Physics 5054/41 — October/November 2021

Cambridge O-Level · Alternative to Practical · worked solutions for every part, with the mark scheme

questions

marks

minutes

Topics Experimental Contexts · Observations and Measurements · Analysis, Conclusions and Evaluation · Use of Techniques, Apparatus and Materials · Planning Experiments and Investigations

Q114MExperimental ContextsObservations and MeasurementsAnalysis, Conclusions and EvaluationUse of Techniques, Apparatus and MaterialsFree sample

A student investigates how the period of a pendulum depends upon its length.

Fig. 1.1

The student:

arranges the apparatus, as shown in Fig. 1.1
clamps the string of the pendulum in position.

The length of the pendulum is the distance from the centre of the pendulum bob to the point of support.

(a)

(i)

Measure the distance $l$ on Fig. 1.1 to the nearest millimetre. Record your result.

$l$ = ______ $\text{cm}$

(ii)

Fig. 1.1 is drawn to a scale of one-eighth of the full size.

Determine the actual length $L$ of the pendulum from the point of support to the centre of the pendulum bob.

$L$ = ______ $\text{cm}$

(b)

The period $T$ is the time taken for one complete oscillation of the pendulum.

One complete oscillation is one complete swing, e.g. from the middle to one side, through the middle to the other side and back to the middle.

(i)

The student:

adjusts the length of the thread until $L$ is 15.0 cm
gives the bob a small sideways displacement and releases it so that it oscillates
records the time for 10 complete oscillations
repeats this procedure two more times.

The following values of the time for 10 complete oscillations are recorded:

7.4 s 7.8 s 7.7 s

Calculate $T_{10}$ , the average value of the time for 10 complete oscillations. Give your answer to 2 significant figures.

$T_{10}$ = ______ $\text{s}$

(ii)

The student repeats the procedure in (b)(i) for length $L = 20.0\ \text{cm}$ , $25.0\ \text{cm}$ , $30.0\ \text{cm}$ and $35.0\ \text{cm}$ . The results are shown in Table 1.1.

Complete Table 1.1 using your answer from (b)(i). You will need to calculate $T$ and $T^2$ .

Table 1.1

$L\ /\ \text{cm}$	$T_{10}\ /\ \text{s}$	$T\ /\ \text{s}$	$T^2\ /\ \text{s}^2$
15.0
20.0	8.9	0.89	0.79
25.0	9.9	0.99	0.98
30.0	10.8	1.08	1.17
35.0	11.8	1.18	1.39

(iii)

Explain why the student measures the time for 10 complete oscillations, rather than for 1 complete oscillation.

(iv)

On the grid in Fig. 1.2, plot a graph of $T^2$ ( $y$ -axis) against $L$ ( $x$ -axis). Start your axes from the origin (0,0). Draw the straight line of best fit.

Fig. 1.2

(v)

Determine the gradient $G$ of your line.

Show your working and indicate on the graph the values you use.

$G$ = ______

(vi)

Theory suggests that the gravitational field strength $g$ is equal to:

g = \frac{0.39}{G}

Use this equation and your value of $G$ in (b)(v) to calculate a value for $g$ .

$g$ = ______

(vii)

Compare the value of $g$ you obtained in (b)(vi) with the accepted value of $10\ \text{N/kg}$ .

State whether the two values agree with each other and justify your answer.

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