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A student wishes to investigate projectile motion.
A small ball is rolled with velocity $v$ along a horizontal surface. When the ball reaches the end of the horizontal surface, it falls and lands on a lower horizontal surface. The vertical displacement of the ball is $p$ and the horizontal displacement of the ball is $q$, as shown in Fig 1.1.
It is suggested that $gq^2 = 2pv^2$ where $g$ is the acceleration of free fall.
Design a laboratory experiment to investigate how $q$ is related to $p$ and how $v$ may be determined from the results. 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.
536
531
594
A student is investigating a non-inverting operational amplifier (op-amp) circuit. The circuit is set up as shown in Fig. 2.1.
The op-amp is connected to a +18V and –18V power supply.
E is the e.m.f. of the cell, which has a value of 1.6 ± 0.1 V.
An experiment is carried out to investigate how the reading V on the voltmeter varies with resistance R.
It is suggested that V and R are related by the equation
$$ V = \frac{F}{R} E + E $$
where F is the resistance of the fixed resistor in the circuit.
(a) A graph is plotted of \( \frac{V}{E} \) on the y-axis against \( \frac{1}{R} \) on the x-axis. Express the gradient in terms of F. [1]
(b) Values of R and V are given in Fig. 2.2.
Calculate and record values of \( \frac{1}{R} / 10^{-3} \Omega^{-1} \) and \( \frac{V}{E} \) in Fig. 2.2. Include the absolute uncertainties in \( \frac{V}{E} \). [3]
(c) (i) Plot a graph of \( \frac{V}{E} \) against \( \frac{1}{R} / 10^{-3} \Omega^{-1} \). Include error bars for \( \frac{V}{E} \). [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 in (c)(iii), determine the value of F. Include the absolute uncertainty in your value and an appropriate unit. [2]
(e) For one measurement, R has a value of 120Ω ± 5%.
(i) Determine the value of \( \frac{V}{E} \) using the relationship given and your answer in (d).
Include the absolute uncertainty in your answer. [2]
(ii) Determine the expected voltmeter reading. [1]
590
572
583
