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A fairground ride carries passengers in chairs which are attached by metal rods to a rotating central pole, as shown in Fig 1.1. When the pole rotates with angular velocity $\omega$, the rods make an angle $\theta$ to the vertical.
It is suggested that $\cos \theta$ is inversely proportional to $\omega^2$.
Design a laboratory experiment, using a small object to represent an occupied chair, to test the relationship between $\theta$ and $\omega$. You should draw a diagram, on page 3, showing the arrangement of your equipment. In your account you should pay particular attention to
(a) the procedure to be followed,
(b) the measurements to be taken,
(c) the control of variables,
(d) the analysis of the data,
(e) the safety precautions to be taken.
540
562
535
A current-carrying wire is clamped at each end, as shown in Fig 2.1. A student investigates how the deflection $y$ at the centre of the wire varies with the current $I$.
For different currents, the deflection is recorded.
It is suggested that $y$ and $I$ are related by the equation $y = sI^r$ where $r$ and $s$ are constants.
(a) A graph is plotted of lg $y$ on the $y$-axis against lg $I$ on the $x$-axis. Determine expressions for the gradient and $y$-intercept in terms of $r$ and $s$. [1]
(b) Values of $I$ and $y$ are given in Fig. 2.2.
Calculate and record values of lg ($I$/$10^{-2}$ A) and lg ($y$/mm) in Fig. 2.2. Include the absolute uncertainties in lg ($y$/mm). [3]
(c) (i) Plot a graph of lg ($y$/mm) against lg ($I$/$10^{-2}$ A). Include error bars for lg ($y$/mm). [2]
(ii) Draw the straight line of best fit and a worst acceptable straight line on your graph. Both lines should be clearly labelled. [2]
(iii) Determine the gradient of the line of best fit. Include the uncertainty in your answer. [2]
(iv) Determine the $y$-intercept of the line of best fit. Include the uncertainty in your answer. [2]
(d) Using your answers to (c)(iii) and (c)(iv), determine values for $r$ and $s$. Include the uncertainties in your answers. You need not be concerned with the units of $r$ and $s$. [3]
561
548
557
