Physics 9702/31 — October/November 2017

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

questions

marks

120

minutes

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

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

In this experiment, you will investigate the motion of a Y-shaped pendulum.

(a)

You have been provided with two pieces of string. The longer piece of string has a loop at each end. The shorter piece of string is attached to a bob.

Set up the apparatus as shown in Fig. 1.1.

Attach the shorter string to the middle of the longer string with a knot.

Ensure the two rods of the clamps are at the same height above the bench.

Position the stands approximately $35\text{ cm}$ apart.

Fig. 1.1

The angle $\theta$ is the angle between the two halves of the longer string.

(b)

Measure and record $\theta$ .

$\theta$ = ______

(c)

Pull the bob a short distance towards you. Release the bob. The bob will oscillate.

Determine the period $T$ of these oscillations.

$T$ = ______

(d)

Vary the distance between the stands and repeat (b) and (c) until you have six sets of values of $\theta$ and $T$ .

Record your results in a table. Include values of $\cos \left( \frac{\theta}{2} \right)$ and $T^2$ in your table.

10M

(e)

(i)

Plot a graph of $T^2$ on the $y$ -axis against $\cos \left( \frac{\theta}{2} \right)$ 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 = ______

(f)

It is suggested that the quantities $T$ and $\theta$ are related by the equation

T^2 = P \cos \left( \frac{\theta}{2} \right) + Q

where $P$ and $Q$ are constants.

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

$P$ = ______
$Q$ = ______

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