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When a current passes through a wire, the wire becomes hot and expands.
This can be investigated in a laboratory by passing a current through a wire of diameter $d$ and measuring the displacement $y$, as shown in Fig. 1.1.
It is suggested that the diameter $d$ of the wire is related to $y$ by the equation
$y = pd^q$
where $p$ and $q$ are constants.
Design a laboratory experiment to investigate the relationship between $d$ and $y$, so as to determine a value for $q$. You should draw a diagram 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.
521
557
558
An experiment is carried out to investigate how the time t for a steel ball to fall through air varies with the height h through which it falls.
The equipment is set up as shown in Fig. 2.1.
An electromagnet is used to release the ball. As soon as the ball is released, it passes a light gate, which starts a timer. As the ball passes the lower light gate, the timer is stopped.
It is suggested that $t$ and $h$ are related by the equation
$h = \frac{1}{2}gt^2$
where $g$ is the acceleration of free fall.
(a) A graph is plotted with $t^2$ on the $y$-axis and $h$ on the $x$-axis. Express the gradient in terms of $g$. [1]
(b) Values of $h$ and $t$ are given in Fig. 2.2.
Calculate and record values of $t^2$ in Fig. 2.2. Include the absolute uncertainties. [3]
(c) (i) Plot a graph of $t^2 / s^2$ against $h / m$. Include error bars for $t^2$. [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]
(d) Using your answer to (c)(iii), determine the value of $g$. Include the absolute uncertainty in your value and an appropriate unit. [3]
(e) The experiment is repeated from the top of a building.
(i) The time taken for the steel ball to fall is 2.21 ± 0.01 s. Using your value of $g$, calculate the height $b$ of the building. [1]
(ii) Determine the percentage uncertainty in $b$. [1]
557
589
520
