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In this experiment, you will investigate the potential difference between two points in a circuit.
(a) Assemble the circuit of Fig. 1.1.
(b) (i) Connect the voltmeter across the power supply.
Record the voltmeter reading $E$.
$$E = ext{..................................................} \; [1]$$
(ii) Disconnect the voltmeter from the power supply.
(c) (i) Position the voltmeter leads on the wires at distance $x$ from the zero ends of both rules as shown in Fig. 1.2, where $x$ is approximately 20 cm.
(ii) Record $x$ and record the voltmeter reading $V$.
Include the sign ($+$ or $−$) of $V$.
$$x = ext{..................................................}$$
$$V = ext{..................................................}$$
(iii) By moving both contacts, change $x$ until the voltmeter reads zero.
Record $x$.
$$x = ext{..................................................} \; [1]$$
(d) Repeat (c)(i) and (c)(ii) with different values of $x$ until you have six sets of values of $x$ and $V$.
Include values of $\frac{V}{E}$ in your table.
(e) (i) Plot a graph of $\frac{V}{E}$ 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 $= ext{..................................................}$
$y$-intercept $= ext{..................................................} \; [2]$$
(f) The quantities $V$, $E$ and $x$ are related by the equation
$$\frac{V}{E} = ax + b$$
where $a$ and $b$ are constants.
Use your answers from (e)(iii) to determine the values of $a$ and $b$.
Give appropriate units.
$$a = ext{..................................................}$$
$$b = ext{..................................................} \; [2]$$
590
573
564
(a) You are provided with three spheres as shown in Fig. 2.1.
[Image_1: Fig. 2.1]
(i) Measure and record the mass $m_A$ of the sphere labelled A.
$m_A = \text{.............................} \text{g}$ [1]
(ii) Measure and record the mass $m_B$ of the smaller of the two spheres labelled B.
$m_B = \text{.............................} \text{g}$
(iii) Calculate the value of $R$, where
$$R = \left(\frac{2m_A}{m_A + m_B}\right)^2.$$
$R = \text{.............................}$ [1]
(iv) Justify the number of significant figures you have given for your value of $R$.
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(b) You are provided with a track mounted on a board.
Place the smaller sphere B on the track at the lowest point.
Measure and record the height $h_0$ of the bottom of the sphere above the bench, as shown in Fig. 2.2.
$h_0 = \text{.............................}$ [1]
[Image_2: Fig. 2.2]
(c) Place sphere A on the track and resting against the tape, then release it so that it collides with sphere B.
Take measurements to find the maximum height $h_B$ reached by sphere B after the collision, as shown in Fig. 2.3.
$h_B = \text{.............................}$ [2]
[Image_3: Fig. 2.3]
(d) Estimate the percentage uncertainty in your value of $h_B$.
percentage uncertainty = \text{.............................} [1]
(e) Copy the value of $m_A$ from (a)(i). Repeat steps (a)(ii), (a)(iii) and (c) using sphere A and the larger of the two spheres labelled B.
$m_A = \text{.............................} \text{g}$
$m_B = \text{.............................} \text{g}$
$R = \text{.............................}$
$h_B = \text{.............................}$ [3]
(f) It is suggested that the relationship between $h_B$ and $R$ is
$$h_B - h_0 = kR$$
where $k$ is a constant.
(i) Using your data, calculate two values of $k$.
first value of $k = \text{.............................}$
second value of $k = \text{.............................}$ [1]
(ii) Explain whether your results support the suggested relationship.
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(g) (i) Describe four sources of uncertainty or limitations of the procedure for this experiment.
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[4]
(ii) Describe four improvements that could be made to this experiment. You may suggest the use of other apparatus or different procedures.
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[4]
536
600
598
