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(a) (i) You have been provided with two metre rules. One is labelled P and the other is labelled Q.
• Set up the circuit shown in Fig. 1.1.
• F, G, H and J are crocodile clips. Place H approximately half-way along the wire on rule P.
• The distance between F and H is $d$, as shown in Fig. 1.1.
Record $d$.
$d = \text{..............................................................}$
• Place J on the wire on rule Q so that the distance between G and J is approximately 60 cm. The distance between G and J is $c$, as shown in Fig. 1.1.
• Record $c$.
$c = \text{..............................................................}$
• Calculate $n$, where $n = \frac{c-d}{d}$.
$n = \text{..............................................................}$ [1]
(ii) • Close the switch.
• Record the ammeter reading $I$.
$I = \text{..............................................................}$
• Open the switch. [1]
(b) Keeping $d$ constant, vary $c$ until you have six sets of readings of $c$ and $I$. Do not use values of $c$ less than $d$.
Record your results in a table. Include values of $n$ and $\frac{(n+2)}{(n+1)}$ in your table. [9]
(c) (i) Plot a graph of $I$ on the $y$-axis against $\frac{(n+2)}{(n+1)}$ on the $x$-axis. [3]
(ii) Draw the straight line of best fit. [1]
(iii) Determine the gradient and $y$-intercept of this line.
gradient = \text{................................................}
$y$-intercept = \text{.........................................} [2]
(d) It is suggested that the quantities $I$ and $n$ are related by the equation
$$I = S \frac{(n+2)}{(n+1)} + T$$
where $S$ and $T$ are constants.
Using your answers in (c)(iii), determine values for $S$ and $T$. Give appropriate units.
$S = \text{..............................................................}$
$T = \text{..............................................................}$ [2]
(e) Theory suggests that $S$ is inversely proportional to $d$ and that $T$ is independent of $d$. The experiment is repeated using the same equipment but a larger value of $d$.
For this experiment, draw a second line on the graph to show the expected results. Label this line $W$. [1]
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(a) • Set up the apparatus as shown in Fig. 2.1.
• The distance between the strings supporting the wooden strip is $x$.
The distances between the top of the strip and the bottom of the small pieces of wood should be equal. These distances are both $L_1$.
The distance between the centre of the bob and the bottom of the small pieces of wood is $L_2$.
Adjust the position of the strings so that $x \approx 25 \text{ cm}, L_1 \approx 25 \text{ cm}$ and $L_2 \approx 45 \text{ cm}$.
• The strings should be vertical, the strip should be parallel to the bench and the strip should be supported centrally by the strings.
Measure and record $x$ and $L_1$.
$x = \text{.......................................................} \text{ cm}$
$L_1 = \text{.......................................................} \text{ cm}$
(b) (i)
• Pull the bob and end B of the strip towards you through a short distance.
• Release the bob and the strip together so that they oscillate.
• Adjust $L_2$ until the periods of the oscillations of the bob and of the strip are the same.
• Measure and record $L_2$.
$L_2 = \text{.......................................................} \text{ cm}$ [1]
(ii) Estimate the percentage uncertainty in your value of $L_2$:
percentage uncertainty = .............................................. [1]
(iii) Calculate $\dfrac{L_1}{L_2}$.
$\dfrac{L_1}{L_2} = \text{.......................................................}$ [1]
(iv) Justify the number of significant figures that you have given for your value of $\dfrac{L_1}{L_2}$.
.................................................................................................................
.................................................................................................................
.................................................................................................................
................................................................................................................. [1]
(c) • Change $x$ to approximately 30 cm and $L_1$ to approximately 20 cm.
• The strings should be vertical, the strip should be parallel to the bench and the strip should be supported centrally by the strings.
Measure and record $x$ and $L_1$.
$x = \text{.......................................................} \text{ cm}$
$L_1 = \text{.......................................................} \text{ cm}$
• Repeat (b)(i) and (b)(iii).
$L_2 = \text{.......................................................} \text{ cm}$
$\dfrac{L_1}{L_2} = \text{.......................................................}$ [3]
(d) It is suggested that the relationship between $L_1, L_2$ and $x$ is $\dfrac{L_1}{L_2} = kx^2$ 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.
.................................................................................................................
.................................................................................................................
.................................................................................................................
................................................................................................................. [1]
(e) Theory suggests that $k = \dfrac{3}{l^2}$ where $l$ is the length of the strip.
Using your second value of $k$, calculate $l$. Give an appropriate unit.
$l = \text{.......................................................}$ [1]
(f) (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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