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A student is investigating how the resistance $R$ of nichrome in the form of a wire varies with temperature $\theta$.
It is suggested that
$$R = R_0(1 + \alpha \theta)$$
where $R_0$ is the resistance at $0\,^{\circ}\text{C}$, $\alpha$ is a constant and $\theta$ is the temperature measured in $^{\circ}\text{C}$.
Design a laboratory experiment to test the relationship between $\theta$ and $R$ and determine the value of $\alpha$. 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.
544
591
530
A student is investigating the stopping distance for a motorcycle with high-performance brakes. A motorcyclist riding and stopping a motorcycle on a test track is recorded on film. The stopping distance $d$ is measured for different speeds $v$.
[Image_1: Motorcycle with arrow indicating speed $v$]
It is suggested that $v$ and $d$ are related by the equation $d = \frac{v^2}{2a} + vt$ where $a$ is the deceleration of the motorcycle and $t$ is the thinking time of the rider.
(a) A graph is plotted of $\frac{d}{v}$ on the $y$-axis against $v$ on the $x$-axis. Determine expressions for the gradient and $y$-intercept in terms of $a$ and $t$.
gradient = ...........................................
y-intercept = ........................................... [1]
(b) Values of $v$ and $d$ are given in Fig. 2.2.
[Table_1: Fig. 2.2]
\[
\begin{array}{|c|c|}
\hline
v/\text{ms}^{-1} & d/\text{m} \\
\hline
10 \pm 1 & 13.0 \pm 0.5 \\
15 \pm 1 & 24.5 \pm 0.5 \\
20 \pm 1 & 39.5 \pm 0.5 \\
25 \pm 1 & 57.5 \pm 0.5 \\
30 \pm 1 & 79.0 \pm 0.5 \\
35 \pm 1 & 103.0 \pm 0.5 \\
\hline
\end{array}
\]
Calculate and record values of $\frac{d}{v}/s$ in Fig. 2.2. Include the absolute uncertainties in $\frac{d}{v}$. [3]
(c) (i) Plot a graph of $\frac{d}{v}/s$ against $v/\text{ms}^{−1}$. Include error bars for $\frac{d}{v}$. Do not include horizontal error bars for $v$. [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]
[Graph space provided]
(iv) Determine the $y$-intercept of the line of best fit. Include the uncertainty in your answer. [2]
(d) (i) Using your answers to (c)(iii) and (c)(iv), determine values for $a$ and $t$. Include an appropriate unit for each value.
$a = ...........................................$
$t = ...........................................$ [2]
(ii) Using your answers to (c)(iii) and (c)(iv), determine the percentage uncertainty in $a$ and $t$.
percentage uncertainty in $a = ...........................................$ %
percentage uncertainty in $t = ...........................................$ % [1]
545
537
517
