Force density pressure work power and energy

Overview

Force, density, pressure, work, power, and energy are connected ideas in mechanics and matter. They help learners explain why objects start moving or stop, why some materials feel heavy for their size, why a sharp nail enters wood more easily than a blunt object, and why machines need energy to do useful work.

This chapter introduces each idea at Form I level. The main aim is to connect meaning, SI units, simple formulae, and careful substitution. A learner should be able to read a short physical situation, identify the quantity involved, choose the correct formula, calculate with units, and interpret the answer.

These ideas also prepare learners for later topics. Force connects with motion. Density connects with sinking and floating. Pressure connects with fluids and practical tools. Work, power, and energy connect mechanics with heat, electricity, and machines.

Prerequisites

• Physical quantities and SI units - Learners should know that a physical quantity is written with a number and a unit.
• Measuring instruments in Physics - Force, mass, length, time, volume, and area depend on suitable measuring instruments.
• Measuring instruments and physical quantities - Learners should be able to match a quantity with its instrument and unit.
• Mathematical relationships among physical quantities - Formula substitution, rearrangement, and unit checking support all calculations in this chapter.
• Linear motion - Force is easier to understand after studying motion, speed, velocity, and acceleration.
• Basic arithmetic - Learners should be able to multiply, divide, square simple lengths, and convert common units.

Learning Scope

This chapter covers introductory meanings, SI units, and simple calculations for force, density, pressure, work, power, and energy. It includes weight as a force, the formula for density, pressure on a solid surface, work done by a force, power as rate of doing work, and common forms of energy.

This page does not fully teach Newton's laws, moments, machines, fluid pressure in depth, Archimedes' principle, advanced energy transformations, electricity, heat, or detailed sinking and floating. Those ideas belong to related or later Physics pages, including Linear motion, Density sinking and floating, and later mechanics and matter topics.

Subtopics

Force

A force is a push or pull. It can change the motion, shape, or state of an object. A force may start motion, stop motion, change speed, change direction, or deform an object.

The SI unit of force is the newton, symbol $\text{N}$. A spring balance can be used to measure force.

Examples of forces include:

• pushing a desk
• pulling a drawer
• weight of a book due to gravity
• friction opposing motion
• tension in a string
• upthrust from a liquid

Key insight: A force is a vector quantity. This means it has magnitude and direction. Saying $10\ \text{N}$ is incomplete when the direction matters; $10\ \text{N}$ downward or $10\ \text{N}$ to the right gives a clearer Physics description.

Effects Of Force

A force can have several observable effects.

It can change speed:

• A push can make a stationary cart move.
• A braking force can slow a bicycle.

It can change direction:

• A kicked ball changes direction when another player deflects it.

It can change shape:

• A spring stretches when pulled.
• Clay changes shape when pressed.

It can balance another force:

• A book resting on a table has its weight downward and a support force upward.

Key insight: If forces are balanced, the object's motion does not change. If forces are unbalanced, the object's motion can change. Detailed laws of motion are studied beyond this introductory page, but this idea prepares learners for them.

Mass And Weight

Mass is the amount of matter in an object. Its SI unit is kilogram, symbol $\text{kg}$. Mass is measured using a balance.

Weight is the gravitational force acting on an object. Its SI unit is newton, symbol $\text{N}$. Weight is measured using a spring balance.

The simple relationship is:

$$ W = mg $$

where:

• $W$ is weight in newtons, $\text{N}$
• $m$ is mass in kilograms, $\text{kg}$
• $g$ is gravitational field strength in newtons per kilogram, $\text{N/kg}$

In many school calculations, $g$ may be taken as $10\ \text{N/kg}$ when a question gives or expects that value.

For a mass of $3\ \text{kg}$:

$$ \begin{aligned} W &= mg \\ &= 3\ \text{kg} \times 10\ \text{N/kg} \\ &= 30\ \text{N} \end{aligned} $$

Key insight: Mass and weight are not the same. Mass is measured in $\text{kg}$; weight is a force measured in $\text{N}$.

Density

Density tells how much mass is packed into a given volume. A material with high density has a large mass in a small volume. A material with low density has less mass in the same volume.

The formula for density is:

$$ \rho = \frac{m}{V} $$

where:

• $\rho$ is density
• $m$ is mass
• $V$ is volume

The SI unit of density is kilogram per cubic metre, written as $\text{kg/m}^3$ or $\text{kg m}^{-3}$. In school laboratory work, grams per cubic centimetre, $\text{g/cm}^3$, is also common.

For example, if a block has mass $200\ \text{g}$ and volume $50\ \text{cm}^3$:

$$ \begin{aligned} \rho &= \frac{m}{V} \\ &= \frac{200\ \text{g}}{50\ \text{cm}^3} \\ &= 4\ \text{g/cm}^3 \end{aligned} $$

Key insight: Density is not the same as mass. A small object can have high density, and a large object can have low density.

Finding Volume For Density

To calculate density, volume must be known. The method depends on the shape of the object.

For a regular rectangular solid:

$$ V = l \times w \times h $$

where $l$ is length, $w$ is width, and $h$ is height.

For a liquid, volume can be read using a measuring cylinder.

For an irregular solid that does not dissolve in water, volume may be found by water displacement. If the water level rises from $40\ \text{cm}^3$ to $55\ \text{cm}^3$, then:

$$ \begin{aligned} V &= 55\ \text{cm}^3 - 40\ \text{cm}^3 \\ &= 15\ \text{cm}^3 \end{aligned} $$

Key insight: Density calculations depend on good measurement. Wrong volume readings give wrong density values, even if the formula is remembered correctly.

Density, Sinking, And Floating

Density helps explain why some objects sink while others float. A simple comparison is useful at this level:

• an object denser than the liquid it is placed in tends to sink
• an object less dense than the liquid it is placed in tends to float

This chapter introduces the density idea. A fuller treatment of floating, sinking, and related observations belongs to Density sinking and floating.

Key insight: Sinking and floating depend on density and fluid effects, not only on whether an object is "heavy". A large wooden log can float while a small metal nail sinks.

Pressure

Pressure is force acting normally on a unit area. In simple terms, pressure tells how concentrated a force is over a surface.

The formula for pressure is:

$$ P = \frac{F}{A} $$

where:

• $P$ is pressure
• $F$ is force in newtons, $\text{N}$
• $A$ is area in square metres, $\text{m}^2$

The SI unit of pressure is newton per square metre, $\text{N/m}^2$. This unit is also called the pascal, symbol $\text{Pa}$.

For example, if a force of $60\ \text{N}$ acts on an area of $3\ \text{m}^2$:

$$ \begin{aligned} P &= \frac{F}{A} \\ &= \frac{60\ \text{N}}{3\ \text{m}^2} \\ &= 20\ \text{N/m}^2 \\ &= 20\ \text{Pa} \end{aligned} $$

Key insight: The same force can produce different pressures depending on the area. Smaller area gives greater pressure. Larger area gives smaller pressure.

Everyday Pressure Examples

Pressure explains many ordinary situations.

A sharp knife cuts more easily than a blunt knife because the force is concentrated on a smaller edge area.

A pointed nail enters wood more easily than a flat-ended object because the point produces high pressure.

Wide straps on a school bag reduce pressure on the shoulder because the force is spread over a larger area.

Wide tyres or wide shoes can reduce pressure on soft ground because the weight is spread over a larger contact area.

Key insight: To increase pressure, increase force or decrease area. To decrease pressure, decrease force or increase area.

Work Done

In Physics, work is done when a force moves an object through a distance in the direction of the force. Work is not just tiredness or effort. If a learner pushes a wall and the wall does not move, no mechanical work is done on the wall in this simple sense.

The formula for work done is:

$$ W = Fd $$

where:

• $W$ is work done in joules, $\text{J}$
• $F$ is force in newtons, $\text{N}$
• $d$ is distance moved in the direction of the force in metres, $\text{m}$

The SI unit of work is the joule, symbol $\text{J}$.

Since:

$$ 1\ \text{J} = 1\ \text{N m} $$

a force of $1\ \text{N}$ doing work over $1\ \text{m}$ does $1\ \text{J}$ of work.

Key insight: Work done needs both force and movement in the direction of the force. Force alone is not enough.

Energy

Energy is the ability to do work. Its SI unit is the joule, symbol $\text{J}$, the same unit used for work.

Common forms of energy include:

• kinetic energy - energy of motion
• gravitational potential energy - energy due to position in a gravitational field
• elastic potential energy - energy stored when an object is stretched or compressed
• chemical energy - energy stored in substances such as food and fuels
• thermal energy - energy associated with temperature and heat effects
• electrical energy - energy transferred by electric current
• light energy - energy carried by light
• sound energy - energy carried by vibrations through a medium

Energy can be transferred from one object or form to another. For example, when a falling stone strikes the ground, gravitational potential energy is changed mainly into kinetic energy before impact, then into sound, thermal energy, and deformation after impact.

Key insight: Energy is not created from nothing in ordinary physical processes. It is transferred or transformed from one form to another. Detailed conservation of energy is developed further in later topics.

Power

Power is the rate of doing work or the rate of transferring energy. It tells how quickly work is done.

The formula for power is:

$$ P = \frac{W}{t} $$

where:

• $P$ is power in watts, $\text{W}$
• $W$ is work done or energy transferred in joules, $\text{J}$
• $t$ is time in seconds, $\text{s}$

The SI unit of power is the watt, symbol $\text{W}$.

Since:

$$ 1\ \text{W} = 1\ \text{J/s} $$

a machine with power $1\ \text{W}$ transfers $1\ \text{J}$ of energy each second.

For example, if $600\ \text{J}$ of work is done in $30\ \text{s}$:

$$ \begin{aligned} P &= \frac{W}{t} \\ &= \frac{600\ \text{J}}{30\ \text{s}} \\ &= 20\ \text{W} \end{aligned} $$

Key insight: Two learners may do the same work but have different powers if one finishes faster.

SI Units And Formula Discipline

The main quantities in this chapter are:

| Quantity | Common symbol | SI unit | Unit symbol | Simple formula | |---|---:|---|---:|---:| | force | $F$ | newton | $\text{N}$ | measured directly or related to weight | | mass | $m$ | kilogram | $\text{kg}$ | measured by balance | | weight | $W$ | newton | $\text{N}$ | $W = mg$ | | volume | $V$ | cubic metre | $\text{m}^3$ | depends on shape or displacement | | density | $\rho$ | kilogram per cubic metre | $\text{kg/m}^3$ | $\rho = \frac{m}{V}$ | | area | $A$ | square metre | $\text{m}^2$ | depends on surface shape | | pressure | $P$ | pascal | $\text{Pa}$ | $P = \frac{F}{A}$ | | distance | $d$ | metre | $\text{m}$ | measured by ruler, tape, or metre rule | | work | $W$ | joule | $\text{J}$ | $W = Fd$ | | energy | $E$ | joule | $\text{J}$ | related to work done or transferred | | time | $t$ | second | $\text{s}$ | measured by clock or stopwatch | | power | $P$ | watt | $\text{W}$ | $P = \frac{W}{t}$ |

Some symbols repeat. For example, $W$ can mean weight or work, and $P$ can mean pressure or power. The meaning depends on the context and unit.

Key insight: The unit protects the meaning. Weight in $\text{N}$ is not work in $\text{J}$, even if both are sometimes written with the symbol $W$.

Key Terms

• Area: size of a surface; SI unit $\text{m}^2$.
• Density: mass per unit volume; SI unit $\text{kg/m}^3$.
• Energy: ability to do work; SI unit $\text{J}$.
• Force: a push or pull that can change motion, shape, or state; SI unit $\text{N}$.
• Joule: SI unit of work and energy; $1\ \text{J} = 1\ \text{N m}$.
• Mass: amount of matter in an object; SI unit $\text{kg}$.
• Newton: SI unit of force.
• Pascal: SI unit of pressure; $1\ \text{Pa} = 1\ \text{N/m}^2$.
• Power: rate of doing work or transferring energy; SI unit $\text{W}$.
• Pressure: force per unit area; SI unit $\text{Pa}$.
• Volume: space occupied by an object or substance; SI unit $\text{m}^3$.
• Watt: SI unit of power; $1\ \text{W} = 1\ \text{J/s}$.
• Weight: gravitational force on an object; SI unit $\text{N}$.
• Work done: product of force and distance moved in the direction of the force; SI unit $\text{J}$.

Worked Examples

Example 1: Weight From Mass

A stone has mass $5\ \text{kg}$. Find its weight if $g = 10\ \text{N/kg}$.

Use:

$$ W = mg $$

Substitute:

$$ \begin{aligned} W &= 5\ \text{kg} \times 10\ \text{N/kg} \\ &= 50\ \text{N} \end{aligned} $$

The stone's weight is $50\ \text{N}$.

Example 2: Density Of A Block

A block has mass $360\ \text{g}$ and volume $120\ \text{cm}^3$. Find its density.

Use:

$$ \rho = \frac{m}{V} $$

Substitute:

$$ \begin{aligned} \rho &= \frac{360\ \text{g}}{120\ \text{cm}^3} \\ &= 3\ \text{g/cm}^3 \end{aligned} $$

The density of the block is $3\ \text{g/cm}^3$.

Example 3: Volume By Water Displacement

A stone is placed in a measuring cylinder. The water level rises from $30\ \text{cm}^3$ to $46\ \text{cm}^3$. The stone has mass $80\ \text{g}$. Find the volume and density of the stone.

First find the volume displaced:

$$ \begin{aligned} V &= 46\ \text{cm}^3 - 30\ \text{cm}^3 \\ &= 16\ \text{cm}^3 \end{aligned} $$

Then find density:

$$ \begin{aligned} \rho &= \frac{m}{V} \\ &= \frac{80\ \text{g}}{16\ \text{cm}^3} \\ &= 5\ \text{g/cm}^3 \end{aligned} $$

The stone's volume is $16\ \text{cm}^3$, and its density is $5\ \text{g/cm}^3$.

Example 4: Pressure On A Surface

A box exerts a force of $120\ \text{N}$ on the floor. The contact area is $0.5\ \text{m}^2$. Find the pressure.

Use:

$$ P = \frac{F}{A} $$

Substitute:

$$ \begin{aligned} P &= \frac{120\ \text{N}}{0.5\ \text{m}^2} \\ &= 240\ \text{N/m}^2 \\ &= 240\ \text{Pa} \end{aligned} $$

The pressure on the floor is $240\ \text{Pa}$.

Example 5: Work Done By A Force

A learner pushes a box with a force of $40\ \text{N}$. The box moves $3\ \text{m}$ in the direction of the force. Find the work done.

Use:

$$ W = Fd $$

Substitute:

$$ \begin{aligned} W &= 40\ \text{N} \times 3\ \text{m} \\ &= 120\ \text{J} \end{aligned} $$

The work done is $120\ \text{J}$.

Example 6: Power From Work And Time

A machine does $900\ \text{J}$ of work in $45\ \text{s}$. Find its power.

Use:

$$ P = \frac{W}{t} $$

Substitute:

$$ \begin{aligned} P &= \frac{900\ \text{J}}{45\ \text{s}} \\ &= 20\ \text{W} \end{aligned} $$

The power of the machine is $20\ \text{W}$.

Example 7: Same Work, Different Power

Two learners each lift the same load, so each does $300\ \text{J}$ of work. Learner A takes $10\ \text{s}$ and Learner B takes $20\ \text{s}$. Compare their powers.

For Learner A:

$$ \begin{aligned} P_A &= \frac{300\ \text{J}}{10\ \text{s}} \\ &= 30\ \text{W} \end{aligned} $$

For Learner B:

$$ \begin{aligned} P_B &= \frac{300\ \text{J}}{20\ \text{s}} \\ &= 15\ \text{W} \end{aligned} $$

Both learners do the same work, but Learner A has greater power because the work is done in a shorter time.

Common Mistakes

• Confusing mass with weight. Mass is in $\text{kg}$; weight is in $\text{N}$.
• Writing force in kilograms. A kilogram is a unit of mass, not force.
• Forgetting that force has direction.
• Treating density as heaviness only. Density compares mass with volume.
• Using mass instead of weight when a pressure question gives force.
• Forgetting to square length units when finding area.
• Dividing pressure as area divided by force instead of force divided by area.
• Saying work is done whenever someone feels tired. In Physics, work requires movement in the direction of the force.
• Using seconds incorrectly in power calculations. Power is work divided by time, not work multiplied by time.
• Confusing the symbols $W$ for work and weight, or $P$ for pressure and power.
• Giving answers without units.
• Mixing $\text{g}$ with $\text{m}^3$ or $\text{kg}$ with $\text{cm}^3$ without thinking about unit consistency.
• Treating the 2022 examination format as the syllabus. It is an assessment signal only.

Practice Tasks

1. Define force, density, pressure, work, power, and energy.
2. State the SI unit of force, density, pressure, work, power, and energy.
3. Give three possible effects of a force on an object.
4. Explain the difference between mass and weight.
5. A body has mass $4\ \text{kg}$. Find its weight if $g = 10\ \text{N/kg}$.
6. A block has mass $250\ \text{g}$ and volume $50\ \text{cm}^3$. Find its density.
7. A liquid has mass $600\ \text{g}$ and volume $300\ \text{cm}^3$. Find its density.
8. A stone raises water in a measuring cylinder from $25\ \text{cm}^3$ to $41\ \text{cm}^3$. Find the stone's volume.
9. A force of $80\ \text{N}$ acts on an area of $4\ \text{m}^2$. Find the pressure.
10. A learner presses a thumbtack with a force of $20\ \text{N}$. Explain why the sharp end produces high pressure.
11. A box has weight $200\ \text{N}$ and rests on an area of $2\ \text{m}^2$. Find the pressure on the floor.
12. A force of $25\ \text{N}$ moves an object $6\ \text{m}$ in the direction of the force. Find the work done.
13. A person pushes a wall with a force of $100\ \text{N}$, but the wall does not move. How much mechanical work is done on the wall in this simple model? Explain.
14. A motor does $1200\ \text{J}$ of work in $60\ \text{s}$. Find its power.
15. Two machines do $5000\ \text{J}$ of work. Machine A takes $50\ \text{s}$ and Machine B takes $25\ \text{s}$. Which has greater power? Show calculations.
16. List four forms of energy and give one example of each.
17. Explain why a wide school-bag strap is more comfortable than a narrow strap carrying the same load.
18. A learner writes: "The density of the block is $2\ \text{N}$." Identify and correct the mistake.
19. A learner writes: "The power is $300\ \text{J}$." Identify and correct the likely unit mistake.
20. Describe a simple method for finding the density of an irregular stone using a balance and measuring cylinder.

Generated Question Layer

• Direct recall: definitions and SI units for force, density, pressure, work, power, and energy.
• Unit matching: connect $\text{N}$, $\text{kg/m}^3$, $\text{Pa}$, $\text{J}$, and $\text{W}$ to their quantities.
• Formula substitution: simple calculations using $W = mg$, $\rho = \frac{m}{V}$, $P = \frac{F}{A}$, $W = Fd$, and $P = \frac{W}{t}$.
• Measurement-to-formula tasks: use mass, volume, area, force, distance, and time readings to calculate derived quantities.
• Concept comparison: distinguish mass from weight, density from mass, work from effort, and pressure from force.
• Everyday application: explain sharp tools, wide straps, floating and sinking clues, lifting loads, and machine power.
• Error correction: identify wrong units, inverted formulae, missing movement in work, and symbol confusion.
• Multi-step reasoning: combine weight, pressure, work, and power in short practical contexts without extending beyond Form I scope.

Learner Aid Opportunities

• diagram: Labelled sketches showing force arrows, contact area for pressure, water displacement for volume, and work done by a moving object.
• chart: Quantity-symbol-unit-formula table for force, density, pressure, work, power, and energy.
• interactive: Formula practice where learners choose the correct quantity and unit before calculating.
• animation: Pressure change as contact area changes, and energy transfer during lifting or falling.
• video: Short practical demonstration measuring mass, volume, force, distance, and time before calculating derived quantities.
• LLM tutor: Adaptive checks for unit discipline, formula choice, mass-weight confusion, and work-power distinction.

Exam-Derived Signals

• No past-paper or examination-format mappings have been reviewed for this Physics topic yet.
• The 2022 CSEE examination format may provide future assessment signals for calculation style, practical contexts, and wording, but it does not replace the 2023 syllabus placement used here.
• This learner expansion keeps the 2022 exam format assessment-only and does not use it to add advanced content beyond the official Form I syllabus topic.

Source And Review Notes

• Official syllabus status: extracted from the 2023 Physics syllabus as a Form I topic under the mechanics hub.
• Registry source: data/curricula/csee/physics/2023.json identifies the topic title, competence, form, source topic ID, and page path.
• Existing repo context used: Form I Physics topic spine, Mechanics, Measurement, Physical quantities and SI units, Measuring instruments in Physics, Measuring instruments and physical quantities, Linear motion, and Density sinking and floating.
• Content authorship status: Explanations, worked examples, and practice tasks are original learner-facing prose written from the official syllabus topic and existing repo context.
• External enrichment status: no external web enrichment was used.
• Exam signal status: 2022 examination format is treated only as assessment guidance and has not been used to define scope.
• Textbook status: no textbook wording was used.
• Review risk: A Physics reviewer should check local classroom conventions for $g$, preferred density units, symbol choices where $W$ and $P$ repeat, and the intended Form I depth for energy forms and pressure examples.