Physics 9702/31 — May/June 2012

Cambridge AS Level · Advanced Practical Skills · worked solutions for every part, with the mark scheme

questions

marks

120

minutes

Topics Manipulation, Measurement and Observation · Analysis, Conclusions and Evaluation · Presentation of Data and Observations

Q1Manipulation, Measurement and ObservationPresentation of Data and ObservationsAnalysis, Conclusions and EvaluationFree sample

You may not need to use all of the materials provided.

In this experiment, you will investigate how the motion of a pendulum whose swing is interrupted depends on its length.

(a)

(i)

Lay the pendulum next to the rule and use the pen to make a mark on the string so that the distance $L$ is $0.180\ \text{m}$ , as shown in Fig. 1.1.

Fig. 1.1

(ii)

Set up the apparatus, fixing the string in the split bung so that the string is just touching the wooden rod at the mark you have made.

Fig. 1.2 shows a side view and a front view of the apparatus.

Fig. 1.2

The centre of the bob should be approximately $5\ \text{cm}$ above the bench.

The distance $x$ between the bottom of the bung and the centre of the bob should be approximately $55\ \text{cm}$ .

The mark on the string should be level with the centre of the rod.

(iii)

Measure and record the distance $x$ .

$x$ = ______ $\text{m}$

(b)

(i)

Move the bob sideways through a distance of approximately $5\ \text{cm}$ , as shown in Fig. 1.3.

Fig. 1.3

(ii)

Release the bob and watch its movement. The bob will move to the right and then to the left again completing a swing, as shown in Fig. 1.4. Let the pendulum swing to and fro, counting the number of swings.

Fig. 1.4

Measure and record the time for at least 10 consecutive swings.

Record enough readings to determine an accurate value for the time $T$ taken for one complete swing.

$T$ = ______

(c)

Reduce the distance $x$ . Keep $L$ constant, by adjusting the height of the wooden rod if necessary. Repeat (a)(iii) and (b) until you have six sets of values of $x$ and $T$ .

Include values of $\sqrt{x}$ in your table.

(d)

(i)

Plot a graph of $T$ on the $y$ -axis against $\sqrt{x}$ on the $x$ -axis.

(ii)

Draw the straight line of best fit.

(iii)

Determine the gradient and $y$ -intercept of this line.

gradient = ______
$y$ -intercept = ______

(e)

The quantities $T$ and $x$ are related by the equation

T = P\sqrt{x} + Q

where $P$ and $Q$ are constants.

Using your answers from (d)(iii), determine the values of $P$ and $Q$ .
Give appropriate units.

$P$ = ______
$Q$ = ______

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