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A student is investigating the motion of a small cube on a turntable connected to an electric motor as shown in Fig. 1.1.
[Image: Fig_1.1]
The cube is placed at a distance $r$ from the centre of the turntable. It is suggested that the relationship between $r$ and the maximum frequency $f$ of the turntable for which the cube does not move relative to the turntable is
$$ K = 4 \pi^2 m f r $$
where $m$ is the mass of the cube and $K$ is a constant.
Design a laboratory experiment to test the relationship between $f$ and $r$. Explain how your results could be used to determine a value for $K$. You should draw a diagram, on page 3, showing the arrangement of your equipment. In your account you should pay particular attention to
• the procedure to be followed,
• the measurements to be taken,
• the control of variables,
• the analysis of the data,
• any safety precautions to be taken.
530
543
544
A student is investigating the current in a circuit. The circuit is set up as shown in Fig. 2.1.
Two resistors P and Q are connected to a power supply of e.m.f. $E$ and negligible internal resistance. The current $I$ is measured.
The resistance of resistor P is P. The experiment is repeated for different values of $P$.
It is suggested that $I$ and $P$ are related by the equation $E = I(P + Q)$ where $Q$ is the resistance of resistor $Q$.
(a) A graph is plotted of $\frac{1}{I}$ on the y-axis against $P$ on the x-axis.
Determine expressions for the gradient and the y-intercept.
gradient = ....................................................
y-intercept = ................................................
(b) Values of $P$ and $I$ are given in Fig. 2.2.
The tolerance of each value of $P$ is ±5%.
[Table_1]
Calculate and record values of $\frac{1}{I}\text{ A}^{-1}$ in Fig. 2.2.
Determine the absolute uncertainties in $P$. [2]
(c) (i) Plot a graph of $\frac{1}{I}\text{ A}^{-1}$ against $P/\Omega$. Include error bars for $P$. [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 absolute uncertainty in your answer.
gradient = ....................................................[2]
(iv) Determine the y-intercept of the line of best fit. Include the absolute uncertainty in your answer.
y-intercept = ...................................................[2]
(d) (i) Using your answers to (a), (c)(iii) and (c)(iv), determine the values of $E$ and $Q$. Include appropriate units.
$E$ = ................................................
$Q$ = ................................................[2]
(ii) Determine the percentage uncertainties in $E$ and $Q$.
percentage uncertainty in $E$ = ................................................... %
percentage uncertainty in $Q$ = ................................................... %[2]
505
592
506
