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(a) (i) You have been provided with some masses.
Set up the apparatus as shown in Fig. 1.1.
* Mass Q should be 200 g.
* The distance between the 50 cm mark on the rule and the string loop supporting the rule is \( x \). Adjust the position of the metre rule so that \( x \) is approximately 15 cm.
* The distance between the string loop supporting mass P and the string loop supporting the rule is \( z \). Adjust the position of mass P so that \( z \) is approximately 30 cm.
* The distance between the string loop supporting the rule and the string loop supporting mass Q is \( y \). Adjust the position of mass Q until the rule is balanced.
* Measure and record \( z \).
\( z = \text{.................................} \) \([1]\)
(ii) Measure and record \( x \).
\( x = \text{.................................} \)
* Measure and record \( y \).
\( y = \text{.................................} \text{[1]} \)
(b) * Write down your value of \( z \) from (a)(i).
\( z = \text{.............................} \)
* Keeping \( z \) constant, change \( x \) and adjust \( y \) until the rule is balanced. Repeat until you have six sets of values of \( x \) and \( y \). Record your results in a table.
You may include readings where \( x \) is measured to the left of the 50 cm mark. In such cases \( x \) has a negative value.
(c) (i) Plot a graph of \( y \) on the \( y \)-axis against \( x \) 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{.................................} \text{[2]}
(d) It is suggested that the quantities \( y \) and \( x \) are related by the equation
\( y = Ax + B \)
where \( A \) and \( B \) are constants.
Using your answers in (c)(iii), determine the values of \( A \) and \( B \). Give appropriate units.
\( A = \text{.................................} \)
\( B = \text{.................................} \text{[2]}
(e) The mass of P is \( p \). The mass of Q is \( q \), where \( q = 0.200\text{ kg} \).
The constants \( A \) and \( B \) are related to \( p \), \( q \) and \( z \) by
\( A = \frac{p}{q} \) and \( B = \frac{pz}{q} \).
Calculate \( p \).
\( p = \text{.................................} \text{ kg [1]} \)
(f) The experiment is repeated using the same equipment but a smaller value of \( z \). For this experiment, draw a second line on the graph to show the expected results. Label this line W. \text{[1]}
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(a) (i) You have been provided with a bar magnet, masses and Blu-Tack.
• The total mass of the mass hanger and mass should be 200 g. Use the Blu-Tack to fix the bar magnet to the mass hanger, as shown in Fig. 2.1.
• Set up the apparatus as shown in Fig. 2.2.
• Pull the mass down through a short distance. Release the mass. The mass and magnet will oscillate.
• Determine the period $T$ of these oscillations.
$T =$ ........................................................... [1]
(ii) Calculate the frequency $f$ of the oscillations where $f = \frac{1}{T}$.
$f =$ ......................................................... Hz [1]
(iii) Justify the number of significant figures that you have given for your value of $f$.
................................................................. [1]
(b) (i) Take the cardboard tube with more turns of wire.
• Count and record the number $n$ of turns of wire around the tube.
$n =$ ......................................................... [1]
(ii) • Connect the ammeter to the ends of the wire around the tube and place the tube below the magnet.
• Adjust the height of the bottom of the magnet so that it is level with the top of the tube as shown in Fig. 2.3.
• Pull the mass down so that it rests on the top of the tube with the magnet passing centrally through the tube. Release the mass. The mass will oscillate.
• Measure and record the maximum current $I$ shown by the ammeter.
$I =$ .......................................................... μA [1]
(iii) Estimate the percentage uncertainty in your value of $I$.
percentage uncertainty = ............................................. [1]
(c) (i) • Remove the tube.
• Increase the total mass to 500 g.
• Take measurements to determine the period $T$ and frequency $f$ of the oscillations of the mass and the magnet.
$T =$ ............................................................
$f =$ .......................................................... Hz [2]
(ii) Keep the mass as 500 g and use the tube with fewer turns of wire to repeat (b)(i) and (b)(ii).
$n =$ ............................................................
$I =$ ............................................................ μA [2]
(d) It is suggested that the relationship between $I$, $n$ and $f$ is
$$I = knf$$
where $k$ is a constant.
(i) Using your data, calculate two values of $k$.
first value of $k =$ ............................................................
second value of $k =$ ........................................................ [1]
(ii) Explain whether your results support the suggested relationship.
................................................................. [1]
(e) (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. .......................................................................
.......................................................................... [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. .......................................................................
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3. .......................................................................
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4. .......................................................................
.......................................................................... [4]
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