Technology practice questions.

Curve-fitting software returns the best fit y = 3.0·x^2.0 for a data set. What does this tell you about the relationship?

• y is proportional to the square of x
• y is directly proportional to x itself
• y gets smaller as x is made larger
• y stays the same for every value of x

Answer: y is proportional to the square of x

The fitted exponent of 2.0 means y varies as x squared; the coefficient 3.0 is only the constant of proportionality. Reading the exponent as a simple linear factor is the usual mistake.

A student tracks a falling ball frame by frame using video-analysis software. Which of these is a genuine limitation of the method?

• The frame rate limits the time resolution of the data
• The software removes all random and systematic error from the data
• The measured positions become better than the true accepted values
• Every error in the on-screen distance scale is corrected automatically

Answer: The frame rate limits the time resolution of the data

Positions can only be found once per frame, so a low frame rate coarsens the timing. The software cannot invent accuracy or remove a scale-calibration error the student sets up.

Which component changes its electrical resistance in response to the brightness of the light falling on it?

• A thermistor mounted on a small aluminium block
• A light-dependent resistor
• A Hall probe held with its face towards the source
• A strain gauge glued to the surface of a beam

Answer: A light-dependent resistor

An LDR's resistance falls as the illumination rises, so it is the sensor of choice for light-intensity work. The thermistor responds to temperature, the Hall probe to magnetic flux density and the strain gauge to extension.

A data logger set to take 20 readings per second is used to record an oscillation of frequency 50 Hz. What is the main problem with this setting?

• Each individual reading carries a much larger random uncertainty than usual
• The logger will run out of storage space long before the oscillation has finished recording
• The readings will all be shifted by a fixed amount away from their true values
• Fewer than one reading is taken per cycle, so the shape of the oscillation is lost

Answer: Fewer than one reading is taken per cycle, so the shape of the oscillation is lost

Sampling at 20 Hz means one reading every 50 ms, while a cycle lasts only 20 ms; the recorded trace shows a slow false oscillation instead of the real one. The sampling rate must be several times the frequency being recorded.

What does a calibration graph for a sensor allow the user to do?

• Convert the electrical output of the sensor into the physical quantity it measures
• Remove the random uncertainty from every one of the readings that the sensor produces
• Increase the resolution of the sensor beyond the value quoted for it
• Show that the sensor responds instantly to any change in its surroundings

Answer: Convert the electrical output of the sensor into the physical quantity it measures

Calibration relates output voltage to the quantity of interest, using known reference values. It corrects for a non-linear or offset response — it cannot make individual readings less scattered.

Graphing software has joined the plotted points with straight segments from one point to the next. Why is this poor practice for experimental data?

• Joined segments make the printed graph harder to read at a small scale
• The software can no longer calculate a value for R² once the points have been joined
• It implies every point is exact and hides the scatter a best-fit line reveals
• The axes can no longer be labelled with the quantity and its unit

Answer: It implies every point is exact and hides the scatter a best-fit line reveals

Dot-to-dot treats each reading as if it had no uncertainty, so genuine scatter is turned into apparent structure. A best-fit line assumes a trend and lets the scatter about it be judged.