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(a) (i) Set up the circuit as shown in Fig. 1.1.
!(###).
Attach the crocodile clips to the wire so that the distance $x$ is approximately 30 cm.
(ii) Measure and record $x$.
$x = ...........................................................[1]$
(b) (i) Close the switch.
(ii) Record the voltmeter readings $V_1$ and $V_2$.
$V_1 = .........................................................$
$V_2 = .......................................................... \, [1]$
(iii) Open the switch.
(c) Change $x$ and repeat (a)(ii) and (b) until you have six sets of readings of $x$, $V_1$ and $V_2$.
Include values of $\frac{V_2}{V_1}$ in your table.
[10]
(d) (i) Plot a graph of $\frac{V_2}{V_1}$ on the $y$-axis against $x$ on the $x$-axis.
[3]
(ii) Draw the straight line of best fit.
[1]
(iii) Determine the gradient and $y$-intercept of this line.
$\text{gradient} = ............................................................$
$y\text{-intercept} = .......................................................... \,[2]$
(e) The quantities $V_2$, $V_1$ and $x$ are related by the equation
$$ \frac{V_2}{V_1} = \frac{Ax}{P} + \frac{Q}{B} $$
where $P = 15 \Omega$, $Q = 10 \Omega$ and $A$ and $B$ are constants.
Use your answers in (d)(iii) to determine values for $A$ and $B$. Give appropriate units.
$A = ............................................................$
$B = ............................................................. \,[2]$
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(a) Use the loops on one piece of string to arrange the string on a wooden rod as shown in Fig. 2.1. The loops of the string on the rod should be approximately 18 cm apart. Repeat for the other rod and string.
(b) Set up the apparatus as shown in Fig. 2.2. The two wooden rods should be parallel, equal heights above the bench and 50 cm apart. The two strings supporting the metal rod should be 50 cm apart.
(c) (i) Measure and record the angle $\theta$ as shown in Fig. 2.3. $\theta = \text{...............................................................} \;[1]$
(ii) Estimate the percentage uncertainty in your value of $\theta$.
percentage uncertainty = .........................................................\; [1]
(iii) Calculate the value of $\cos \left( \frac{\theta}{2} \right)$.
$\cos \left( \frac{\theta}{2} \right) = \text{........................................................} \;[1]$
(d) (i) Move the metal rod to the left. Release the metal rod and watch the movement. The metal rod will move to the right and then to the left again, completing a cycle as shown in Fig. 2.4.
(ii) The time taken for one complete cycle is $T_1$. By timing several of these complete cycles, determine an accurate value for $T_1$.
$T_1 = \text{...............................................................} \;[2]$
(e) (i) Move the centre of the metal rod towards you through a small distance. Release the metal rod and watch the movement. The metal rod will move away from you and then back towards you completing a cycle as shown in Fig. 2.5.
(ii) The time taken for one complete cycle is $T_2$. By timing several of these complete cycles, determine an accurate value for $T_2$.
$T_2 = \text{...............................................................} \;[1]$
(f) (i) Reduce the distance between the loops of string on each wooden rod to approximately 9 cm as shown in Fig. 2.6.
(ii) Repeat (b), (c)(i), (c)(iii), (d) and (e).
$\theta = \text{............................................................}$
$\cos \left( \frac{\theta}{2} \right) = \text{............................................................}$
$T_1 = \text{............................................................}$
$T_2 = \text{............................................................}$ \;[3]
(g) It is suggested that the relationship between $T_1$, $T_2$ and $\theta$ is $$ \frac{T_1}{T_2} = k \cos \left( \frac{\theta}{2} \right) $$ 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 (g)(i) support the suggested relationship.
...................................................................................................
...................................................................................................
...................................................................................................
................................................................................................... \;[1]
(h) (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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