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Two identical light sources are viewed from a distance, as shown in Fig 1.1. When the angle θ between the light sources is large, they are seen as separate.
The sources are moved closer together. At a particular angle θ₁ the two sources appear as a single source.
It is suggested that θ₁ is directly proportional to the wavelength λ of the light from the sources.
Design a laboratory experiment using two light sources to test the relationship between θ₁ and λ. 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.
587
520
580
A trolley is attached to springs, as shown in Fig 2.1. When the trolley is displaced and then released, the trolley oscillates.
A student investigates how the maximum speed $v$ of a trolley varies with the total mass $M$ of the trolley.
The maximum speed is determined using the time $t$ taken for the card to pass through a light gate connected to an electronic timer. The length of the card is $5.0 \pm 0.1 \text{ cm}$.
It is suggested that $v$ and $M$ are related by the equation $$v = A \sqrt{\frac{k}{M}}$$ where $A$ is the initial displacement and $k$ is the spring constant of the springs.
(a) A graph is plotted of $v^2$ on the $y$-axis against $1/M$ on the $x$-axis. Determine an expression for the gradient in terms of $A$ and $k$. [1]
(b) Values of $M$ and $t$ are given in Fig. 2.2.
Calculate and record values of $(1/M)/\text{kg}^{-1}$ and $v^2/\text{m}^2\text{s}^{-2}$ in Fig. 2.2. Include the absolute uncertainties in $v^2$. [3]
(c) (i) Plot a graph of $v^2/\text{m}^2\text{s}^{-2}$ against $(1/M)/\text{kg}^{-1}$. Include error bars for $v^2$. [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) (i) The value of $A$ is $0.200 \pm 0.005\text{ m}$. Using your answer to (c)(iii), determine a value for $k$. Include an appropriate unit in your answer. [2]
(ii) Determine the percentage uncertainty in your value of $k$. [1]
(e) The experiment is repeated using the same springs and a trolley with total mass $0.75\text{ kg}$. The initial displacement is $0.100 \pm 0.005\text{ m}$.
Determine the maximum speed of the trolley. Include the absolute uncertainty in your answer. [2]
563
593
575
