Paper 4 Measurement Practical-Style Drills

Topic-local practical/data-analysis practice. These questions are original and should be checked against the answer file.

Question 1: Spring data, graph and gradient [22]

A student investigates a light spring. Different masses $m$ are suspended from the spring and the extension $x$ is measured after the load has come to rest. The spring is not stretched beyond its elastic limit. The results are shown below.

$m/\mathrm{kg}$	0.050	0.100	0.150	0.200	0.250	0.300
$x/\mathrm{m}$	0.020	0.039	0.061	0.080	0.100	0.121

For loads within the elastic limit, the model is

$$x=\frac{g}{k}m,$$

where $k$ is the spring constant and $g=9.81\mathrm{m}{\mathrm{s}}^{-2}$.

(a) State the independent variable and dependent variable in this investigation. [2]

(b) State two features of the table headings that make the data presentation clear. [2]

(c) Plot $x$ against $m$ on the grid below and draw a straight line of best fit. [5]

(d) Use a large triangle on your best-fit line to determine the gradient. State its unit. [3]

(e) Use your gradient to determine $k$. [2]

(f) State what a significant non-zero intercept could suggest in this experiment. [2]

(g) Identify one source of random uncertainty and one possible systematic error in measuring $x$. For each, explain its effect. [4]

(h) Suggest one improvement that would reduce uncertainty in the gradient. [2]

Question 2: Planning a diameter and density measurement [20]

A student is asked to determine the density of a long thin metal wire. The wire is approximately cylindrical. The available apparatus includes a metre rule, micrometer screw gauge, balance, retort stand, adhesive tape and scissors.

(a) State the quantities that must be measured to determine the density. [3]

(b) Write an equation for the density in terms of the measured quantities. [3]

(c) Describe how the diameter should be measured to reduce random uncertainty. [4]

(d) Explain why a micrometer screw gauge is more suitable than a metre rule for measuring the diameter. [2]

(e) State how a zero error in the micrometer would affect the result if it is not corrected. [2]

(f) Describe how to record the raw measurements in a clear table. [3]

(g) State one safety precaution for this experiment. [1]

(h) State two checks on the final answer that would help identify a calculation or unit error. [2]