A mass is dropped from rest, and falls through a distance of 2.0 m in a vacuum. An observer records the time taken for the mass to fall through this distance using a manually operated stopwatch and repeats the measurements a further two times.

Question 11

A mass is dropped from rest, and falls through a distance of 2.0 m in a vacuum. An observer records the time taken for the mass to fall through this distance using a manually operated stopwatch and repeats the measurements a further two times. The average result of these measured times, displayed in the table below, was used to determine a value for the acceleration of free fall. This was calculated to be 9.8 m s^-2.

first measurement    second measurement   third measurement    average

time / s            0.6                               0.73                             0.59                 0.64

Which statement best relates to the experiment?

A The measurements are precise and accurate with no evidence of random errors.

B The measurements are not accurate and not always recorded to the degree of precision of the measuring device but the calculated experimental result is accurate.

C The measurements are not always recorded to the degree of precision of the measuring device but are accurate. Systematic errors may be present.

D The range of results shows that there were random errors made but the calculated value is correct so the experiment was successful.

Reference: Past Exam Paper – June 2012 Paper 12 Q5

Solution:

Answer: B. 

Precision is how close the measured values are to each other. In a measuring instrument, the precision is indicated by the number of significant figures (decimal places) that the instrument can give.

From the measurements, we can observe that the readings are not very closed to each other. This scatter of readings indicate the presence of random errors (possibly due to the experimenter).

Additionally, even though the same instrument is used, the measurements are not given to the same number of decimal places (i.e. they are not recorded to the same degree of precision). So, the measurements are NOT precise.

Accuracy is how close a measured value is to the actual (true) value.

It can be seen that the individual measured values are not close to the average value of time. So, the measurements are NOT accurate. [A is incorrect]

However, the calculated value for g is found to be 9.8 ms^-2, which is close to the reference value. So, the calculated experimental result IS accurate. [C is correct]

The significant random errors indicate that the experiment was not successful, even though the calculated value is close to the actual (reference) value. [D is incorrect]

Systematic errors are due to the instrument being used. The measurements would either be smaller or larger than the correct value. The measurements do not indicate such a trend in the values. So, no systematic errors are present. [C is incorrect]