Analysis, Conclusions and Evaluation

Method 1

The student:

• takes 1 sheet of paper from a pack of 500 sheets and folds it in half
• folds the paper in half again
• repeats this process until the paper has been folded in half 5 times
• measures and records the thickness of the folded sheet.

Thickness of folded paper = 0.4 cm

The folded sheet is now 32 sheets of paper thick.

Calculate the mean thickness of 1 sheet of paper.

mean thickness of 1 sheet = ______ $\text{cm}$

Calculate the mean thickness of the pack.

Give your answer to 2 significant figures.

mean thickness of pack = ______ $\text{cm}$

Calculate the mean thickness of 1 sheet of paper.

mean thickness of 1 sheet = ______ $\text{cm}$

State which method of measuring the mean thickness of a sheet of paper is more accurate. Give one reason for your answer.

The time $t$ for the water level to fall a distance $h$ is measured three times.

When $h = 14.0\,\text{cm}$, the times measured in seconds are:

$35.4 \qquad 35.6 \qquad 35.3$

Calculate the average time $t_{\mathrm{av}}$.

$t_{\mathrm{av}} = \_\_\_\_\_\_$

The experiment is repeated for a range of values of $h$. The results are shown in Fig. 2.2.

Fig. 2.2

On Fig. 2.2, add your value for $t_{av}$ from (a).

On Fig. 2.3, plot a graph of $t_{av} / \text{s}$ on the y-axis against $h / \text{cm}$ on the x-axis. Start both axes from the origin. Draw the smooth curve of best fit.

The diameter $d$ of the bottle is $10.0\text{ cm}$. The average flow rate $R$ of water is given by the equation

Use your answer to (a) to find the average flow rate for $h = 14.0\text{ cm}$. Give your answer to two significant figures.

$R$ = ______ $\text{cm}^3\text{ / s}$

The student increases the diameter of the hole in the bottle and repeats the experiment.

On Fig. 2.3, draw a possible second curve to represent the results you expect from this larger hole. Label this line S.

Suggest why the student did not measure the time taken for the bottle to empty completely.

Calculate $t_{av}$, the average value of $t$. Give your answer to 1 decimal place.

$t_{av}$ = ______

The time taken for one complete swing is called the period $T$. Calculate $T$.

$T$ = ______

The student has a reaction time of about $0.2\ \text{s}$. Explain why the student measures the time for ten swings rather than the time for one swing.

On Fig. 2.3, on page 5, plot the graph of $T / \text{s}$ on the y-axis against $N$ on the x-axis. Start your axes from (0,0). Draw a smooth curve of best fit.

Describe the relationship between $T$ and $N$.

Use your graph to estimate the value of $T$ when 5 paperclips are used. Show on your graph how you obtain your answer.

$T$ = ______

Suggest one effect of using paperclips that are not identical.

The student repeats (a)(i) and records the time $t_2$ shown in Fig. 3.3.

Record $t_2$ and find the average time $t_{av}$ of $t_1$ and $t_2$.

Give your answer to the nearest 0.1 s.

$t_2$ = ______ $\text{s}$
$t_{av}$ = ______ $\text{s}$

The average rate of flow $R$ is given by:

Calculate $R$ and give the unit of your answer.

$R$ = ______ unit ______

The student repeats (a)(i) and (a)(ii) for values of $V = 100\ \text{cm}^3$, $90\ \text{cm}^3$, $80\ \text{cm}^3$, $60\ \text{cm}^3$ and $50\ \text{cm}^3$. The volume of water collected in the measuring cylinder underneath the can is 30 $\text{cm}^3$ for each value of $V$.

The readings are shown in Table 3.1.

In Table 3.1:

• complete the headings, with units, in the top row of the table
• add your readings from (a)(i) and (a)(ii)
• calculate the average time for each set of readings.

Table 3.1

On the grid provided in Fig. 3.4, plot a graph of $t_{av}$ on the $y$-axis against $V$ on the $x$-axis.

You do not need to start your axes at (0,0).

Draw the curve of best fit.

Suggest why times $t_1$ and $t_2$ for values of $V$ below 50 $\text{cm}^3$ are not measured.

On your graph, sketch the line you would expect to see if the small hole in the can is made slightly bigger. Label this line L.

Calculate the average mass of 1 marble.

average mass of 1 marble = ______ $\text{g}$

The student uses the apparatus shown in Fig. 3.3.

The distance between the bench and the bottom side of the rule at the 90 cm mark is $h$.

The ramp is initially arranged with height $h = 4.0\ \text{cm}$ above the bench.

procedure

The student:

• places a marble on the gap between the rules so that its right-hand edge is on the 90.0 cm mark
• releases the marble and records the time $t_1$ for the marble to roll down the ramp until it hits the stopper
• repeats the experiment two more times.

The second and third measurements of time are recorded as $t_2$ and $t_3$.

Times $t_1$, $t_2$ and $t_3$ are shown.

Calculate the average time $t_{av}$ for the marble to travel 90.0 cm down the ramp.

$t_{av}$ = ______ $\text{s}$

The procedure in (b)(i) is repeated for heights $h = 6.0\ \text{cm}$, $8.0\ \text{cm}$, $10.0\ \text{cm}$ and $12.0\ \text{cm}$. All results are recorded in Table 3.1.

Complete Table 3.1, finding the average time $t_{av}$ for each value of $h$.

Include the results from (b)(i) in the table.

Give all values to a suitable number of decimal places.

Table 3.1

On the grid provided in Fig. 3.4 on page 13, plot a graph of $t_{av} / \text{s}$ on the y-axis against $h / \text{cm}$ on the x-axis.

Draw a line of best fit through your points. You do not need to start your axes at (0, 0).

Describe the relationship between $h$ and $t_{av}$.

Use your graph to find $t_{av}$ when $h = 7.0\ \text{cm}$.

Show on the graph how you find $t_{av}$ for $h = 7.0\ \text{cm}$.

$t_{av}$ = ______ $\text{s}$

The average speed $v$ of the marble is given by:

Find the average speed $v$ of the marble when $h = 7.0\ \text{cm}$. Give the unit of your answer.

average speed $v$ = ______ unit ______

Table 2.1

Calculate the current $I$ for each length $L$ shown in Table 2.1 using the equation $I = \frac{V}{10}$.

Record your answers in Table 2.1.

Calculate values of $\frac{1}{I}$ for each length $L$ shown in Table 2.1 and record your answers in Table 2.1.

Write the units in the top row of the table.

On the grid on page 7, plot a graph of $\frac{1}{I}$ on the y-axis against $L$ on the x-axis.

Start both axes at the origin (0,0).

Draw the straight line of best fit. Extend this line to intercept the y-axis.

Determine the gradient $G$ and y-intercept $c$ of this line.

Show clearly on the graph the values you choose and show your working.

gradient $G$ = ______
y-intercept $c$ = ______

Theory suggests that:

where $R_w$ is the resistance of the wire.

Use your answers in (b)(iii) to determine $R_w$.

Show your working.

$R_w$ = ______ $\Omega$

Find the average time $t_{av}$ for the wave to travel $5.0\text{ m}$ along the spring.

$t_{av}$ = ______

Calculate the average speed $v_{av}$ of the wave pulse along the spring.
Give your answer to a suitable number of significant figures.

$v_{av}$ = ______

Explain why, in practice, the position of the students and the metre rules causes a parallax error.

Explain why this parallax error causes the measured values of $t$ to be too small.

Explain one other reason why the times recorded by the students are not all exactly the same.

Describe how the students could measure the time $t$ more accurately.

• The student repeats the procedure for values of mass $m = 30\ \text{g}$, 40 g, 50 g and 60 g.

Table 3.1 shows the results.

Add your value of $d$ for mass $m = 20\ \text{g}$ in (a)(i) to Table 3.1.

Calculate $1/d$ for each mass $m$, and record all values in Table 3.1.

Give your answers to an appropriate number of significant figures.

Table 3.1

Suggest why a value of $d$ cannot be found for mass $m = 10\ \text{g}$.

Using the grid provided in Fig. 3.3 on page 13, plot a graph of $1/d$ on the y-axis against $m$ on the x-axis.

Start your axes from the origin (0, 0).

Draw the straight line of best fit.

Calculate the gradient $G$ of your line.

Show all your working, and indicate on the graph the values you use.

$G$ = ______

The mass $M$ of the metre rule can be calculated using the equation:

Use your value of $G$ in (b)(ii) to calculate $M$.

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

The student is given a piece of modelling clay. He places it on the metre rule as shown in Fig. 3.4. He finds that the metre rule is balanced when the modelling clay is a distance of 40.0 cm from the pivot.

Using your graph in Fig. 3.3 on page 13, find the mass of the piece of modelling clay. Show your working.

mass of piece of modelling clay = ______ $\text{g}$