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(a) (i) Measure and record the diameter $d$ of the short sample of wire that is attached to the card. You may remove the wire from the card.
$d = \text{..................................................}$ [1]
(a) (ii) Calculate the cross-sectional area $A$ of the wire, in m$^2$, using the formula
$A = \frac{\pi d^2}{4}$.
$A = \text{.................................................. m}^2$
(b) (i) Use the wire attached to the metre rule, one of the voltmeters and one of the resistors to set up the partial circuit shown in Fig. 1.1.
There are two crocodile clips, one labelled K and the other labelled L.
Place K and L so that the distance $l$ between them is approximately 30 cm.
(b) (ii) Measure and record the distance $l$ between K and L.
$l$ = .................................................. m
(b) (iii) Use the other resistor and the other voltmeter to complete the circuit shown in Fig. 1.2.
(b) (iv) Place the crocodile clip M at a distance $l$ from L.
The value of $l$ should be the same as in (b)(ii).
(c) (i) Switch on the power supply.
(c) (ii) Record the voltmeter readings $V_1$ and $V_2$ as shown in Fig. 1.2.
$V_1 = \text{.................................................. V}$
$V_2 = \text{.................................................. V}$ [1]
(c) (iii) Switch off the power supply.
(d) Change $l$ and repeat (b)(ii), (b)(iv) and (c) until you have six sets of readings of $l$, $V_1$ and $V_2$. For each set of readings, distances KL and LM should both be $l$.
Include values of $\frac{V_1}{V_2}$ in your table.
(e) (i) Plot a graph of $\frac{V_1}{V_2}$ on the $y$-axis against $l$ on the $x$-axis.
[Table_1]
(e) (ii) Draw the straight line of best fit.
(e) (iii) Determine the gradient and $y$-intercept of this line.
gradient = ..................................................
y-intercept = ..................................................
(f) The quantities $V_1$, $V_2$ and $l$ are related by the equation
$$\frac{V_1}{V_2} = Pl + Q$$
where $P$ and $Q$ are constants.
(i) Use your answers in (e)(iii) to determine values for $P$ and $Q$.
$P = \text{.................................................. m}^{-1}$
$Q = \text{..................................................}$ [1]
(f) (ii) The resistivity $\rho$ of the material of the wire, in $\Omega$ m, can be found using the relationship
$$\rho = PAR$$
where $R = 10 \Omega$.
Use your answers in (a)(ii) and (f)(i) to calculate a value for $\rho$.
$\rho = \text{..................................................} \Omega \text{ m}$ [1]
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In this experiment, you will investigate the change in shape of a rubber band when masses are hung from it.
(a) Set up the apparatus as shown in Fig. 2.1.
Fig. 2.1
The rods of the two clamps must be at the same height above the bench.
Position the stands so that the rubber band has no slack.
(b) Measure and record the mass $m$ of the mass hanger.
$m =$ ......................................................[1]
(c) (i) Suspend the mass hanger from the centre of the lower part of the rubber band as shown in Fig. 2.2.
Fig. 2.2
(ii) Measure and record the angle $\theta$ as shown in Fig. 2.2.
$\theta =$ ......................................................[2]
(iii) Estimate the percentage uncertainty in your value of $\theta$.
percentage uncertainty = ................................[1]
(iv) Calculate $\tan \frac{\theta}{2}$.
$\tan \frac{\theta}{2} =$ ..........................................[1]
(v) Calculate $\tan^2 \frac{\theta}{2}$.
$\tan^2 \frac{\theta}{2} =$ .........................................
(d) (i) Add the slotted mass to the mass hanger.
Measure and record the total mass $m$ of the mass hanger and slotted mass.
$m =$ ......................................................[1]
(ii) For this total mass, repeat (c)(i), (c)(ii), (c)(iv) and (c)(v).
$\theta =$ ......................................................
$\tan \frac{\theta}{2} =$ ..........................................
$\tan^2 \frac{\theta}{2} =$ ......................................... [2]
(e) Remove the slotted mass from the mass hanger.
Measure and record the angle $\theta$.
$\theta =$ ......................................................[1]
(f) It is suggested that the relationship between $m$ and $\theta$ is $$m = \frac{k}{\tan^2 \frac{\theta}{2}}$$ where $k$ is a constant.
(i) Using your data, calculate two values of $k$.
first value of $k =$ ......................................................
second value of $k =$ ......................................................[1]
(ii) Justify the number of significant figures that you have given for your values of $k$.
...................................................................................... [1]
(iii) Explain whether your results in (f)(i) support the suggested relationship.
...................................................................................... [1]
(g) (i) Describe four sources of uncertainty or limitations of the procedure for this experiment.
1. ......................................................................................
2. ......................................................................................
3. ......................................................................................
4. ...................................................................................... [4]
(ii) Describe four improvements that could be made to this experiment. You may suggest the use of other apparatus or different procedures.
1. ......................................................................................
2. ......................................................................................
3. ......................................................................................
4. ...................................................................................... [4]
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