Paper 3 Measurement Drills

Topic-local longer structured practice calibrated to recurring Paper 3 chains of modelling, calculation and interpretation. This is a topic practice set, not a complete Paper 3.

Question 1: Measurement model, transformation and graph analysis [15]

A student measures the period $T$ of a simple oscillator for different values of a length $L$. Theory suggests that

$$T^2=kL,$$

where $k$ is a constant.

The student obtains the following results.

$L/\mathrm{m}$	0.250	0.350	0.450	0.550	0.650
$T/\mathrm{s}$	1.00	1.19	1.34	1.48	1.61

(a) Explain why a graph of $T^2$ against $L$ provides a direct test of the proposed model. [2]

(b) Complete a derived row for $T^2/{\mathrm{s}}^2$, quoting values to a sensible number of significant figures. [3]

(c) Plot $T^2$ against $L$ on the grid below and draw a straight line of best fit. [4]

Use a scale that spreads the data across most of the grid. Plot crosses clearly; do not join adjacent points dot-to-dot.

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

(e) The time for 10 oscillations was measured and divided by 10 to obtain each $T$. Explain why this method reduces the percentage uncertainty in $T$. [2]

(f) State one experimental feature, other than random scatter, that could cause the best-fit line not to pass through the origin. [1]

Question 2: Longer structured vector investigation [20]

A drone is displaced by two horizontal control pulses. The first pulse gives a displacement of $18.0\mathrm{m}$ due east. The second gives a displacement of $24.0\mathrm{m}$ at $60.0^{\circ }$ north of east.

The magnitude of the second displacement is measured with uncertainty $\pm 0.4\mathrm{m}$ and the angle is measured with uncertainty $\pm 1.0^{\circ }$.

(a) Resolve the second displacement into east and north components. [3]

(b) Determine the resultant displacement components after the two pulses. [2]

(c) Calculate the magnitude and direction of the resultant displacement. [4]

(d) Explain why vector addition cannot be replaced by adding the two displacement magnitudes in this situation. [2]

(e) Estimate the percentage uncertainty in the magnitude of the second displacement. [2]

(f) Suggest why angle uncertainty can affect both the east and north components even though the displacement magnitude is unchanged. [3]

(g) Describe how a clear scale drawing could be used to check the calculated resultant. [3]

(h) State one limitation of using a scale drawing as the final method instead of calculation. [1]

This 20-mark topic-local question reproduces the length of a Paper 3 optional question, but it is not intended to reproduce the breadth of a complete official Section B problem.