Physics 9702/32 — May/June 2023

● Assemble the apparatus as shown in Fig. 1.1.

● Adjust the height of the boss and the position of the weight W on the bench so that the metre rule is parallel to the bench and both springs are vertical.

● Slide the rubber band and slotted mass onto the rule so that the rubber band is approximately 30 cm from the end of the rule. The rule will tilt down, as shown in Fig. 1.2.

● Adjust the position of W so that both springs are vertical.

● The distance between the rubber band and the end of the rule is $x$, as shown in Fig. 1.2.

Measure and record $x$.

$x$ = ______

● The angle indicated by the plumb-line on the protractor scale is $\theta$, as shown in Fig. 1.2.

Measure and record $\theta$.

$\theta$ = ______ $^\circ$

Vary $x$ by moving the rubber band along the metre rule. Adjust the position of W so that both springs are vertical. Measure $x$ and $\theta$.

Repeat until you have six sets of values of $x$ and $\theta$.

Record your results in a table. Include values of $\cos \theta$ in your table.

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

$$\cos \theta = ax + b$$

where $a$ and $b$ are constants.

Using your answers in (c)(iii), determine the values of $a$ and $b$. Give appropriate units.

$a$ = ______

$b$ = ______

For this experiment, the constant $a$ is related to the spring constant $S$ of each spring by

$$a = -\frac{p}{S}$$

where $p = 13.15\ \text{N m}^{-2}$.

Determine the value of $S$. Give an appropriate unit.

$S$ = ______