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A student is investigating the bending of a loaded wooden strip. Fig. 1.1 shows a rectangular strip of width $b$ and thickness $t$ overhanging the edge of a bench. A length $L$ of the strip is unsupported.
Fig. 1.1
A load of mass $M$ is positioned at point $P$. This causes the unsupported part of the strip to bend with a deflection $s$, as shown in Fig. 1.2.
Fig. 1.2 (not to scale)
It is suggested that the relationship between $s$ and $L$ is
$$ E = \frac{4MglL^3}{bst^3} $$
where $g$ is the acceleration of free fall and $E$ is the Young modulus of the wood.
Design a laboratory experiment to test the relationship between $s$ and $L$. Explain how your results could be used to determine a value for $E$.
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. [15]
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A student is investigating a rotary variable resistor, as shown in Fig. 2.1.
The variable resistor is connected to a battery of electromotive force (e.m.f.) $E$ and negligible internal resistance, as shown in Fig. 2.2.
The student uses a protractor to measure the angle $\theta$ through which the spindle of the variable resistor is rotated and records the current $I$.
The experiment is repeated for different angles.
It is suggested that $I$ and $\theta$ are related by the equation
$E = IK\theta$
where $K$ is a constant.
(a) A graph is plotted of $\frac{1}{I}$ on the $y$-axis against $\theta$ on the $x$-axis.
Determine an expression for the gradient.
gradient = ...................................................... [1]
(b) Values of $\theta$ and $I$ are given in Fig. 2.3.
[Table_1]
Calculate and record values of $\frac{1}{I}/A^{-1}$ in Fig. 2.3.
Include the absolute uncertainties in $\frac{1}{I}$.
[2]
(c) (i) Plot a graph of $\frac{1}{I}/A^{-1}$ against $\theta/^{\circ}$.
Include error bars for $\frac{1}{I}/A^{-1}$.
[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]
(d) The student measured the e.m.f. of the battery twice. The student's values were 9.6 V and 9.2 V.
Determine the average e.m.f $E$ of the battery. Include the absolute uncertainty in $E$.
$E = ...........................................................$ V [1]
(e) (i) Using your answers to (a), (c)(iii) and (d), determine the value of $K$. Include an appropriate unit.
$K = ...........................................................$ [2]
(ii) Determine the percentage uncertainty in $K$.
percentage uncertainty = ..................................... % [1]
(f) Determine the angle $\theta$ through which the spindle of the variable resistor is rotated so that the current is 10.0 mA. Include the absolute uncertainty in your answer.
$\theta = .....................................................^{\circ}$ [2]
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