Limitation of physical measurements Flashcards – AQA A-level Physics (7408)

What is a measurement error?

The difference between a measured value and the true value of a quantity.

How do random errors affect repeated measurements?

They vary unpredictably, causing readings to scatter.

How can the effect of random errors be reduced?

Take repeated measurements and calculate their mean. This reduces the effect but does not eliminate it.

How do systematic errors affect measurements?

They shift measurements in a consistent direction.

What are two instrument-related causes of systematic error?

A zero offset and incorrect calibration.

How can a systematic error be dealt with?

Identify and correct it, or improve the measurement method to reduce it. More readings under the same conditions do not remove it.

What does an uncertainty express?

The extent to which a measured or calculated value is uncertain.

In a result written as $x \pm \Delta x$, what does $\Delta x$ represent, and what units does it have?

The absolute uncertainty, in the same units as $x$.

What is the fractional uncertainty of a nonzero value $x$ with absolute uncertainty $\Delta x$?

$\frac{\Delta x}{|x|}$

What is the percentage uncertainty of a nonzero value $x$ with absolute uncertainty $\Delta x$?

$\frac{100\Delta x}{|x|}\%$

How should the significant figures reported for a result relate to its uncertainty?

They should reflect the uncertainty, without implying unsupported precision.

How many significant figures are commonly used to quote an absolute uncertainty?

Usually one, sometimes two.

To what decimal place should a value be rounded when reporting it with an absolute uncertainty?

To the same decimal place as the quoted uncertainty.

How are uncertainties combined when measured quantities are added or subtracted?

Add their absolute uncertainties.

How are uncertainties combined when measured quantities are multiplied or divided?

Add their fractional uncertainties. Percentage uncertainties can be added instead.

How does raising a quantity to a power affect its fractional or percentage uncertainty?

Multiply the uncertainty by the magnitude of the power.

How should uncertainty be handled in a calculation with several stages?

Apply the appropriate rule at each stage, then express the final uncertainty in a form suitable for the result.

What kind of estimate do the uncertainty-addition rules give?

A conservative estimate of the combined uncertainty.

What does an error bar on a plotted measurement represent?

The measurement’s uncertainty, extending from the plotted value to the limits indicated by that uncertainty.

What do vertical and horizontal error bars represent?

Uncertainties in the quantities on the vertical and horizontal axes, respectively.

How can reasonable straight lines be used to estimate the uncertainty in a best-fit gradient?

Use the gradients of the steepest and shallowest reasonable lines consistent with the data and any shown error bars to estimate a range around the best-fit gradient.

How can reasonable straight lines be used to estimate the uncertainty in a best-fit intercept?

Compare the best-fit intercept with the extreme reasonable intercepts.

Are the lines with extreme reasonable intercepts necessarily the same as those with extreme gradients?

No. The lines giving extreme intercepts need not be the lines giving extreme gradients.

How can reasonable alternative lines be chosen when a graph has no error bars?

Use the scatter of the points as a guide.

When error bars are absent, can the graph alone determine a unique uncertainty for each point?

No. The graph alone does not provide a uniquely defined uncertainty for each point.