In this experiment, you will investigate oscillations of card shapes. (a) You have been provided with a circular card of radius $10.0\ \text{cm}$. ● Draw a circle on the card of radius $9.0\ \text{cm}$, as shown in Fig. 1.1. ● Fold the card in half. Cut carefully along the line, as shown in Fig. 1.2, and keep both parts of the card. ● The distance between the centre of one side of the card shape and the centre of the other side is $d$, as shown in Fig. 1.3. Measure and…

Physics 9702/31 — October/November 2022

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 oscillations of card shapes.

(a)

You have been provided with a circular card of radius $10.0\ \text{cm}$ .

● Draw a circle on the card of radius $9.0\ \text{cm}$ , as shown in Fig. 1.1.

Fig. 1.1

● Fold the card in half. Cut carefully along the line, as shown in Fig. 1.2, and keep both parts of the card.

Fig. 1.2

● The distance between the centre of one side of the card shape and the centre of the other side is $d$ , as shown in Fig. 1.3.

Fig. 1.3

Measure and record $d$ .

$d$ = ______

(b)

● Stand the card shape on the bench.

● Adjust the loops of card until the distance between the points where the loops touch the bench is approximately $3\ \text{cm}$ , as shown in Fig. 1.4.

Fig. 1.4

● Gently press down one side of the card shape through a short distance. Release the card shape so that it oscillates.

● Determine the period $T$ of these oscillations.

$T$ = ______

(c)

Use the remaining card to cut out shapes of smaller radius, each with the same width of $1.0\ \text{cm}$ .

For each card shape, measure $d$ and repeat (b). Repeat until you have five sets of values of $d$ and $T$ .

Record your results in a table. Include values of $T^2$ in your table.

(d)

(i)

Plot a graph of $T^2$ on the $y$ -axis against $d$ 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)

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

T^2 = Ad + B

where $A$ and $B$ are constants.

Using your answers in (d)(iii), determine the values of $A$ and $B$ . Give appropriate units.

$A$ = ______
$B$ = ______

(f)

Theory suggests that

A = \frac{2\pi^2}{g}

where $g$ is the acceleration of free fall.

Use your value of $A$ in (e) to determine a value for $g$ . Give an appropriate unit.

$g$ = ______

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