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Rearranging relationships into linear form

Table of results and graph plotting

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191 questions

Physics/Paper 5/Analysis, Conclusions and Evaluation

CAIEA-Level9702-a · Paper 5

Analysis, Conclusions and Evaluation

191 questions· page 1 of 20

Q12025 Feb/Mar·P5215MMedium-HardPlanning

Fig. 1.1 shows two identical cylindrical metal conductors P and Q, each of length $L$ and cross-sectional area $A$ .

The conductors are placed parallel to each other. The perpendicular distance from the midpoint of P to point X is $p$ . The perpendicular distance from the midpoint of Q to point X is $q$ .

The two conductors are electrically connected in parallel. This parallel combination is connected in series to a power supply and a resistor. The potential difference $V$ between the ends of P is the same as the potential difference between the ends of Q.

The magnetic flux density at X due to the currents in the conductors is $B$ .

It is suggested that $B$ is related to $p$ by the relationship

B = \frac{YAV}{Lp} + \frac{YZAV}{Lq}

where $Y$ and $Z$ are constants.

Plan a laboratory experiment to test the relationship between $B$ and $p$ .

Draw a diagram showing the arrangement of your equipment.

Explain how the results could be used to determine values for $Y$ and $Z$ .

In your plan you should include:

the procedure to be followed
the measurements to be taken
the control of variables
the analysis of the data
any safety precautions to be taken.

Similar questions

Q22025 Feb/Mar·P529 partsMedium-EasyAnalysis, Conclusions and Evaluation

(a)

A graph is plotted of $\ln(\theta - \theta_R)$ on the $y$ -axis against $t$ on the $x$ -axis.

Determine expressions for the gradient and $y$ -intercept.

gradient = ______
$y$ -intercept = ______

(b)

Values of $t$ and $\theta$ are given in Table 2.1.

Table 2.1

$t$ / min	$\theta$ / °C	$(\theta - \theta_R)$ / °C	$\ln((\theta - \theta_R) / \text{°C})$
6.0	75.0 $\pm$ 0.5
12.0	64.5 $\pm$ 0.5
18.0	57.0 $\pm$ 0.5
24.0	50.0 $\pm$ 0.5
30.0	44.5 $\pm$ 0.5
36.0	41.0 $\pm$ 0.5

The value of $\theta_R$ is $(18.5 \pm 0.5)\ \text{°C}$ .

Calculate and record values of $(\theta - \theta_R) / \text{°C}$ and $\ln((\theta - \theta_R) / \text{°C})$ in Table 2.1. Include the absolute uncertainties in $(\theta - \theta_R)$ and $\ln((\theta - \theta_R) / \text{°C})$ .

(c)(i)

Plot a graph of $\ln((\theta - \theta_R) / \text{°C})$ against $t / \text{min}$ . Include error bars for $\ln((\theta - \theta_R) / \text{°C})$ .

(c)(ii)

Draw the straight line of best fit and a worst acceptable straight line on your graph. Label both lines.

(c)(iii)

Determine the gradient of the line of best fit. Include the absolute uncertainty in your answer.

gradient = ______

(c)(iv)

Determine the $y$ -intercept of the line of best fit. Include the absolute uncertainty in your answer.

$y$ -intercept = ______

(d)(i)

Using your answers to (a), (c)(iii) and (c)(iv), determine the values of $K$ and $\theta_0$ . Include appropriate units.

$K$ = ______ $\text{min}$
$\theta_0$ = ______ $\text{°C}$

(d)(ii)

Determine the absolute uncertainty in your value of $\theta_0$ .

absolute uncertainty = ______ $\text{°C}$

(e)

Determine the time $t$ for the temperature to reach $25.0\ \text{°C}$ .

$t$ = ______ $\text{min}$

Similar questions

Q12025 May/Jun·P5115MMedium-HardPlanning

Fig. 1.1 shows a thin coil of cross-sectional area $A$ and length $l$ connected to a resistor of resistance $S$ and two terminals.

An alternating voltage is applied to the terminals. The peak value of the alternating voltage is $E$ and the frequency is $f$ . The peak value of the potential difference $V$ across the resistor is determined using an oscilloscope.

It is suggested that $V$ is related to $f$ by the relationship

\frac{ES}{V} = \frac{KAN^2f}{l}

where $N$ is the number of turns on the coil and $K$ is a constant.

Plan a laboratory experiment to test the relationship between $V$ and $f$ .

Draw a diagram showing the arrangement of your equipment.

Explain how the results could be used to determine a value for $K$ .

In your plan you should include:

the procedure to be followed
the measurements to be taken
the control of variables
the analysis of the data
any safety precautions to be taken.

Similar questions

Q22025 May/Jun·P519 partsMedium-EasyAnalysis, Conclusions and Evaluation

(a)

A graph is plotted of $\frac{1}{I}$ on the $y$ -axis against $\frac{1}{n}$ on the $x$ -axis.

Determine expressions for the gradient and $y$ -intercept.

gradient = ______
$y$ -intercept = ______

(b)

Values of $n$ , $\frac{1}{n}$ and $I$ are given in Table 2.1.

Table 2.1

$n$	$\frac{1}{n}$	$I / \mu\text{A}$	$\frac{1}{I} / 10^3\ \text{A}^{-1}$
5	0.200	$455 \pm 5$
6	0.167	$525 \pm 5$
7	0.143	$580 \pm 5$
8	0.125	$635 \pm 5$
9	0.111	$685 \pm 5$
11	0.0909	$765 \pm 5$

Calculate and record values of $\frac{1}{I} / 10^3\ \text{A}^{-1}$ in Table 2.1. Include the absolute uncertainties in $\frac{1}{I}$ .

(c)(i)

Plot a graph of $\frac{1}{I} / 10^3\ \text{A}^{-1}$ against $\frac{1}{n}$ . Include error bars for $\frac{1}{I}$ .

(c)(ii)

Draw the straight line of best fit and a worst acceptable straight line on your graph. Label both lines.

(c)(iii)

Determine the gradient of the line of best fit. Include the absolute uncertainty in your answer.

gradient = ______

(c)(iv)

Determine the $y$ -intercept of the line of best fit. Include the absolute uncertainty in your answer.

$y$ -intercept = ______

(d)(i)

Using your answers to (a), (c)(iii) and (c)(iv), determine the values of $R$ and $Z$ . Include appropriate units.

$R$ = ______
$Z$ = ______

(d)(ii)

Determine the percentage uncertainty in your value of $R$ .

percentage uncertainty = ______ $\%$

(e)

The experiment is repeated with 20 resistors, each of resistance $R$ , connected in parallel between P and Q. Determine the total current $I$ in the circuit.

$I$ = ______ $\text{A}$

Similar questions

Q12025 May/Jun·P5215MMedium-HardPlanning

A thin solid disc of radius $r$ and thickness $z$ is attached to a thin axle. String is wrapped around the axle, as shown in Fig. 1.1.

A block of mass $m$ is attached to the string.

The block is released from rest and falls downwards. The block has speed $v$ when it has fallen through a distance $h$ from the point of release. The value of $v$ is determined using one light gate connected to a timer.

It is suggested that $v$ is related to $m$ by the relationship

\frac{h}{v^2} = \frac{\pi r^2 z}{2PQm} + \frac{1}{P}

where $P$ and $Q$ are constants.

Plan a laboratory experiment to test the relationship between $v$ and $m$ .

Draw a diagram showing the arrangement of your equipment.

Explain how the results could be used to determine values for $P$ and $Q$ .

In your plan you should include:

the procedure to be followed
the measurements to be taken
the control of variables
the analysis of the data
any safety precautions to be taken.

Similar questions

Q22025 May/Jun·P529 partsMedium-EasyAnalysis, Conclusions and Evaluation

(a)

A graph is plotted of $\frac{1}{V}$ on the $y$ -axis against $n$ on the $x$ -axis.

Determine expressions for the gradient and $y$ -intercept.

gradient = ______
$y$ -intercept = ______

(b)

Values of $n$ and the two measured values of the maximum potential difference $V_1$ and $V_2$ are given in Table 2.1.

Table 2.1

$n$	$V_1 / \text{V}$	$V_2 / \text{V}$	$V / \text{V}$	$\frac{1}{V} / \text{V}^{-1}$
2	4.30	4.20
3	3.65	3.75
4	3.30	3.20
5	2.85	2.95
6	2.65	2.55
7	2.30	2.40

Calculate and record values of $V / \text{V}$ and $\frac{1}{V} / \text{V}^{-1}$ in Table 2.1. Include the absolute uncertainties in $V$ and $\frac{1}{V}$ .

(c)(i)

Plot a graph of $\frac{1}{V} / \text{V}^{-1}$ against $n$ . Include error bars for $\frac{1}{V}$ .

(c)(ii)

Draw the straight line of best fit and a worst acceptable straight line on your graph. Label both lines.

(c)(iii)

Determine the gradient of the line of best fit. Include the absolute uncertainty in your answer.

gradient = ______

(c)(iv)

Determine the $y$ -intercept of the line of best fit. Include the absolute uncertainty in your answer.

$y$ -intercept = ______

(d)(i)

Using your answers to (a), (c)(iii) and (c)(iv), determine the values of $E$ and $C$ . Include appropriate units.

Data: $A = (2.2 \pm 0.2)\ \text{mF}$

$E$ = ______
$C$ = ______

(d)(ii)

Determine the percentage uncertainty in your value of $C$ .

percentage uncertainty = ______ $\%$

(e)

The experiment is repeated with 10 capacitors, each of capacitance $C$ , connected in parallel between P and Q. Determine the maximum potential difference $V$ between P and Q.

$V$ = ______ $\text{V}$

Similar questions

Q12025 May/Jun·P5315MMedium-HardPlanning

Fig. 1.1 shows a thin coil of cross-sectional area $A$ and length $l$ connected to a resistor of resistance $S$ and two terminals.

An alternating voltage is applied to the terminals. The peak value of the alternating voltage is $E$ and the frequency is $f$ . The peak value of the potential difference $V$ across the resistor is determined using an oscilloscope.

It is suggested that $V$ is related to $f$ by the relationship

\frac{ES}{V} = \frac{KAN^2f}{l}

where $N$ is the number of turns on the coil and $K$ is a constant.

Plan a laboratory experiment to test the relationship between $V$ and $f$ .

Draw a diagram showing the arrangement of your equipment.

Explain how the results could be used to determine a value for $K$ .

In your plan you should include:

the procedure to be followed
the measurements to be taken
the control of variables
the analysis of the data
any safety precautions to be taken.

Similar questions

Q22025 May/Jun·P539 partsMedium-EasyAnalysis, Conclusions and Evaluation

(a)

A graph is plotted of $\frac{1}{I}$ on the $y$ -axis against $\frac{1}{n}$ on the $x$ -axis.

Determine expressions for the gradient and $y$ -intercept.

gradient = ______
$y$ -intercept = ______

(b)

Values of $n$ , $\frac{1}{n}$ and $I$ are given in Table 2.1.

Table 2.1

$n$	$\frac{1}{n}$	$I / \mu\text{A}$	$\frac{1}{I} / 10^3\text{ A}^{-1}$
5	0.200	$455 \pm 5$
6	0.167	$525 \pm 5$
7	0.143	$580 \pm 5$
8	0.125	$635 \pm 5$
9	0.111	$685 \pm 5$
11	0.0909	$765 \pm 5$

Calculate and record values of $\frac{1}{I} / 10^3\text{ A}^{-1}$ in Table 2.1. Include the absolute uncertainties in $\frac{1}{I}$ .

(c)(i)

Plot a graph of $\frac{1}{I} / 10^3\text{ A}^{-1}$ against $\frac{1}{n}$ . Include error bars for $\frac{1}{I}$ .

(c)(ii)

Draw the straight line of best fit and a worst acceptable straight line on your graph. Label both lines.

(c)(iii)

Determine the gradient of the line of best fit. Include the absolute uncertainty in your answer.

gradient = ______

(c)(iv)

Determine the $y$ -intercept of the line of best fit. Include the absolute uncertainty in your answer.

$y$ -intercept = ______

(d)(i)

Using your answers to (a), (c)(iii) and (c)(iv), determine the values of $R$ and $Z$ . Include appropriate units.

$R$ = ______
$Z$ = ______

(d)(ii)

Determine the percentage uncertainty in your value of $R$ .

percentage uncertainty = ______ %

(e)

The experiment is repeated with 20 resistors, each of resistance $R$ , connected in parallel between P and Q. Determine the total current $I$ in the circuit.

$I$ = ______ $\text{A}$

Similar questions

Q12025 May/Jun·P5415MMedium-HardPlanning

A ball is dropped on to an inclined thin metal sheet, as shown in Fig. 1.1.

The angle between the sheet and the horizontal bench is $\theta$ . The height of the point of contact of the ball and the sheet is $z$ . The horizontal distance travelled by the ball between its points of contact with the sheet and the bench is $d$ , as shown in Fig. 1.1.

It is suggested that $d$ is related to $\theta$ by the relationship

d = \frac{Pv^2 \sin 4\theta}{g} + Q\sqrt{z}

where $v$ is the speed of the ball as it makes contact with the sheet, $g$ is the acceleration of free fall, and $P$ and $Q$ are constants.

Plan a laboratory experiment to test the relationship between $d$ and $\theta$ .

Draw a diagram showing the arrangement of your equipment.

Explain how the results could be used to determine values for $P$ and $Q$ .

In your plan you should include:

the procedure to be followed
the measurements to be taken
the control of variables
the analysis of the data
any safety precautions to be taken.

Diagram

Similar questions

Q22025 May/Jun·P548 partsMedium-EasyAnalysis, Conclusions and Evaluation

(a)

A graph is plotted of $\lg \lambda$ on the $y$ -axis against $\lg \mu$ on the $x$ -axis.

Determine expressions for the gradient and $y$ -intercept.

gradient = ______
$y$ -intercept = ______

(b)

Values of $\mu$ and $\lambda$ are given in Table 2.1.

Table 2.1

$\mu$	$\lambda$	$\lg \mu$	$\lg \lambda$
$4.6 \pm 0.4$	$500$
$5.4 \pm 0.4$	$800$
$8.4 \pm 0.4$	$3200$
$11 \pm 1$	$7000$
$16 \pm 1$	$25000$
$18 \pm 1$	$38000$

Calculate and record values of $\lg \mu$ and $\lg \lambda$ in Table 2.1.
Include the absolute uncertainties in $\lg \mu$ .

(c)(i)

Plot a graph of $\lg \lambda$ against $\lg \mu$ .
Include error bars for $\lg \mu$ .

(c)(ii)

Draw the straight line of best fit and a worst acceptable straight line on your graph. Label both lines.

(c)(iii)

Determine the gradient of the line of best fit. Include the absolute uncertainty in your answer.

gradient = ______

(c)(iv)

Determine the $y$ -intercept of the line of best fit. Include the absolute uncertainty in your answer.

$y$ -intercept = ______

(d)

Using your answers to (a), (c)(iii) and (c)(iv), determine the values of $k$ and $n$ . Include the absolute uncertainties in your values. You need not be concerned with units.

$k$ = ______
$n$ = ______

(e)

The mass of the Sun is $2.0 \times 10^{30}\ \text{kg}$ . The star Alpha Centauri B has a value of $\lambda$ of $0.46$ .

Determine the mass $M$ of Alpha Centauri B.

$M$ = ______ $\text{kg}$

Similar questions

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