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In this experiment, you will investigate an electrical circuit.
(a) • Assemble the circuit as shown in Fig. 1.1.
• A and B are crocodile clips. P Q and R S are wires. Connect A near the midpoint of P Q.
• Measure and record the length x of wire between P and A.
$$x = \text{................................................ cm}$$ [1]
(b) • Connect B to R S.
• Close the switch.
• Adjust the position of B until the voltmeter reading is as close as possible to zero.
• Measure and record the length y of wire between R and B.
$$y = \text{................................................ cm}$$
• Open the switch. [1]
(c) Change x and repeat (b) until you have six sets of values of x and y. Record your results in a table.
Include values of $\frac{1}{x}$ and $\frac{1}{y}$ in your table.
[10]
(d) (i) Plot a graph of $\frac{1}{y}$ on the y-axis against $\frac{1}{x}$ on the x-axis. [3]
(ii) Draw the straight line of best fit. [1]
(iii) Determine the gradient and y-intercept of this line.
gradient $= \text{................................................}$
y-intercept $= \text{................................................}$ [2]
(e) It is suggested that the quantities y and x are related by the equation
$$\frac{1}{y} = \frac{a}{x} + b$$
where a and b are constants.
Use your answers in (d)(iii) to determine the values of a and b. Give appropriate units.
$$a = \text{................................................}$$
$$b = \text{................................................}$$ [2]
563
564
591
(a) • Set up the apparatus as shown in Fig. 2.1.
• Adjust the apparatus until the angle $\theta$ between the board and the bench has a value between $32^{\circ}$ and $38^{\circ}$.
• Measure and record $\theta$.
$\theta = \text{...................................................} ^{\circ}$ [1]
(b) • Attach the newton meter to the wooden block using the string loop.
• Place the block on the board, with the label of the block at the top.
• Pull the newton meter and block up the board at a constant speed. Keep the string loop parallel to the board, as shown in Fig. 2.2.
• Record the force $F$ when the block is travelling at a constant speed.
$F = \text{...................................................}$ [2]
(c) Estimate the percentage uncertainty in your value of $F$.
percentage uncertainty = ................................................... [1]
(d) (i) • Adjust the board so that $\theta$ is between $12^{\circ}$ and $18^{\circ}$.
• Measure and record $\theta$.
$\theta = \text{...................................................} ^{\circ}$ [1]
(ii) Repeat (b).
$F = \text{...................................................}$ [2]
(e) Using the newton meter, measure and record the weight $W$ of the block and hook.
$W = \text{...................................................}$ [1]
(f) It is suggested that the relationship between $F$, $W$ and $\theta$ is $\frac{F}{W} = \sin \theta + \mu \cos \theta$ where $\mu$ is a constant.
(i) Using your data, calculate two values of $\mu$.
first value of $\mu = \text{...................................................}$
second value of $\mu = \text{...................................................}$ [1]
(ii) Explain whether your results support the suggested relationship. [1]
(g) Using your second value of $\mu$, calculate the value of $F$ when $\theta = 65^{\circ}$. Give your answer to an appropriate number of significant figures.
$F = \text{...................................................}$ [2]
(h) (i) Describe four sources of uncertainty or limitations of the procedure for this experiment.
1. ...............................................................................................................................
...............................................................................................................................
2. ...............................................................................................................................
...............................................................................................................................
3. ...............................................................................................................................
...............................................................................................................................
4. ...............................................................................................................................
............................................................................................................................... [4]
(ii) Describe four improvements that could be made to this experiment. You may suggest the use of other apparatus or different procedures.
1. ...............................................................................................................................
...............................................................................................................................
2. ...............................................................................................................................
...............................................................................................................................
3. ...............................................................................................................................
...............................................................................................................................
4. ...............................................................................................................................
............................................................................................................................... [4]
545
512
578
