Force and pressure

Key idea: Contact and non-contact forces, mass and weight, gravitational fields, density and pressure.

SEC G2 Science Physics component 2027

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Learning objectives

Distinguish contact forces from non-contact forces
State that mass measures the amount of matter in a body
Describe a gravitational field as a region where a mass experiences gravitational force
Define gravitational field strength as gravitational force per unit mass
Apply weight = mass × gravitational field strength
Distinguish mass from weight
Apply density = mass ÷ volume
Define pressure as force per unit area
Apply pressure = force ÷ area

Syllabus and review details

Keep Newton's laws, free-body diagrams and friction for the following Dynamics topic. Hydraulic systems, liquid pressure, barometers and manometers are not required for this Science course.

K223 / K224 Science Physics componentK223 / K224 · 2027Checked against the syllabus · complete topic coverageK223/K224 2027 syllabus, Force and Pressure topic 3

Forces are contact or non-contact interactions

A force is a push or pull caused by an interaction. Name the specific force, then decide whether the interacting objects must touch.

Contact forces

The objects must touch.

friction opposes relative sliding or attempted sliding;
air resistance opposes motion through air;
tension pulls along a taut string or cable;
normal force acts perpendicular to a contact surface.

Non-contact forces

The interaction can act across a distance.

gravitational force acts between masses;
electrostatic force acts between charges;
magnetic force acts between magnets or magnetic materials.

“Contact force” is a category, not usually the best force label. Write “normal force,” “friction,” “tension” or “air resistance” when the situation identifies it.

Mass measures the amount of matter

Mass, m, measures the amount of matter in a body. Its SI unit is the kilogram (kg). Moving an object from Earth to the Moon does not change its mass.

A gravitational field is a region of interaction

A gravitational field is a region in which a mass experiences a force due to gravitational attraction. Near Earth, that force acts towards Earth’s centre.

Field strength compares force with mass

The gravitational field strength, g, at a point is the gravitational force per unit mass placed at that point.

g=gravitational forcemass

Its unit is newtons per kilogram (N/kg). Near Earth’s surface, questions commonly use g = 10 N/kg unless another value is supplied.

Weight is the gravitational force on a mass

Weight, W, is measured in newtons (N). Use the mass and the local gravitational field strength:

W=m×g

Convert the mass to kilograms.
Use the value of g given for that location.
Calculate W = mg and state the answer in newtons.

Mass and weight are not interchangeable

Mass	Weight
amount of matter	gravitational force on the body
measured in kilograms (kg)	measured in newtons (N)
unchanged when location changes	changes if gravitational field strength changes
scalar quantity	force with a direction towards the attracting body

Density compares mass with volume

Density, ρ, is the mass per unit volume of a substance.

ρ=mV

Use kilograms with cubic metres to obtain kg/m³, or grams with cubic centimetres to obtain g/cm³. Do not mix the two unit systems in one calculation. To change between them, convert the mass and the volume together: 1 g/cm³ = 10⁻³ kg ÷ 10⁻⁶ m³ = 1000 kg/m³.

Finding the volume

A regular solid, such as a cuboid: measure its length, width and height with a rule, then V = l × w × h.
An irregular solid that sinks, such as a stone: read the water level in a measuring cylinder, lower the solid in until it is fully under water, and read the level again. The volume of the solid is the rise, V = V₂ − V₁, not the final reading. The method needs a solid that sinks and does not absorb or dissolve in water.
A liquid: read its volume in a measuring cylinder, and find its mass as the mass of the cylinder with the liquid minus the mass of the empty cylinder.

Density depends on the material, not on the size of the sample, so a measured density can be compared with known values: water is about 1.0 g/cm³, aluminium about 2.7 g/cm³ and iron about 7.9 g/cm³.

Density uses mass, not weight. A sample taken to another planet keeps the same mass and volume, so its density is unchanged even though its weight changes.

Pressure compares perpendicular force with area

Pressure, p, is the force acting perpendicular to a surface per unit area.

p=FA

Pressure is measured in pascals (Pa), where 1 Pa = 1 N/m². For the same force, a smaller contact area produces a greater pressure.

Choose the force and contact area before calculating

Identify the force perpendicular to the surface. For a resting object, this is often its weight.
If needed, calculate the weight using W = mg.
Identify the face that touches the surface. Its area is the contact area; the other faces, and the total surface area, play no part.
Convert the contact area to square metres.
Use p = F/A and state the answer in pascals.

Area conversions are squared: 1 cm² = 10⁻⁴ m², not 10⁻² m².

Common mistakes

“Mass and weight are both measured in kilograms.”: Mass is measured in kg. Weight is a gravitational force measured in N.
“A larger object must have greater density.”: Density is a ratio. Cutting a uniform material changes its mass and volume by the same factor.
“The pressure force is always the mass.”: Mass is not a force. Use the perpendicular force in newtons, often W = mg.
“The area in p = F/A is the whole surface area of the object.”: Only the face touching the surface carries the force. Turning a block onto a smaller face keeps its weight the same but raises the pressure.
“In the displacement method, the volume is the final water level.”: The final level includes the water that was already there. The solid’s volume is the rise in level, V₂ − V₁.
“Non-contact means no force acts.”: It means the objects need not touch; gravitational, electrostatic and magnetic forces still act.

Worked applications

1. Mass and weight on another world

A rover has mass 75 kg. On Mars, g = 3.7 N/kg. Find its mass and weight on Mars.

Mass is unchanged: 75 kg.

W = mg = 75 × 3.7 = 277.5 N

To two significant figures, the weight is 280 N.

2. Density from mass and volume

A metal block has mass 540 g and volume 200 cm³. Find its density.

ρ = m/V = 540/200 = 2.7 g/cm³

The units are consistent, so no conversion is needed.

3. Density of a regular block

A wooden block measures 5.0 cm by 4.0 cm by 2.0 cm and has mass 24 g. Find its density in g/cm³ and in kg/m³.

V = l × w × h = 5.0 × 4.0 × 2.0 = 40 cm³

ρ = m/V = 24/40 = 0.60 g/cm³

Since 1 g/cm³ = 1000 kg/m³, the density is 0.60 g/cm³, or 600 kg/m³.

4. Density of an irregular solid by displacement

A brass key has mass 42 g. When it is lowered into a measuring cylinder, the water level rises from 30 cm³ to 35 cm³. Find the density of the key.

V = V₂ − V₁ = 35 − 30 = 5 cm³

ρ = m/V = 42/5 = 8.4 g/cm³

The density is 8.4 g/cm³, close to the known value for brass. With a volume this small, a narrower cylinder with finer divisions would give a more precise result.

5. Pressure caused by weight

A 60 kg student stands on two shoes with total area 400 cm². Take g = 10 N/kg. Find the pressure on the floor.

F = W = mg = 60 × 10 = 600 N

A = 400 cm² = 400 × 10⁻⁴ m² = 0.040 m²

p = F/A = 600/0.040 = 15 000 Pa

The pressure is 1.5 × 10⁴ Pa.

6. Choose the face in contact

A brick of weight 20 N measures 20 cm by 10 cm by 5.0 cm. Find the pressure it exerts on the ground when it rests on its largest face and when it rests on its smallest face.

The force is the weight, 20 N, whichever face is down.

Largest face: 20 cm × 10 cm = 200 cm² = 0.020 m², so p = 20/0.020 = 1.0 × 10³ Pa.

Smallest face: 10 cm × 5.0 cm = 50 cm² = 0.0050 m², so p = 20/0.0050 = 4.0 × 10³ Pa.

A quarter of the contact area gives four times the pressure. Using the brick’s total surface area, 700 cm², would give one pressure for every orientation, which cannot be right.

Connect force, gravity, density and pressure

A 60 kg equipment case rests on a 0.080 m² base where g = 10 N/kg. Its weight is W = mg = 600 N, so the contact pressure is p = F/A = 600/0.080 = 7.5 × 10³ Pa. Moving the case to a weaker gravitational field changes its weight and contact pressure, but not its mass or material density.

Guided practice

A 45 kg crate has volume 0.018 m³ and rests on a 0.030 m² face where g = 4.0 N/kg. Find its density, weight and contact pressure, then classify its weight and the normal force.

Check the guided reasoning

ρ = 45/0.018 = 2.5 × 10³ kg/m³; W = 45 × 4.0 = 180 N; and p = 180/0.030 = 6.0 × 10³ Pa. Weight is a non-contact gravitational force; the normal force is a contact force.

Independent practice

Repeat the method for a 72 kg case of volume 0.024 m³ resting on 0.060 m² where g = 2.5 N/kg. State which answers would remain unchanged if the case moved back to Earth.

Check your answer

ρ = 72/0.024 = 3.0 × 10³ kg/m³; W = 72 × 2.5 = 180 N; and p = 180/0.060 = 3.0 × 10³ Pa. Back on Earth, the case still has the same mass, volume and density. Its weight increases because the gravitational field is stronger, so its contact pressure also increases when it rests on the same face.

Challenge yourself

A 12 kg block measures 0.50 m by 0.20 m by 0.10 m. Take g = 10 N/kg. Find its density, then calculate the pressure it exerts when it rests on its largest and smallest faces.

Check your thinking

The volume is 0.50 × 0.20 × 0.10 = 0.010 m³, so density = 12/0.010 = 1200 kg/m³. Its weight is 12 × 10 = 120 N. The largest face has area 0.50 × 0.20 = 0.10 m², giving 120/0.10 = 1200 Pa. The smallest face has area 0.20 × 0.10 = 0.020 m², giving 120/0.020 = 6000 Pa. The force stays the same; the smaller contact area produces the greater pressure.

Independent self-check

Classify tension, magnetic force and air resistance as contact or non-contact forces.
A 2.4 kg object weighs 9.6 N. Calculate the gravitational field strength.
A liquid has mass 360 g and volume 300 cm³. Calculate its density.
A 250 N perpendicular force acts over 0.050 m². Calculate the pressure.
Explain why the same person produces greater pressure when standing on one foot instead of two.

Check your answers

Tension and air resistance are contact forces; magnetic force is non-contact.
g = W/m = 9.6/2.4 = 4.0 N/kg.
ρ = m/V = 360/300 = 1.2 g/cm³.
p = F/A = 250/0.050 = 5.0 × 10³ Pa.
The weight is unchanged but one foot has a smaller contact area, so p = F/A is greater.

If an answer was wrong, identify whether the difficulty was the quantity, equation, unit or causal link. Re-read that section, then try the fresh question below without looking back.

Try this next

A 3.0 kg box measures 30 cm by 20 cm by 10 cm. Take g = 10 N/kg. Calculate the greatest and the least pressure it can exert when resting on one face.

Show answer

W = mg = 3.0 × 10 = 30 N. The least pressure is on the largest face, 30 cm × 20 cm = 0.060 m²: p = 30/0.060 = 500 Pa. The greatest pressure is on the smallest face, 20 cm × 10 cm = 0.020 m²: p = 30/0.020 = 1.5 × 10³ Pa.

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The Force and Pressure check matches this course. Use the feedback to revisit the right explanation, then come back later for a fresh check.

Force and Pressure check

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Practise: Force and pressure

A text-first Force and Pressure assessment with labelled controls and explicit interactions, quantities and units.

About 10 minutes

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A toy car is pulled by a taut string while a nearby magnet repels a magnet fixed to the car. How should the two forces be classified?

Tension is contact; magnetic force is non-contact.
Tension is non-contact; magnetic force is contact.
Both forces are contact.
Both forces are non-contact.

A sealed 9.0 kg toolkit is moved from one shelf to another without adding or removing material. What is its mass after the move?

0 kg
Less than 9.0 kg because its position changed
9.0 kg because the amount of matter is unchanged
More than 9.0 kg because it travelled

No probe is currently placed at a point above Earth. Which statement about Earth's gravitational field at that point is correct?

The field still exists because Earth would exert force on a mass placed there.
The field exists only after a probe is placed there.
The field disappears whenever the point is empty.
The field is a force stored inside the probe.

A 3.0 kg instrument is where gravitational field strength is 4.0 N/kg. Which row correctly interprets the field strength and records its mass and weight?

4.0 N per kilogram; mass 3.0 kg; weight 12 N
0.25 N per kilogram; mass 3.0 kg; weight 0.75 N
4.0 N per kilogram; mass 3.0 N; weight 12 kg
4.0 N on every object; mass 3.0 kg; weight 4.0 N

A component has mass 0.36 kg and volume 0.00015 m³. What is its density?

0.000054 kg/m³
240 kg/m³
2400 kg/m³
24 000 kg/m³

A normal force of 450 N acts uniformly over 0.090 m². Which option gives the pressure and interprets it correctly?

5000 Pa; 5000 N of normal force per square metre
40.5 Pa; normal force multiplied by area
0.00020 Pa; area divided by normal force
5000 N; the total force without reference to area

A small test mass is placed to the right of an isolated planet. In which direction does the planet's gravitational field act at the test mass?

Towards the planet
Away from the planet
Vertically upward on the page
There is no direction because a field is not a force

A beam balance is level when sealed sample X is compared with standard masses totalling 650 g. What mass should be recorded for X?

650 g
325 g
1300 g
650 N

A falling sheet slows as it moves through air. Name and classify the upward force.

gravitational force, a contact force
normal force, a non-contact force
magnetic force, a non-contact force
air resistance, a contact force

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Practise after feedback: Force and pressure

A text-first Force and Pressure assessment with labelled controls and explicit interactions, quantities and units.

About 10 minutes

Practise

Questions are selected when you start. Use the feedback to decide what to practise next; this does not prove mastery.

Recent attempts

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No completed attempts are saved yet.

This check needs JavaScript to record answers. The reviewed questions are listed below for study.

Which pair consists of two contact forces that require the interacting objects to touch?

Friction and tension
Gravitational force and magnetic force
Friction and gravitational force
Tension and magnetic force

A sealed 2.4 kg sample is moved from one laboratory bench to another without adding or removing material. What is its mass after the move?

2.4 kg
0 kg
1.2 kg
4.8 kg

No test object is present at a point above a planet. Which statement about the gravitational field there is correct?

The field exists because a mass placed there would experience gravitational attraction.
The field appears only when a test object is placed there.
The field is material stored inside a test object.
The field cannot extend through empty space.

A 5.0 kg package is where gravitational field strength is 4.0 N/kg. Which record correctly interprets the field strength and gives the package's mass and weight?

Each kilogram experiences 4.0 N; mass 5.0 kg; weight 20 N.
Each kilogram experiences 0.25 N; mass 5.0 kg; weight 1.25 N.
Each kilogram experiences 4.0 N; mass 5.0 N; weight 20 kg.
Every object experiences 4.0 N; mass 5.0 kg; weight 4.0 N.

A component has mass 0.48 kg and volume 0.00020 m³. What is its density?

96 kg/m³
240 kg/m³
2400 kg/m³
9600 kg/m³

A perpendicular force of 600 N acts uniformly over 0.030 m². Which option gives both the pressure and its meaning?

20 000 Pa; pressure is perpendicular force per unit area.
20 Pa; pressure is area per unit perpendicular force.
18 Pa; pressure is perpendicular force multiplied by area.
20 000 N; pressure is the total force on a surface.

Check what I know

Check what I know: Force and pressure

A text-first Force and Pressure assessment with labelled controls and explicit interactions, quantities and units.

About 8 minutes

Check what I know

Answer 6 short questions. This starting check helps choose what to work on; it does not prove mastery.

Recent attempts

History is stored only in this browser.

No completed attempts are saved yet.

This check needs JavaScript to record answers. The reviewed questions are listed below for study.

Which pair consists of two contact forces that require the interacting objects to touch?

Friction and tension
Gravitational force and magnetic force
Friction and gravitational force
Tension and magnetic force

A sealed 2.4 kg sample is moved from one laboratory bench to another without adding or removing material. What is its mass after the move?

2.4 kg
0 kg
1.2 kg
4.8 kg

No test object is present at a point above a planet. Which statement about the gravitational field there is correct?

The field exists because a mass placed there would experience gravitational attraction.
The field appears only when a test object is placed there.
The field is material stored inside a test object.
The field cannot extend through empty space.

A 5.0 kg package is where gravitational field strength is 4.0 N/kg. Which record correctly interprets the field strength and gives the package's mass and weight?

Each kilogram experiences 4.0 N; mass 5.0 kg; weight 20 N.
Each kilogram experiences 0.25 N; mass 5.0 kg; weight 1.25 N.
Each kilogram experiences 4.0 N; mass 5.0 N; weight 20 kg.
Every object experiences 4.0 N; mass 5.0 kg; weight 4.0 N.

A component has mass 0.48 kg and volume 0.00020 m³. What is its density?

96 kg/m³
240 kg/m³
2400 kg/m³
9600 kg/m³

A perpendicular force of 600 N acts uniformly over 0.030 m². Which option gives both the pressure and its meaning?

20 000 Pa; pressure is perpendicular force per unit area.
20 Pa; pressure is area per unit perpendicular force.
18 Pa; pressure is perpendicular force multiplied by area.
20 000 N; pressure is the total force on a surface.

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Check my progress: Force and pressure

A text-first Force and Pressure assessment with labelled controls and explicit interactions, quantities and units.

About 10 minutes

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A text-first Force and Pressure assessment with labelled controls and explicit interactions, quantities and units.

About 10 minutes

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Review: Force and pressure

A text-first Force and Pressure assessment with labelled controls and explicit interactions, quantities and units.

About 10 minutes

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Answer 9 questions. A scheduled review can contribute to your course progress only when it is due and the result is accepted.

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Course and syllabus information

Course: SEC G2 Science Physics component
Edition: SEC G2 Science Physics component 2027

Continue where you stopped

Learning objectives

Forces are contact or non-contact interactions

Contact forces

Non-contact forces

Mass measures the amount of matter

A gravitational field is a region of interaction

Field strength compares force with mass

Weight is the gravitational force on a mass

Mass and weight are not interchangeable

Density compares mass with volume

Finding the volume

Pressure compares perpendicular force with area

Choose the force and contact area before calculating

Common mistakes

Worked applications

1. Mass and weight on another world

2. Density from mass and volume

3. Density of a regular block

4. Density of an irregular solid by displacement

5. Pressure caused by weight

6. Choose the face in contact

Connect force, gravity, density and pressure

Guided practice

Independent practice

Challenge yourself

Independent self-check

Try this next

Practise this topic

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Starting check complete

Progress check complete

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