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(a) Set up the apparatus as shown in Fig. 1.1, with the distance $x$ approximately equal to 25 cm.
(b) (i) Ensure that the spring is vertical and the wooden strip is parallel to the bench.
(ii) Measure and record the distance $x$ between the string loop and the end of the wooden strip, as shown in Fig. 1.1.
$x = \text{.......................................}$ [1]
(iii) Push down the free end of the wooden strip by approximately 2 cm. Release it so that it oscillates.
(iv) Take measurements to find the period $T$ of the oscillations. Record $T$.
$T = \text{............................................ s}$ [2]
(c) Vary $x$ by moving the string loop along the wooden strip and repeat (b) until you have six sets of values for $x$ and $T$. Do not use values of $x$ less than 15 cm. Include values for $\frac{1}{T^2}$ in your table. [9]
(d) (i) Plot a graph of $\frac{1}{T^2}$ 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.
gradient $= \text{................................................}$
$y$-intercept $= \text{................................................}$ [2]
(e) The quantities $x$ and $T$ are related by the equation $\frac{1}{T^2} = px + q$
where $p$ and $q$ are constants.
Use your answers from (d)(iii) to determine the values of $p$ and $q$. Give appropriate units.
$p = \text{.........................................................}$
$q = \text{.........................................................}$ [2]
578
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(a) Set up the apparatus with the metre rule resting on the rods of the clamps, as shown in Fig. 2.1. The metre rule should be parallel to the bench.
(b) Measure and record the length $L$ of the wooden strip labelled A.
$L = \text{...................}$ [1]
(c) (i) Position the stands so that the rod of one of the clamps is supporting the metre rule at the 10 cm mark, and the rod of the other clamp is supporting the metre rule at the 90 cm mark.
(ii) Using Blu-Tack, fix the wooden strip labelled A to the metre rule at the 0 cm end, as shown in Fig. 2.2.
(iii) Without touching the metre rule, slowly slide the stands towards each other until their bases touch each other, as shown in Fig. 2.3.
(iv) Measure and record the distances $x_1$ and $x_2$ of the points of contact from the end of the rule, as shown in Fig. 2.3.
$x_1 = \text{................... cm}$
$x_2 = \text{................... cm}$ [2]
(v) Calculate the value of $X$, where $X = \frac{(x_1 + x_2)}{2}$.
$X = \text{................... cm}$ [1]
(d) Estimate the percentage uncertainty in your value of $X$.
percentage uncertainty = \text{...................} [1]
(e) Repeat (b) and (c) using the wooden strip labelled B.
$L = \text{...................}$
$x_1 = \text{................... cm}$
$x_2 = \text{................... cm}$
$X = \text{................... cm}$ [3]
(f) It is suggested that the relationship between $L$ and $X$ is
$$LX = k(d - X)$$
where $d = 50.0 \text{ cm}$ and $k$ is a constant.
(i) Using your data, calculate two values of $k$.
first value of $k = \text{...................}$
second value of $k = \text{...................}$ [1]
(ii) Justify the number of significant figures you have given for your values of $k$.
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[1]
(iii) Explain whether your results in (f)(i) support the suggested relationship.
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[1]
(g) Suggest the value of $X$ you would expect to obtain if the experiment was repeated with an identical wooden strip fixed at each end of the metre rule.
$X = \text{................... cm}$ [1]
(h) (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]
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