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Frequently-Asked Questions about Labs
Question: How do I make a matching table?

Answer: Examples are given here . The table template is here.

Question: How do I write an equation of fit?

Answer:

  1. Replace the generic x- and y-variables with the symbols that represent the relevant physical quantities.
  2. Replace the coefficients with the numerical values obtained by the fit. Round these to the proper number of significant figures and include units.
Question: Why would I use a graph of residuals, and how do I create such a graph in Logger Pro?

Answer: The process is described in L113. Residuals are used to assess goodness of fit.

Question: How do I assess the reproducibility of a measurement?

Answer: This involves taking repeated measurements, finding mean deviations, and finding the percent mean deviation. The process is described in L101.

Question: How do I know whether to calculate a percentage difference or a percentage error between two values?

Answer: When you have no reason to expect that one value is any better than the other, find the percentage difference. When one of the values is taken as an accepted value because it is trusted by the scientific community (for example, the value of g), find the percentage error.

Question: How do I calculate percentage difference?

Answer:  Simply divide the difference of two values by the sum of the values and multiply the quotient by 100.

% Difference = 100 ∙ (Value 1 - Value 2) ÷  (Value 1 + Value 2)

Note that the sign of the result tells you by inspection which value is the larger. This is helpful when looking for systematic errors in a measurement technique.

Question: How do I calculate experimental error?

Answer:  Divide the difference of two values by the accepted (or expected) value and multiply the quotient by 100.

% Error = 100 ∙ |Measured Value - Accepted Value| ÷  (Accepted Value)

Finding the absolute value of the difference is an accepted practice, although it's not essential.

Question: Why do I always get the wrong number of significant figures in calculations of errors?

Answer: The experimental error and percentage difference formulas involve both subtraction and division. You must use both the addition/subtraction and multiplication/division rules for significant figures. Apply the subtraction rule first and retain the smaller number of decimal digits. Then apply the division rule and retain the smaller number of significant figures. Most people use only the division rule. This almost always gives the incorrect number of significant figures.

Question: How do I estimate percentage uncertainties (relative error) in measurements, and why would I do this?

Answer:  Measurements are inherently uncertain. The uncertainty is affected by such things as the method of measurement, the measuring instrument, and variations in the measured characteristic. Suppose you were measuring the diameter of a cylinder. Some ways of doing this are to lay a ruler across the diameter and sight the edges of the cylinder, to roll the cylinder without slipping through one complete rotation on a piece of paper and divide the result by π, or to place the cylinder between the jaws of vernier calipers. Each method has a different uncertainty, and different measuring instruments can be read with different precisions. If the cylinder is out of round, that influences the results as well.

See L101 and L103 to review how to calculate uncertainties.

Question: How do I determine the number of significant figures in calculations of mean deviation and % mean deviation?

The same rules for significant figures apply here as to all situations. However, you can save time by noting the following:

  • The mean of a set of measurements, the deviations from the mean, and the mean deviation should all have the same number of decimal digits.
  • The % mean deviation is the ratio of the mean deviation to the mean. Apply the multiplication rule to determine the number of significant figures in this final calculation.

Important note about rounding error: The determination of % mean deviation requires a number of arithmetic operations. There is the potential for rounding error in each step. In order to minimize rounding error, carry extra digits in intermediate calculations and round in the final step. Here's a shortcut method.

Question: Why is the phrase human error unacceptable in a discussion of errors?

Answer: The phrase human error is non-descriptive.  It doesn't show a critical examination of the process of measurement in the experiment in question.

Question: What determines the number of significant figures in a measurement?

Answer:  The significant figures include those digits that are certain as well as the first uncertain digit. Leading 0's are not considered significant, because they don't result from a measurement. They're simply placeholders.

Question: How do I know what digits are certain? Stated differently, how do I meet a criterion for a particular number of significant figures?

Answer:  A method that isn't correct is to assume that every digit in the readout of an instrument is significant. For example, if you measure one oscillation of a spring and obtain a reading of 1.32 s, don't assume that all three digits are significant. But how do you know which of those digits are significant? That is, which ones can you be sure of and what is the first digit of which you are unsure? You can take repeated measurements. Let's suppose your measurements are 1.32, 1.19, 1.27, 1.34, 1.21 s. You can be certain the first digit is 1, but there's variation in the second digit. That's the first uncertain digit, so that makes this a 2 significant figure measurement. The third digit of the readings is meaningless.

Question: How can I increase the number of significant figures in a measurement?

Answer:  Generally you find a way to make the measurement larger. For example, if you're measuring the diameter of a penny, you place several pennies side-by-side along a ruler as shown here. This method works because all pennies have the same diameter or nearly so. If you're measuring a repeated time interval such as the oscillation of a spring or pendulum, you time several cycles instead of just one. In these methods, you reduce the percentage uncertainty--also called relative uncertainty--in the measurement as follows:

Measurements of distance and time intervals have endpoint errors. These are inherent errors in judging the position of the ends of an object on a ruler or in judging when to start and stop a stopwatch. The errors have about the same size whether you're measuring a small interval or a large one. However, the error becomes a smaller percentage of the measurement itself the larger the measurement becomes. The goal is generally to reduce the percentage (or relative) errors. Suppose, for example, that you wanted to achieve a precision of 1 part in a 100 (1%) in a measurement of the period of a pendulum. How many consecutive cycles would you have to time. First, you need to estimate your endpoint timing uncertainty. This is a personal judgment. For sake of this example, suppose the uncertainty is 0.1 s. In order to achieve the 1% criterion, your time intervals would need to be 10 s. (0.1 is 1% of 10.) If the period of the pendulum was about half a second, then you'd need to measure the time for 20 consecutive cycles. You would make this measurement several times and calculate the percentage mean deviation in order to verify that you did indeed meet the 1% criterion.

Question: How can I minimize rounding error in calculating % mean deviation?

Answer: Click here

 


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