Physics 9702/31 — May/June 2023

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 a balanced metre rule.

You have been provided with three springs and a metre rule with masses attached to its centre.

(a)

The unstretched length of the single spring is $S_1$ , as shown in Fig. 1.1.

Fig. 1.1

The unstretched length of the connected springs is $S_2$ , as shown in Fig. 1.2.

Fig. 1.2

Measure and record $S_1$ and $S_2$ .

$S_1$ = ______
$S_2$ = ______

(b)

(i)

● Set up the apparatus as shown in Fig. 1.3.

Fig. 1.3

● Two string loops A and B are supporting the rule.

Loop A should be placed $10.0\text{ cm}$ from one end of the rule.

● The distance between the end of the rule and loop B is $x$ . Move loop B until $x$ is approximately $75\text{ cm}$ .

● Measure and record $x$ .

$x$ = ______

● Without changing the positions of the string loops, adjust the apparatus until the rule is parallel to the bench and the springs and the string loops are vertical.

● The extended length of the single spring is $L_1$ .
The extended length of the connected springs is $L_2$ .

Measure and record $L_1$ and $L_2$ .

$L_1$ = ______
$L_2$ = ______

(ii)

Calculate $e_1$ and $e_2$ , where

e_1 = L_1 - S_1 \text{ and } e_2 = L_2 - S_2.

$e_1$ = ______
$e_2$ = ______

(c)

Vary $x$ by changing the position of loop B. Loop B must remain on the right-hand side of the masses. Keep loop A in the same position.

For each value of $x$ , adjust the apparatus until the rule is parallel to the bench and the springs and the string loops are vertical. Measure $x$ , $L_1$ and $L_2$ . Repeat until you have five sets of values.

Record your results in a table. Include values of $e_1$ , $e_2$ and $\frac{e_2}{e_1}$ in your table.

(d)

(i)

Plot a graph of $\frac{e_2}{e_1}$ on the $y$ -axis against $x$ 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)

It is suggested that the quantities $e_1$ , $e_2$ and $x$ are related by the equation

\frac{e_2}{e_1} = Px - Q

where $P$ and $Q$ are constants.

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

$P$ = ______
$Q$ = ______

(f)

The distance between string loop A and the centre of the rule is $w$ , as shown in Fig. 1.4.

Fig. 1.4

$P$ and $Q$ are each inversely proportional to $w$ .

A student repeats the experiment with loop A placed further from the left-hand end of the rule.

Sketch a second line on the graph to show the expected results. Label this line W.

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