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(a) (i) Set up the circuit shown in Fig. 1.1. The distance $y$ between the crocodile clips should be approximately 80 cm. The resistor in the component holder labelled $R$ should have a resistance $R$ of 10Ω.
(ii) Record the value of $R$. $R = \text{.....................................................} \Omega$
(iii) Measure and record $y$. $y = \text{.....................................................}$
(iv) Close the switch.
(v) Record the ammeter reading $I$. $I = \text{..............................................}[1]$
(vi) Open the switch.
(b) (i) Remove the resistor in the component holder labelled $R$. Select a different resistor labelled with a numerical value and connect it in the component holder labelled $R$. Record the value of resistance $R$. $R = \text{.....................................................} \Omega$
(ii) Close the switch.
(iii) Adjust the position of the crocodile clips on the wire until the ammeter reading $I$ has the same value as in (a)(v).
(iv) Measure and record $y$. $y = \text{.....................................................}$
(v) Open the switch.
(c) Repeat (b) until you have six sets of readings of $R$ and $y$. Include values of $\frac{1}{y}$ and $\frac{1}{R}$ in your table.
(d) (i) Plot a graph of $\frac{1}{y}$ on the $y$-axis against $\frac{1}{R}$ 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) The quantities $y$ and $R$ are related by the equation $\frac{1}{y} = -\frac{P}{R} + Q$ where $P$ and $Q$ are constants. Using your answers in (d)(iii), determine values for $P$ and $Q$. Give appropriate units. $P = \text{.....................................................}$ $Q = \text{.....................................................}$ [2]
(f) (i) The e.m.f. $E$ of the d.c. power supply is given on the card. Record $E$. $E = \text{.....................................................}V$
(ii) Theory suggests that $Q = \frac{PI}{E - XI}$ where $X$ is the resistance of resistor $X$. Use values in (a)(v), (e) and (f)(i) to determine the value of $X$. $X = \text{.....................................................} \Omega [1]$
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In this experiment, you will investigate the motion of an oscillating mass.
(a) Set up the apparatus as shown in Fig. 2.1.
The value of $m$ should be 300 g.
(b) (i) Record $m$.
$$m = \text{..................................................}$$
(ii) Pull the mass hanger down through a short distance.
Release the mass hanger and watch the vertical oscillations.
(iii) Take measurements to determine the period $T$ of the vertical oscillations.
Record $T$. Your value of $T$ should be less than 1 s.
$$T = \text{..................................................} \text{[2]}$$
(c) (i) Calculate the value of $l$ using the equation
$$l = \frac{gT^2}{\pi^2}$$
where $g = 9.81 \text{ m s}^{-2}$.
$$l = \text{.................................................. m [1]}$$
(ii) Justify the number of significant figures that you have given for your value of $l$.
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$$\text{[1]}$$
(d) (i) Set up the apparatus shown in Fig. 2.2 using some of the string.
The length $d$ is the distance from the top of the string to the centre of the masses.
Tie knots so that length $d$ is approximately equal to your calculated value of $l$.
(ii) Measure and record $d$.
$$d = \text{.................................................. m [1]}$$
(iii) Estimate the percentage uncertainty in your value of $d$.
$$\text{percentage uncertainty} = \text{..................................................} [1]$$
(e) (i) Displace the mass approximately 10 cm to the right.
Release the mass. The mass will move to the left and back again.
Now ignore the movement of the mass and watch the coils of the spring.
Observe the coils moving further apart, then closer, further apart then closer.
At certain times the coils appear to stay the same distance apart.
(ii) Determine the time interval $t$ between two consecutive times when the coils appear to stay the same distance apart. Record $t$.
$$t = \text{..................................................} [1]$$
(iii) Remove the string from the mass and spring.
(f) Using a mass $m$ of 400 g, set up the apparatus as shown in Fig. 2.1.
Repeat (b), (c)(i), (d)(i), (d)(ii) and (e).
$$m = \text{..................................................}$$
$$T = \text{..................................................}$$
$$l = \text{.................................................. m}$$
$$d = \text{.................................................. m}$$
$$t = \text{..................................................} [3]$$
(g) It is suggested that the relationship between $t$ and $m$ is
$$t = km$$
where $k$ is a constant.
(i) Using your data, calculate two values of $k$.
$$\text{first value of } k = \text{..................................................}$$
$$\text{second value of } k = \text{..................................................} [1]$$
(ii) Explain whether your results support the suggested relationship.
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$$\text{[1]}$$
(h) (i) Describe four sources of uncertainty or limitations of the procedure for this experiment.
1. .........................................................................................................................
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2. .........................................................................................................................
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3. .........................................................................................................................
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4. .........................................................................................................................
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$$\text{[4]}$$
(ii) Describe four improvements that could be made to this experiment. You may suggest the use of other apparatus or different procedures.
1. .........................................................................................................................
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2. .........................................................................................................................
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3. .........................................................................................................................
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4. .........................................................................................................................
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$$\text{[4]}$$.
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