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In this experiment, you will investigate a wooden strip acted on by several forces.
(a) (i) Set up the apparatus as shown in Fig. 1.1.
The mass $m$ should be 100g. The angle $\theta$ between the wooden strip and the string should be approximately $45^\circ$.
(ii) Adjust the apparatus so that the spring is vertical and the wooden strip is parallel to the bench.
(b) (i) Record the mass $m$.
$m = \text{................................................}$
(ii) Measure and record the length $y$ of the coiled part of the spring.
$y = \text{..................................................[1]}$
(iii) Measure and record $\theta$.
$\theta = \text{..................................................[1]}$
(c) (i) Add 100 g to the mass hanger.
(ii) Adjust the height of the boss holding the nail until the wooden strip is parallel to the bench.
(iii) Measure and record $m$, $y$ and $\theta$.
$m = \text{................................................}$
$y = \text{................................................}$
$\theta = \text{................................................}$
(d) Change $m$ and repeat (c)(ii) and (c)(iii) until you have six sets of values of $m$, $y$ and $\theta$. You may include your values from (b) and (c). Include values of $msin\theta$ in your table.
(e) (i) Plot a graph of $y$ on the $y$-axis against $msin\theta$ on the $x$-axis. [10]
(ii) Draw the straight line of best fit. [3]
(iii) Determine the gradient and $y$-intercept of this line. [1]
$\text{gradient} = \text{..................................................}$
$\text{y-intercept} = \text{..................................................[2]}$
(f) The quantities $y$, $m$ and $\theta$ are related by the equation
$$y = Pmsin\theta + Q$$
where $P$ and $Q$ are constants.
Using your answers in (e)(iii), determine the values of $P$ and $Q$. Give appropriate units.
$P = \text{..................................................}$
$Q = \text{..................................................[2]}$
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(a) (i) Take the \textbf{shorter} of the two wires.
(ii) Measure and record the diameter \( d \) of the wire.
\[ d = \text{..................................................} \; [1] \]
(iii) Calculate the cross-sectional area \( A \) of the wire using
\[ A = \frac{\pi d^2}{4} \]
\[ A = \text{..................................................} \; [1] \]
(b) (i) Secure the hook of the mass hanger to one end of the wire leaving at least 20 cm of excess wire. The wire may be wrapped around the hook several times.
(ii) Set up the apparatus as shown in Fig. 2.1.
The length \( L \) of wire between the clip and the hook of the mass hanger should be approximately 15 cm.
(iii) Measure and record \( L \).
\[ L = \text{..................................................} \; [1] \]
(iv) Estimate the percentage uncertainty in your value of \( L \).
percentage uncertainty = \text{..................................................} \; [1]
(c) (i) Calculate \( C \) where
\[ C = \sqrt{\frac{L}{A}} \]
\[ C = \text{..................................................} \; [1] \]
(ii) Justify the number of significant figures that you have given for your value of \( C \).
.............................................................................................................
.............................................................................................................
............................................................................................................. \; [1]
(d) (i) Twist the mass hanger through approximately 180°. Release the mass hanger. The mass hanger will oscillate as shown in Fig. 2.2.
(ii) Take measurements to determine the period \( T \) of the oscillations. Record \( T \).
\[ T = \text{..................................................} \; [1] \]
(iii) Remove the wire from the mass hanger.
(e) (i) Take the \textbf{longer} wire. Repeat (a)(ii) and (a)(iii).
\[ d = \text{..................................................} \]
\[ A = \text{..................................................} \]
(ii) Secure the hook of the mass hanger to one end of the wire leaving 40 cm of excess wire. Repeat (b)(ii), (b)(iii), (c)(i) and (d) for a value of \( L \) of approximately 30 cm.
\[ L = \text{..................................................} \]
\[ C = \text{..................................................} \]
\[ T = \text{..................................................} \; [3] \]
(f) It is suggested that the relationship between \( T \) and \( C \) is
\[ T = kC \]
where \( k \) is a constant.
(i) Using your data, calculate two values of \( k \).
\[ \text{first value of } k = \text{..................................................} \]
\[ \text{second value of } k = \text{..................................................} \; [1] \]
(ii) 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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