Density and pressure questions

Density and pressure syllabus

Questions on density and pressure can test recall, calculations, explanations, diagrams, data handling and practical skills. You should be able to:

• 5.3 know and use the relationship between density, mass and volume: density = mass / volume ρ = m / V
• 5.4 practical: investigate density using direct measurements of mass and volume
• 5.5 know and use the relationship between pressure, force and area: pressure = force / area p = F / A
• 5.6 understand how the pressure at a point in a gas or liquid at rest acts equally in all directions
• 5.7 know and use the relationship for pressure difference: pressure difference = height × density × gravitational field strength p = h × ρ × g

How to answer density and pressure questions

1. Sketch or describe particle spacing, arrangement and motion before explaining bulk behaviour.
2. Convert volumes and temperatures carefully; gas-law temperatures must be in kelvin.
3. State which variables are fixed when describing pressure-volume or pressure-temperature changes.
4. For practical methods, identify direct measurements, repeated readings and the calculation used.

Density and pressure example questions and worked answers

These examples show how information in a diagram, graph or experimental context becomes part of a complete exam answer.

Example 1: Plotting the depth of draining water

June 2015 · Paper 2P · Question 4(b)(i)

Question 1

The photograph shows a water barrel with a tap.

The barrel is used to store rainwater.

A student investigates the water depth in the barrel.

She measures the depth and then opens the tap.

As water flows out of the barrel, she measures the depth every minute.

The table shows her results.

Time in minutes	Depth in cm
0	86
1	52
2	31
3	18
4	11
5	7
6	4

Plot a graph to show how the depth changes with time, and draw the curve of best fit.

Final answer

See the graph below, with all seven measurements plotted and a smooth curve of best fit.

Mark scheme points

1. M1 — Choose suitable scales so that the plotted data use more than 50% of the grid.
2. M2 — Label both axes with the quantity and unit: time in minutes and water depth in cm. Either axis orientation is accepted.
3. M3 and M4 — Plot all seven points correctly to the nearest half small square. Two marks are available for plotting; lose one mark for each plotting error, down to zero.
4. M5 — Draw a smooth curve of best fit within one small square of every point.

Explanation

The depth falls rapidly at first, then more slowly. The curve therefore slopes downwards and gradually becomes less steep.

• Use evenly spaced scales. Here, each large horizontal interval represents 1 minute and each large vertical interval represents 10 cm.
• Include units in both axis labels so that the values have a clear meaning.
• Plot each time–depth pair using a small, precise cross. Include the starting point at 0 minutes and 86 cm.
• Draw one smooth curve following the pattern of the points, rather than straight segments joining them.

Common mistakes

• Writing “m” for minutes: this is rejected. Use “minutes” or “min”.
• Choosing scales that squeeze the points into less than half the grid, or using uneven numerical intervals.
• Joining points with straight lines or drawing a curve too far from a point. Keep the curve smooth and within one small square of every point.

Example 2: Explaining pressure at the tip of a nail

June 2016 · Paper 2P · Question 6(c)

Question 2

The photograph shows a hammer just before it hits a nail.

Both ends of the nail exert pressure when the nail goes into the wood.

Explain why the nail exerts more pressure on the wood than it does on the hammer.

Final answer

The forces exerted by the nail on the wood and on the hammer are equal. Pressure = force ÷ area, and the pointed end has a smaller contact area with the wood than the nail head has with the hammer, so the pressure on the wood is greater.

Mark scheme points

Any two of the following points are needed for 2 marks:

1. M1 Pressure is force divided by area.
2. M2 The forces exerted on the wood and hammer are equal.
3. M3 The nail has a smaller contact area with the wood than with the hammer.

Explanation

Pressure depends on both force and area: for the same force, a smaller contact area produces a greater pressure. The force at the two ends of the nail is equal, but the pointed end touching the wood has the smaller contact area. Therefore, it exerts more pressure on the wood.

Common mistakes

• Do not claim that the nail exerts a greater force on the wood; explain that the contact area is smaller.
• State which end has the smaller area and link this to greater pressure.

Practise Density and pressure questions

Build a focused practice set from this part of the Edexcel IGCSE Physics syllabus.