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In this experiment, you will investigate an electrical circuit.
(a) (i) Assemble the circuit shown in Fig. 1.1.
The two resistors are identical. A, B and C are crocodile clips. Connect C to the screw.
(ii) Connect A to the wire at a distance $p$ of approximately 25 cm from the screw, as shown in Fig. 1.2.
(iii) Close the switch.
(iv) Position B on the other side of the screw so that the two voltmeter readings have the same value $V$.
The distance between the screw and B is $q$, as shown in Fig. 1.2.
(v) Measure and record the distances $p$ and $q$. Record $V$.
$p = \text{..........................}$
$q = \text{..........................}$
$V = \text{..........................}$
(vi) Open the switch.
(b) Change $p$ and repeat (a)(iii), (a)(iv), (a)(v) and (a)(vi) until you have six sets of values of $p$, $q$ and $V$.
Record your results in a table.
Include values of $\frac{1}{p}$ and $\frac{1}{q}$ in your table.
(c) (i) Plot a graph of $\frac{1}{q}$ on the $y$-axis against $\frac{1}{p}$ on the $x$-axis.
(ii) Draw the straight line of best fit.
(iii) Determine the gradient and $y$-intercept of this line.
gradient $= \text{..........................}$
$y$-intercept $= \text{..........................}$
(d) It is suggested that the quantities $q$ and $p$ are related by the equation
$$\frac{1}{q} = \frac{a}{p} + b$$
where $a$ and $b$ are constants.
Use your answers in (c)(iii) to determine the values of $a$ and $b$.
Give appropriate units.
$a = \text{..........................}$
$b = \text{..........................}$
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(a) (i) You are provided with two joined springs and three joined springs. Using the two joined springs, set up the apparatus as shown in Fig. 2.1.
(ii) Measure and record the height $h_1$ of the bottom of the mass hanger above the bench, as shown in Fig. 2.1.
$h_1$ = .................................................. m [1] ☐
(iii) Add the 100 g mass to the mass hanger. Measure and record the height $h_2$ of the bottom of the mass hanger above the bench.
$h_2$ = .................................................. m [1] ☐
(iv) Estimate the percentage uncertainty in your value of $h_2$.
percentage uncertainty = .................................................. [1] ☐
(b) (i) Calculate the spring constant $k$ for the combination, using the expression
$$k = \frac{mg}{(h_1 - h_2)}$$
where $m = 0.100\text{kg}$ and $g = 9.81\text{N kg}^{-1}$.
$k$ = .................................................. $\text{N m}^{-1}$ [1] ☐
(ii) Justify the number of significant figures you have given for your value of $k$.
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(c) (i) Use small pieces of adhesive tape to reduce movement at the joints between components, as shown in Fig. 2.2.
(ii) Rotate the mass hanger and mass through one turn and release them. The masses make rotational oscillations, as shown in Fig. 2.3.
(iii) Take measurements to find the period $T$ of the rotational oscillations.
$T$ = .................................................. s [2] ☐
(d) Repeat (a)(ii), (a)(iii), (b)(i) and (c) using the three joined springs.
$h_1$ = .................................................. m
$h_2$ = .................................................. m
$k$ = .................................................. $\text{N m}^{-1}$
$T$ = .................................................. s [3] ☐
(e) It is suggested that the relationship between $T$ and $k$ is
$$T^3 = \frac{C}{k^2}$$
where $C$ is a constant.
(i) Using your data, calculate two values of $C$.
first value of $C$ = ..................................................
second value of $C$ = .................................................. [1] ☐
(ii) Explain whether your results in (e)(i) support the suggested relationship.
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............................................................................................................................... [1] ☐
(f) (i) Describe four sources of uncertainty or limitations of the procedure for this experiment.
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(ii) Describe four improvements that could be made to this experiment. You may suggest the use of other apparatus or different procedures.
1. .....................................................................................................................
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