measurement shows how large the uncertainty actually is, and has the same units as the quantity being measured, and is generally quoted to 1sf. When taking single readings, the absolute uncertainty is usually given as the smallest division on the measuring instrument. What about our experiment, what do you think the absolute uncertainty in the readings was? You can indicate the absolute uncertainties using error bars on your graph Now draw in a line of worst fit (this may be more steep or less steep that the line of best fit). Find the gradient of this line and calculate the percentage uncertainty in the experimental value of g Uncertainty = gradient of best fit line – gradient of worst fit line Calculate the percentage uncertainty in the gradient using the following equation Percentage uncertainty = 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡 𝑜𝑓 𝑏𝑒𝑠𝑡 𝑓𝑖𝑡 𝑙𝑖𝑛𝑒 𝑥 100%.

Absolute uncertainty example Absolute uncertainty of a single value Example. A metre ruler is used to measure the height of a table and it is found to be 780mm. The ruler has a mm scale. What is the absolute uncertainty? 780mm ± 1mm

Percentage uncertainty Percentage uncertainty of a single value We often need to calculate a percentage uncertainty and include it in our evaluation. The percentage uncertainty is the absolute uncertainty divided by the measured value expressed as a percentage To calculate a percentage uncertainty of a single value, we use the equation Percentage uncertainty = uncertainty x 100% measured value Example A digital ammeter is used to measure the current flowing in a series circuit and it is precise to 0.01A. What is the percentage uncertainty for a current of a) 0.80A, b) 4.30A? Percentage uncertainty = 0.01 0.8 x 100% = 1.25% = ±1% (to 1sf)

Absolute and percentage uncertainties Uncertainty for a number of repeat readings The steps we take are: Find and record the mean of the readings Find the range of the repeat readings (largest value – smallest value) Halve the range to find the absolute uncertainty Divide the absolute uncertainty value by the mean value and multiply by 100 to give the percentage uncertainty. Example Range: 3.90 - 3.86 = 0.04V Absolute uncertainty = ±0.02V Percentage uncertainty = 0.02V x 100% = 0.5% 3.88V Reading 1 (V) Reading 2 (V) Reading 3 Reading 4 Mean value (V) 3.89 3.88 3.86 3.90

You try The temperature of a room was measured several times and the values recorded in the table. Calculate the absolute uncertainty Calculate the percentage uncertainty in the readings Reading 1 (°C) Reading 2 (°C) Reading 3 (°C) Reading 4 (°C) Mean value (°C) 21.4 21.3 21.1

Rules for combining percentage uncertainties You will be expected to determine the final percentage uncertainty in a compound quantity. This is based on calculations that need to be carried out in order to find the quantity.

Combining uncertainties For a compound quantity in the form y = ab, the rule is % uncertainty in y = % uncertainty in a + % uncertainty in b For a compound quantity in the form y = 𝒂 𝒃 , the rule is For a compound quantity in the form y = an, the rule is % uncertainty in y = n x % uncertainty in a

Examples Potential difference is calculated using the equation V=IR. If the % uncertainty in the current ,I, is 10% and the % uncertainty in the resistance, R, is 5%, then what is the % uncertainty in the potential difference, V?

Examples A Young Modulus is calculated using the equation Young’s Modulus = 𝑆𝑡𝑟𝑒𝑠𝑠 𝑆𝑡𝑟𝑎𝑖𝑛 If the % uncertainty in the stress is 8% and the % uncertainty in the strain is 6%, then what is the % uncertainty in the value of Young’s modulus?

Example The density of a cube is calculated using density = 𝑚𝑎𝑠𝑠 𝑣𝑜𝑙𝑢𝑚𝑒 . If the % uncertainty in the mass is 1% and the %uncertainty of the length of one of the sides of the cube is 2% then what will be the percentage uncertainty in the density of the cube?

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