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In this experiment you will investigate how the motion of two pendulums depends on the tension in a spring connecting them.
(a) Measure and record the unstretched length $l_0$ of the coiled part of the spring as shown in Fig. 1.1. [1]
(b) (i) Set up the apparatus as shown in Fig. 1.2.
(ii) Position the stands so that the coiled part of the spring has approximate length $l_0 + 2 \text{ cm}$ (so that the spring is extended by approximately 2 cm).
(iii) Measure and record the length $l$ of the coiled part of the spring. Calculate the extension $x$ of the spring, where $x = l - l_0$.
(iv) Gently pull bob A towards you. Release the bob and watch the movement of the two bobs.
Bob A will eventually stop and start moving again. It will then stop for a second time.
Determine and record the time $T$ between these two stops. [2]
(c) By moving the stands further apart, repeat (b)(iii) and (b)(iv) until you have six sets of readings of $l$, $x$ and $T$, with $x$ in the range $2 \text{ cm} \leq x \leq 10 \text{ cm}$. [9]
(d) (i) Plot a graph of $T$ 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. [2]
(e) It is suggested that the quantities $T$ and $x$ are related by the equation $T = px + q$ where $p$ and $q$ are constants.
Use your answers in (d)(iii) to determine the values of $p$ and $q$. Give appropriate units. [1]
(f) Use your values in (e) to determine the extension $x$ that would be expected to give a value of $T = 75 \text{ s}$. [1]
554
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502
In this experiment you will drop a mass onto a rod standing in sand and investigate the distance that the rod moves into the sand.
(a) You have been provided with two wooden rods of different diameters. Measure and record the diameter $d$ of the thicker rod. [2]
(b) Flatten the surface of the sand. Stand the rod vertically in the sand up to the mark drawn on the rod, as shown in Fig. 2.1.
(c) (i) Hold the mass hanger so that the distance $h$ between its bottom and the top of the rod is approximately 10 cm. The centre of the bottom of the mass hanger should be vertically above the wooden rod, as shown in Fig. 2.2.
(ii) Measure and record the height $h$.
(d) (i) Drop the mass hanger from this height $h$ above the rod.
(ii) Without making a further mark on the rod, determine the new length $x$ of the rod below the surface of the sand, as shown in Fig. 2.3. [1]
(iii) Calculate and record the change in depth $y$ of the rod in the sand as a result of the impact of the mass hanger. [1]
(e) Estimate the percentage uncertainty in your value of $y$. [1]
(f) Using the thinner rod repeat (a), (b), (c)(i), and (d). Use the same value of $h$ as in (c)(ii). [3]
(g) It is suggested that the quantities $y$ and $d$ are related by the equation
$$\frac{y}{d^2} = k$$
where $k$ is a constant.
(i) Using your data, calculate two values of $k$. [1]
(ii) Explain whether your results support the suggested relationship. [1]
(iii) Justify the number of significant figures that you have given for your values of $k$. [1]
(h) (i) Describe four sources of uncertainty or limitations of the procedure for this experiment. [4]
(ii) Describe four improvements that could be made to this experiment. You may suggest the use of other apparatus or different procedures. [4]
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