Physics 5054/32 — May/June 2015

Cambridge O-Level · Practical Test · worked solutions for every part, with the mark scheme

questions

marks

120

minutes

Topics Experimental Contexts · Observations and Measurements · Analysis, Conclusions and Evaluation · Use of Techniques, Apparatus and Materials · Planning Experiments and Investigations

Q15MExperimental ContextsObservations and MeasurementsUse of Techniques, Apparatus and MaterialsAnalysis, Conclusions and EvaluationFree sample

In this experiment, you will determine the density of a salt solution.

You have been provided with

a 100 $\text{cm}^3$ measuring cylinder,
a beaker containing salt solution.

You also have access to a top-pan balance.
If your measuring cylinder is calibrated in $\text{ml}$ , then note that 100 $\text{ml}$ = 100 $\text{cm}^3$ .

(a)

(i) Use the top-pan balance to measure the mass $m_E$ of the empty measuring cylinder.

$m_E$ = ______

(ii) Pour a large volume of the salt solution into the measuring cylinder and record accurately the volume $V$ of the solution.

$V$ = ______

(iii) Measure the mass $m_T$ of the measuring cylinder with the solution.

$m_T$ = ______

(iv) Determine the mass $m$ of the solution in the measuring cylinder.

$m$ = ______

DifficultyEasy

Worked solution

Answer

Example readings: $m_E = 50\text{ g}$ , $m_T = 160\text{ g}$ , $m = 110\text{ g}$ , $V = 100\text{ cm}^3$ . All masses to the nearest gram with a unit; $V$ in the range $90 < V \le 100\text{ cm}^3$ .

Final answer

Example: m_E=50 g, m_T=160 g, m=110 g, V=100 cm^3

Detailed explanation

Walkthrough

This part requires you to take and record three mass readings and one volume reading. The balance gives the mass of the empty cylinder ( $m_E$ ), then the cylinder with solution ( $m_T$ ). The mass of the solution is found by subtraction: $m = m_T - m_E$ . The volume $V$ is read from the measuring cylinder. The mark scheme requires that the volume be large, between 90 and 100 cm³, so that the subsequent density calculation is accurate. All readings must be recorded to the nearest gram (or better) and units must be stated at least once.

Key Takeaways

How to use a top-pan balance and measuring cylinder correctly.
The mass of the solution is the difference between the total mass and the empty cylinder mass.
The importance of recording readings with appropriate precision and units.

Common Mistakes

Forgetting to subtract $m_E$ from $m_T$ to get $m$ .
Recording volumes outside the required range (90–100 cm³).
Omitting units or recording masses to the nearest 10 g, which is not precise enough.

Things to Be Careful About

Ensure the balance reads zero before use.
Read the volume at the bottom of the meniscus.
The mark scheme allows any sensible values as long as $m > V$ and $V$ is in the given range.

Techniques used

measure mass using a top-pan balancemeasure volume using a measuring cylinderrecord readings to the nearest gram or bettersubtract masses to find the mass of solution

(b)

Explain, with the aid of a diagram, how you ensured that $V$ was measured as accurately as possible. Show the position of your eye when taking the measurement.

DifficultyEasy

Worked solution

Answer

Draw the measuring cylinder with the liquid inside. Indicate the meniscus (the curved surface of the liquid). Draw an eye at the same height as the bottom of the meniscus, with a horizontal dashed line from the eye to the meniscus to show the line of sight.

Final answer

Diagram showing eye level with the bottom of the meniscus

Detailed explanation

Walkthrough

The most accurate way to read the volume of a liquid in a measuring cylinder is to ensure your eye is exactly level with the bottom of the meniscus. This avoids parallax error, where the reading appears different because of the angle of viewing. The diagram must clearly show the eye positioned horizontally opposite the bottom of the meniscus.

Key Takeaways

The meniscus is the curved surface of the liquid.
Reading must be taken at the bottom of the meniscus.
The eye must be at the same level as the meniscus to avoid parallax error.

Common Mistakes

Drawing the eye above or below the meniscus.
Not showing the meniscus clearly.
Forgetting to label the eye or the line of sight.

Things to Be Careful About

The diagram should be neat and clearly labelled.
The line of sight should be horizontal and meet the meniscus at its lowest point.

Techniques used

draw a diagram of the meniscus in a measuring cylinderposition the eye at the same level as the bottom of the meniscusavoid parallax error when taking the reading

(c)

Calculate the density $\rho$ of the salt solution using $\rho = \frac{m}{V}$ .

$\rho$ = ______

DifficultyEasy

Worked solution

Working

Using the example readings from (a): $m = 110\text{ g}$ , $V = 100\text{ cm}^3$

\rho = \frac{m}{V} = \frac{110\text{ g}}{100\text{ cm}^3} = 1.1\text{ g/cm}^3

Answer

$\rho = 1.1\text{ g/cm}^3$

Final answer

1.1 g/cm^3

Detailed explanation

Walkthrough

Substitute the measured mass and volume into the density formula. The unit of density is grams per cubic centimetre (g/cm³). The final answer should be given to a sensible number of significant figures—here, two significant figures matches the precision of the measurements.

Key Takeaways

Density is mass divided by volume.
The unit of density is g/cm³ when mass is in grams and volume in cm³.
The calculation is a straightforward division.

Common Mistakes

Forgetting to include the unit.
Using the wrong values for $m$ or $V$ (e.g., using $m_T$ instead of $m$ ).
Giving the answer to too many significant figures.

Things to Be Careful About

Ensure the mass used is the mass of the solution ( $m = m_T - m_E$ ), not the total mass.
The answer should lie between 1.0 and 1.2 g/cm³ for a salt solution.

Techniques used

substitute values into the density equationcalculate density with correct unitgive answer to appropriate significant figures

(d)

Explain an advantage of using a large volume of salt solution in this experiment.

DifficultyMedium-Easy

Worked solution

Answer

A large volume of solution gives a large mass, so the percentage error in measuring the mass is smaller, giving a more accurate value for the density.

Final answer

A larger mass reduces the percentage error in the mass measurement, giving a more accurate density.

Detailed explanation

Walkthrough

The balance has a fixed absolute error (e.g., ±1 g). If the mass measured is small, this error is a larger fraction of the reading. By using a large volume, the mass is larger, so the same absolute error becomes a smaller percentage of the measurement. This reduces the percentage error in the mass, leading to a more reliable density value.

Key Takeaways

Percentage error decreases as the measured quantity increases.
Using a larger sample reduces the impact of the instrument's absolute error.
This is a common way to improve experimental accuracy.

Common Mistakes

Saying 'it gives a more accurate result' without explaining why.
Confusing accuracy with precision.
Not linking the larger volume to a larger mass and hence smaller percentage error.

Things to Be Careful About

The explanation must mention the effect on percentage error or relative error.
Avoid vague answers like 'it is more accurate' without justification.

Techniques used

explain how a larger volume reduces percentage errorrelate larger mass to improved accuracy

The rest of this paper

3 more questions

Q2Observations and Measurements · Experimental Contexts · Analysis, Conclusions and Evaluation5M
Q3Experimental Contexts · Observations and Measurements · Analysis, Conclusions and Evaluation5M
Q4Observations and Measurements · Experimental Contexts · Use of Techniques, Apparatus and Materials · Planning Experiments and Investigations · Analysis, Conclusions and Evaluation15M

Loading the full paper…