16 July 2026

Is It a Liquid or a Solid? The Strange Science of Non-Newtonian Fluids


 Is It a Liquid or a Solid? The Strange Science of Non-Newtonian Fluids

Most students learn that matter can be divided into three familiar states: solids, liquids and gases.

A solid keeps its shape. A liquid flows and takes the shape of its container. A gas expands to fill the available space.

That classification is useful, but nature is rarely quite so tidy.

Some materials appear to behave like liquids when they are handled gently, yet become surprisingly solid when they are struck, squeezed or moved rapidly. A simple mixture of cornflour and water can flow through your fingers one moment and resist a sharp impact the next.

It raises a fascinating question:

How can the same material behave like a liquid and a solid without changing temperature or chemical composition?

The answer introduces us to the strange world of non-Newtonian fluids.

A Liquid That Does Not Follow the Normal Rules

Water, cooking oil and many other familiar liquids are described as Newtonian fluids.

In a Newtonian fluid, the viscosity remains approximately constant at a particular temperature.

Viscosity is a measure of how strongly a fluid resists flowing. Water has a relatively low viscosity, so it flows easily. Glycerol and golden syrup have much higher viscosities, so they flow much more slowly.

However, although glycerol is considerably more viscous than water, its viscosity does not suddenly change simply because we stir it faster or apply a greater force.

Cornflour mixed with water behaves differently.

When it is moved slowly, it flows. When it experiences a sudden force, it becomes much more resistant to movement. Its apparent viscosity increases.

This makes it a non-Newtonian fluid.

More precisely, a cornflour-and-water mixture is an example of a shear-thickening suspension. The faster we try to deform it, the more strongly it resists.

What Is Actually Inside the Mixture?

Cornflour does not dissolve in water in the same way that sugar or salt does. Instead, tiny solid particles remain suspended throughout the liquid.

When the mixture is handled gently, the particles have time to move around one another. Water acts as a lubricant between them, allowing the mixture to flow.

A sudden impact changes the situation.

The particles are forced together so quickly that they cannot rearrange themselves easily. They form temporary networks and become jammed against one another. The mixture then strongly resists further movement.

It can feel solid, but it has not undergone a permanent change of state. The effect only continues while the force is being applied.

Release the pressure, and the particles can begin moving again. The material returns to its flowing, liquid-like behaviour.

This is why a ball made from cornflour mixture appears solid while it is being squeezed but collapses into a puddle as soon as it is left alone.

Making a Non-Newtonian Fluid

The experiment is remarkably simple.

You will need:

Cornflour

Water

A large bowl or tray

A spoon

Food colouring, if required

Begin with approximately two parts cornflour to one part water. Add the water gradually because different brands of cornflour may require slightly different quantities.

Mix slowly until the material flows when gently tilted but strongly resists rapid stirring.

The mixture should not be watery. If it splashes easily, add more cornflour. If it remains dry and crumbly, add a small amount of water.

Once the consistency is correct, the investigation can begin.

Demonstration One: Slow Finger, Fast Finger

Place a finger gently onto the surface of the mixture and push down slowly.

Your finger should gradually sink into it.

Remove your finger and then strike the surface quickly with the flat of your hand or tap it sharply with one finger. The surface suddenly feels firm.

The mixture has not had time to flow away from the force. Its particles have become temporarily jammed together.

This is one of the clearest demonstrations because the only variable being changed is the rate at which the force is applied.

The hand is the same. The mixture is the same. The temperature is the same.

Only the speed of the movement has changed.

Yet the behaviour of the material is completely different.

Demonstration Two: Make a Temporary Solid Ball

Pick up some of the mixture and roll it rapidly between your hands.

While you continue applying pressure, it can be shaped into a surprisingly firm ball.

Now stop rolling and open your hands.

The ball immediately loses its shape and flows between your fingers.

Students often find this especially memorable because they can feel the transformation. It is not simply something they are being told about or shown on a diagram.

They experience the change directly.

The material has not chemically reacted, frozen or dried. It appears solid only because continuous force keeps the particles jammed together.

Demonstration Three: Can You Pull Your Hand Out?

Place your fingers into a deeper container of the mixture and try to remove them quickly.

The mixture grips surprisingly firmly.

Now relax and withdraw your fingers slowly. They come out much more easily.

This helps explain why panicking and making rapid movements in mud or other dense suspensions can sometimes make movement more difficult. Slow, controlled movement gives particles and liquid time to rearrange.

However, it is important not to suggest that all mud and quicksand behave exactly like cornflour mixture. Non-Newtonian fluids form a broad family, and different materials respond to force in different ways.

Some become thicker when moved rapidly. Others become thinner.

Demonstration Four: Dancing Cornflour

One of the most spectacular demonstrations involves placing the mixture above a loudspeaker.

The loudspeaker must first be protected with a secure waterproof membrane or covered tray. The mixture should never be poured directly onto the speaker cone.

When a low-frequency sound is played, the speaker vibrates rapidly. These vibrations continually accelerate and compress parts of the mixture.

At suitable frequencies and amplitudes, strange moving columns, folds and finger-like shapes can appear. The material seems to crawl or dance across the surface.

The sound waves are supplying repeated forces. Where the force is greatest, the mixture temporarily stiffens. As the force changes, it begins to flow again.

The resulting patterns can look almost alive.

This demonstration links several areas of science:

sound waves;

frequency;

vibration;

forces;

particle behaviour;

energy transfer;

properties of materials.

It is a particularly good example of how topics normally taught separately are actually connected.

Comparing Different Fluids

A useful investigation is to compare cornflour mixture with water, cooking oil and glycerol.

Pour equal amounts into separate transparent containers and observe how they behave when tilted, stirred or allowed to flow down a ramp.

Water flows quickly because it has a low viscosity.

Cooking oil usually flows more slowly.

Glycerol flows much more slowly because it has a higher viscosity.

However, these liquids do not suddenly become solid when struck. Their viscosities remain relatively predictable under normal classroom conditions.

The cornflour mixture is different because its resistance depends strongly on how rapidly the force is applied.

Students could investigate:

how long each fluid takes to travel down a ramp;

how quickly a ball bearing falls through each fluid;

how stirring speed affects resistance;

how changing the cornflour-to-water ratio affects behaviour;

whether temperature changes the results.

This turns a dramatic demonstration into a genuine scientific investigation involving variables, measurements and evidence.

Not All Non-Newtonian Fluids Become Thicker

The term “non-Newtonian” does not simply mean “a liquid that becomes solid when struck”.

It refers to any fluid whose viscosity does not remain constant under different flow conditions.

Cornflour and water are shear-thickening: they become more resistant when moved rapidly.

Other materials are shear-thinning. Their apparent viscosity decreases when they are stirred, spread or squeezed.

Paint is a familiar example. It needs to be thick enough not to run down the wall after application, but it must also spread easily under a brush or roller.

Tomato ketchup can also become easier to pour after it has been shaken. Toothpaste flows when squeezed but remains on the toothbrush when the pressure is removed.

Some materials require a minimum force before they begin to flow at all. This is why toothpaste can stay inside an open tube until it is squeezed.

The behaviour of non-Newtonian fluids is therefore much broader than the cornflour experiment suggests.

Why Does This Matter Outside the Classroom?

Non-Newtonian fluids are not simply scientific curiosities. Their behaviour is important in engineering, medicine, manufacturing, geology and product design.

Impact-Resistant Materials

Shear-thickening fluids have been investigated for use in protective equipment.

A flexible material is usually more comfortable to wear than a rigid plate. However, a material that temporarily stiffens during an impact could combine flexibility with additional protection.

Researchers have therefore studied fabrics containing shear-thickening fluids for possible use in protective clothing, sports equipment and body-armour systems.

The principle is similar to the cornflour experiment: flexible during ordinary movement, but much more resistant during a sudden impact.

Paints and Printing Inks

Paint needs carefully controlled flow properties.

It must move easily under a brush, roller or spray nozzle, but it should resist dripping once it reaches the wall.

Printing inks must also flow through machinery in a controlled way and then remain in position on the paper or packaging.

Understanding non-Newtonian behaviour allows manufacturers to design products that are easy to apply but remain stable afterwards.

Food Manufacturing

Many foods are non-Newtonian.

Yoghurt, sauces, chocolate, mayonnaise, cream, dough and ketchup all have complicated flow properties.

Manufacturers need to know how these materials will behave while being mixed, pumped, poured, transported and packaged.

A sauce may need to move easily through a factory pipe but remain thick enough to stay on the food when served.

Cosmetics

Shampoo, moisturiser, toothpaste, foundation and other cosmetics need very specific textures.

A cream should spread smoothly across the skin but should not run out of its container. Toothpaste should flow when squeezed but hold its shape on the toothbrush.

These properties are created by controlling the material’s non-Newtonian behaviour.

Geology and Natural Flows

Mud, wet sediment, lava and debris flows can behave in complex ways.

Their movement depends on particle size, water content, pressure, temperature and the forces acting on them.

Understanding these flows is important when studying landslides, volcanic eruptions, river sediment and unstable ground.

However, geological materials do not all behave like cornflour. Some become easier to move once they start flowing, while others can stiffen or jam under particular conditions.

Blood and Biological Fluids

Blood is also non-Newtonian.

It is not simply water with red colouring. It contains cells, proteins and many dissolved substances. Its apparent viscosity changes depending on the size of the blood vessel and the rate of flow.

This has important consequences for circulation and for the design of medical equipment such as pumps, artificial heart valves and blood-flow monitoring systems.

The mucus found in the respiratory and digestive systems also has specialised flow properties. It must be able to move while remaining thick enough to trap particles and protect delicate tissues.

What Looks Like a Simple Mess Is Actually Serious Science

Cornflour and water can easily be dismissed as a messy classroom activity.

In reality, it introduces some profound scientific ideas.

It shows that matter cannot always be placed into simple categories. It demonstrates that the properties of a material may depend not only on what it is made from, but also on how forces are applied to it.

It also encourages students to question the language they use.

Is the mixture really becoming a solid?

Not quite.

It is behaving like a solid for a short period because its internal particles have become jammed together. Once the force disappears, the structure breaks down and the material flows again.

That distinction is important. Scientific explanations should describe what is happening rather than merely repeat what something looks like.

Learning Through Touch, Movement and Surprise

In my experience, students remember science particularly well when an experiment challenges something they thought they already understood.

Most students believe they know the difference between a liquid and a solid. They have used both since early childhood.

Then they meet a substance that refuses to fit neatly into either category.

They press it gently and their finger sinks.

They strike it and it feels hard.

They squeeze it into a ball and then watch it melt through their hands without any change in temperature.

That moment of surprise creates curiosity. Curiosity creates questions, and those questions provide an opportunity for deeper scientific thinking.

At Philip M Russell Ltd, practical demonstrations are not treated as decorations added to a lesson. They are used to create the experience that the explanation must account for.

The student sees something unexpected, proposes an idea, tests it and then improves the explanation.

That is much closer to the way science actually works than simply copying a definition from a worksheet.

Practical Safety and Clearing Up

Cornflour mixture is generally straightforward to handle, but sensible precautions are still needed.

Use a tray to contain spills and protect nearby electrical equipment.

Do not pour large quantities down a sink. The particles can settle and contribute to blockages. Allow the mixture to dry before placing it in household waste, or scrape it into a suitable container for disposal.

If food colouring is used, remember that it may stain clothing and surfaces.

For the loudspeaker demonstration, keep the mixture completely separated from the electrical components by using a strong waterproof membrane or shallow sealed tray. Begin with a low volume and increase it gradually.

The Strangeness Is the Point

Non-Newtonian fluids show us that scientific categories are models rather than unbreakable rules.

Water behaves in a familiar and predictable way, so it is tempting to assume that every liquid must behave similarly.

Cornflour and water demonstrate that this is not true.

A material can flow gently through our fingers, resist a sudden blow and then collapse back into a puddle. Its behaviour depends on the forces acting upon its microscopic particles.

The experiment is inexpensive, memorable and easy to perform, but the ideas behind it connect to advanced materials, medicine, food production, cosmetics, engineering and geology.

The next time someone asks whether cornflour mixture is a liquid or a solid, perhaps the best scientific answer is:

It depends on what you do to it.

That may sound like an evasive answer, but it captures an important truth about science.

The natural world is often far more interesting than the simple categories we first use to describe it.

15 July 2026

Dividing a Line in a Ratio: When Common Sense Works Better Than a Formula

 


Dividing a Line in a Ratio: When Common Sense Works Better Than a Formula

Some mathematical problems look complicated because students are introduced to the formula before they have understood the idea.

Dividing a line in a given ratio is a good example.

Recently, some of my GCSE Further Mathematics students were faced with a coordinate geometry question in which they had to find the point that divided a line in a particular ratio. They knew that there was a formula somewhere in their notes, but they could not remember exactly how it worked.

Which coordinates had to be multiplied by which number?

Did the larger part of the ratio go with the first point or the second point?

Should they add the coordinates before dividing?

The formula had become another piece of information to memorise rather than a useful mathematical tool.

The problem initially stumped them.

However, when we ignored the formula and looked at what the question was actually asking, the solution became surprisingly simple.

What Does It Mean to Divide a Line in a Ratio?

Suppose a point P lies somewhere on the straight line between points A and B.

We are told that:

AP : PB = 2 : 3

This means that the whole line has been divided into five equal parts:

2 + 3 = 5

The distance from A to P represents two of those parts, while the distance from P to B represents the remaining three parts.

Therefore, starting at A, point P must be two-fifths of the way towards B.

That is the key idea.

We do not initially need a special formula. We simply need to:

  1. Find the change from A to B.
  2. Divide that change into the required number of parts.
  3. Move the correct number of parts from the starting point.

This is very similar to following directions on a map.

A Simple Coordinate Example

Suppose:

A = (2, 3)

B = (12, 8)

Point P divides the line AB in the ratio:

AP : PB = 2 : 3

We can solve this using common sense.

Step 1: Find the total number of parts

2 + 3 = 5

The complete journey from A to B has been divided into five equal parts.

Step 2: Find the horizontal change

The x-coordinate changes from 2 to 12.

Horizontal change:

12 − 2 = 10

Divide this change into five equal parts:

10 ÷ 5 = 2

Each ratio part represents a horizontal movement of 2.

To travel two parts from A:

2 × 2 = 4

Starting from the x-coordinate of A:

2 + 4 = 6

Therefore, the x-coordinate of P is 6.

Step 3: Find the vertical change

The y-coordinate changes from 3 to 8.

Vertical change:

8 − 3 = 5

Divide this into five equal parts:

5 ÷ 5 = 1

Each ratio part represents a vertical movement of 1.

To travel two parts from A:

2 × 1 = 2

Starting from the y-coordinate of A:

3 + 2 = 5

Therefore:

P = (6, 5)

No mysterious formula was required. We simply moved two-fifths of the way from A to B.

Seeing the Movement as a Vector

There is another way of presenting exactly the same reasoning.

The movement from A to B is:

(12 − 2, 8 − 3)

= (10, 5)

Point P is two-fifths of the way along this movement.

Therefore:

²⁄₅ × (10, 5) = (4, 2)

Now add this movement to point A:

(2, 3) + (4, 2) = (6, 5)

Again:

P = (6, 5)

This method is particularly useful because it links coordinate geometry with vectors. It helps students see that coordinates are not merely numbers written in brackets. They describe position and movement.

Why the Ratio Order Matters

One common mistake is to see the ratio 2 : 3 and automatically use three-fifths.

The wording must be read carefully:

AP : PB = 2 : 3

The first part, AP, tells us how far we move from A to reach P.

Since AP represents two of the five parts, we move two-fifths of the way from A towards B.

If the ratio were reversed:

AP : PB = 3 : 2

then P would be three-fifths of the way from A to B.

It would therefore be closer to B.

A quick sketch is often enough to prevent this mistake.

A —— —— P —— —— —— B

Here, there are two equal sections between A and P and three between P and B.

The diagram does not need to be accurate. Its purpose is to make the relationship clear.

What Happens When the Coordinates Decrease?

Students sometimes think that the method only works when the coordinates increase.

Consider:

A = (10, 12)

B = (2, 4)

Suppose P divides AB in the ratio:

AP : PB = 3 : 1

There are four parts altogether, and P is three-quarters of the way from A to B.

The change from A to B is:

(2 − 10, 4 − 12)

= (−8, −8)

Three-quarters of this movement is:

¾ × (−8, −8)

= (−6, −6)

Add this to A:

(10, 12) + (−6, −6)

= (4, 6)

Therefore:

P = (4, 6)

The negative values simply tell us that we are moving left and down.

The reasoning remains exactly the same.

A Practical Way to Think About It

Imagine travelling from one town to another.

Town A is 50 kilometres from Town B. A service station divides the journey in the ratio 2 : 3.

The total journey contains five equal parts:

50 ÷ 5 = 10 kilometres per part

The service station is two parts from Town A:

2 × 10 = 20 kilometres

The remaining distance is:

3 × 10 = 30 kilometres

Coordinate geometry uses the same idea, except that we must divide both the horizontal and vertical movements.

This is why practical comparisons can be so useful. They turn an abstract-looking calculation into something familiar.

Why Starting With the Formula Can Cause Problems

The section formula is often written in a form similar to:

P = ((nx₁ + mx₂) ÷ (m + n), (ny₁ + my₂) ÷ (m + n))

where:

AP : PB = m : n

The formula is correct, but it can cause difficulties.

The ratio numbers appear to be attached to the “opposite” coordinates. Students may remember the general shape of the formula but apply the numbers the wrong way around.

They may also complete the calculation successfully without understanding where the point should lie.

A student might obtain an answer outside the line segment and fail to notice that something has gone wrong.

The common-sense method provides a built-in check.

If AP : PB = 2 : 3, then P should:

  • lie between A and B;
  • be closer to A than to B;
  • be two-fifths of the way from A to B.

If the calculated point does not satisfy those conditions, the calculation needs to be reconsidered.

The Formula Should Come From the Reasoning

Once the idea is understood, the formula becomes much easier to explain.

Suppose:

A = (x₁, y₁)

B = (x₂, y₂)

and:

AP : PB = m : n

The total number of parts is:

m + n

Point P is m⁄(m + n) of the way from A to B.

The change from A to B is:

(x₂ − x₁, y₂ − y₁)

Therefore:

P = (x₁, y₁) + m⁄(m + n)(x₂ − x₁, y₂ − y₁)

This is not a separate trick. It is simply the common-sense method written algebraically.

The usual section formula can then be produced by expanding and simplifying this expression.

The formula now has meaning because it has been built from an idea the students already understand.

A Reliable Method for Students

For any question involving the division of a line in a ratio, students can use the following approach.

1. Draw a simple sketch

Mark the two endpoints and show which part of the ratio belongs to each section.

2. Add the ratio numbers

For a ratio of 2 : 3, there are five parts altogether.

3. Decide how far to move

If AP : PB = 2 : 3, move two-fifths of the way from A towards B.

4. Find the change in each coordinate

Calculate:

x₂ − x₁

and:

y₂ − y₁

5. Take the required fraction of each change

For two-fifths of the journey, multiply both changes by ²⁄₅.

6. Add the movement to the starting point

This gives the coordinates of the required point.

7. Check that the answer is sensible

The point should lie between the two endpoints and in the correct relative position.

Why This Matters Beyond One GCSE Question

This small problem illustrates a much wider lesson about mathematics.

Students are often tempted to search immediately for a formula. They ask:

“What equation do I use?”

A more valuable first question is:

“What is actually happening?”

Dividing a line in a ratio connects several important mathematical ideas:

  • fractions;
  • proportion;
  • coordinates;
  • gradients;
  • vectors;
  • interpolation;
  • transformations;
  • movement between points.

It also appears in practical applications such as computer graphics, animation, engineering design, mapping and game development.

For example, a computer game may need to place an object 30% of the way between two positions. An animation may need to calculate an intermediate frame between a starting point and a finishing point. A designer may need to position a support at a particular proportion along a beam.

All these problems use the same underlying principle.

My Reflection as a Teacher

What struck me about this lesson was not that the students lacked the ability to complete the calculation.

They were perfectly capable of working with fractions, coordinates and vectors.

The difficulty was that the problem had been presented as a formula to remember rather than a situation to understand.

Once we stopped searching for the formula and drew a simple line divided into equal parts, the atmosphere changed. The students could see where the point had to be. The arithmetic then became straightforward.

This is something I see repeatedly in mathematics teaching.

A formula can make a solution shorter, but introducing it too early can make the idea harder.

Understanding should come first. The formula should then summarise the understanding.

Conclusion: Draw the Line Before Reaching for the Formula

Dividing a line in a ratio may initially look like a specialised coordinate geometry problem.

In reality, it is simply a journey divided into equal parts.

Find the complete movement.

Divide it into the total number of ratio parts.

Move the required number of parts from the starting point.

Once students see this, the method becomes logical rather than mysterious.

The most useful lesson was not merely how to divide a line in a ratio. It was that when a mathematical formula feels confusing, it is often worth stepping back, drawing a picture and applying some common sense.

Sometimes the simplest route through a Further Mathematics problem is to stop looking for the formula and work out what the numbers actually mean.

#GCSEMaths #FurtherMaths #CoordinateGeometry #MathsTeaching #MathsTutor #MathematicalThinking #Vectors #ProblemSolving #STEMEducation #HemelPrivateTuition

14 July 2026

A Level Physics: Impulse — The Tiny Moment That Changes Everything


A Level Physics: Impulse — The Tiny Moment That Changes Everything

A tennis ball may be in contact with a racket for only a few thousandths of a second. Yet during that tiny interval, the ball can change direction completely and leave the racket travelling at more than 100 miles per hour.

How can such a short contact produce such a dramatic change in motion?

The answer lies in one of the most useful ideas in A Level Physics: impulse.

Impulse connects force, time and momentum. It helps us explain tennis serves, football kicks, car crashes, airbags, rocket engines, jumping, landing and even the way we package delicate objects.

It is also an excellent example of how physics can reveal what is happening during an event that takes place far too quickly for us to see clearly.

What Is Impulse?

Impulse is the product of force and the time for which that force acts.

For a constant force:

Impulse = force × time

J = FΔt

Impulse is also equal to the change in momentum of an object:

J = Δp

Therefore:

FΔt = mv − mu

where:

m = mass
u = initial velocity
v = final velocity
F = average force
Δt = time for which the force acts

This gives us the impulse–momentum relationship:

Impulse = change in momentum

The unit of impulse is the newton second:

N s

This is equivalent to:

kg m s⁻¹

That is not a coincidence. Momentum and impulse have the same units because an impulse produces a change in momentum.

Why Time Matters

Students often concentrate on the size of the force and overlook the importance of time.

However, the same change in momentum can be produced by:

• a large force acting for a short time
• a smaller force acting for a longer time

Rearranging the impulse equation gives:

Average force = change in momentum ÷ time

F = Δp ÷ Δt

This means that, for a fixed change in momentum, increasing the time reduces the average force.

This simple relationship explains a remarkable number of everyday situations.

Catching a Ball Safely

Imagine catching a fast-moving cricket ball.

If you hold your hands rigid and stop the ball almost instantly, the stopping time is very short. The force on your hands will therefore be large.

An experienced player moves their hands backwards while catching the ball. The ball still comes to rest, so the change in momentum is the same, but it is brought to rest over a longer time.

Increasing the stopping time reduces the average force.

The player is not removing the impulse. The impulse must still equal the ball’s change in momentum. They are spreading that impulse over a longer period.

The same principle explains why gymnasts bend their knees when landing and why people instinctively roll after jumping from a height.

Impulse in Tennis

Tennis provides an excellent context for studying impulse because the ball can experience a very large change in momentum during an extremely short contact time.

A tennis ball approaching a player already has momentum. When the racket strikes it, the ball may:

• slow down
• stop momentarily
• reverse direction
• leave with a much greater speed

Because momentum is a vector, direction is essential.

A ball travelling towards the player and then travelling away has undergone a much larger change in momentum than a ball that merely slows down while continuing in the same direction.

A Tennis Calculation

Suppose a tennis ball has a mass of 0.058 kg.

It approaches the racket at 20 m/s and leaves in the opposite direction at 30 m/s.

Let the direction away from the player be positive.

Initial velocity:

u = −20 m/s

Final velocity:

v = +30 m/s

The change in momentum is:

Δp = m(v − u)

Δp = 0.058 × (30 − (−20))

Δp = 0.058 × 50

Δp = 2.9 kg m s⁻¹

Therefore, the impulse delivered to the ball is:

J = 2.9 N s

If the ball is in contact with the racket for 0.005 seconds:

F = Δp ÷ Δt

F = 2.9 ÷ 0.005

F = 580 N

This is the average force. The maximum force during the collision may be considerably greater.

It is impressive to think that such a large force acts during an interval of only five milliseconds.

The Role of the Racket Strings

A modern tennis racket is not completely rigid. The strings deform when the ball strikes them, and the ball itself becomes compressed.

This deformation affects:

• the contact time
• the peak force
• the transfer of energy
• the amount of vibration
• the control the player has over the shot

Looser strings may deform more and can give a different sensation of power and control. Tighter strings usually deform less and may provide a more direct response.

However, racket performance is not determined by impulse alone. Energy transfer, string tension, racket mass, swing speed, spin and the coefficient of restitution all play a part.

Impulse tells us how much the momentum changes. It does not, by itself, tell us how efficiently energy has been transferred.

Does Following Through Increase the Impulse?

Coaches often tell players to follow through after striking the ball.

A common explanation is that following through increases the contact time and therefore increases the impulse. There is some truth in the idea that the racket must continue moving effectively through the impact, but the explanation needs care.

The ball is normally in contact with the racket for only a few milliseconds. Most of the visible follow-through happens after the ball has already left the strings.

The real value of following through is that it encourages the player to:

• maintain racket speed through the contact point
• avoid slowing the racket before impact
• produce a smoother movement
• control the direction of the shot
• reduce unnecessary strain on the arm

A good follow-through is therefore evidence of an effective stroke, rather than simply a way of keeping the ball on the racket for a visibly longer time.

Force–Time Graphs

In real collisions, the force is rarely constant.

When a tennis ball strikes a racket, the force rises rapidly, reaches a maximum and then falls as the ball leaves the strings.

Impulse is found from the area under a force–time graph.

Impulse = area under the force–time graph

This is a very important A Level Physics skill.

For a rectangular graph:

Impulse = force × time

For a triangular graph:

Impulse = ½ × base × height

For an irregular graph, the impulse may be estimated by counting squares, dividing the graph into simpler shapes or using computer data-logging software.

This is where practical physics becomes especially useful. A force sensor can record hundreds or thousands of measurements every second, revealing the shape of a collision that our eyes cannot resolve.

A Practical Investigation with a Dynamics Trolley

One useful experiment is to allow a dynamics trolley or smart cart to collide with different buffers.

Possible buffers might include:

• a rigid wooden block
• a spring
• foam
• rubber
• bubble wrap
• a magnetic bumper

A force sensor can record force against time during each collision.

Students can compare:

• maximum force
• collision time
• area under the force–time graph
• initial and final momentum
• whether momentum is conserved
• how different materials affect the peak force

A soft buffer usually increases the collision time and reduces the maximum force.

However, if the trolley undergoes the same overall change in momentum, the total impulse will be similar.

The shape of the graph changes even when the area under it remains approximately the same.

This is an important distinction:

The material can change how the force is delivered without necessarily changing the total impulse.

A Simple Ball Experiment

Impulse can also be investigated using balls dropped onto different surfaces.

A ball may be dropped onto:

• a hard floor
• carpet
• foam
• sand
• a force plate

A ball that bounces experiences a greater change in momentum than a ball that simply stops.

For example, if a ball approaches the floor with downward momentum and rebounds upwards, the direction of its momentum has reversed.

The change in momentum is therefore greater than it would be if the ball had merely come to rest.

This is why a bouncing object can produce a surprisingly large impulse on the surface.

Students can use video analysis to measure the speed immediately before and after impact. A force plate can then provide a force–time graph for comparison.

Airbags, Seat Belts and Crumple Zones

Impulse is central to vehicle safety.

In a crash, a passenger’s momentum must change. If the vehicle stops, the passenger must also be brought to rest.

The change in momentum cannot simply be avoided.

Safety systems work by increasing the time over which that change occurs.

Seat belts stretch slightly. Airbags compress. Crumple zones deform.

All these features increase the stopping time and reduce the average force acting on the occupants.

F = Δp ÷ Δt

Doubling the stopping time approximately halves the average force, provided the change in momentum remains the same.

Crumple zones also absorb energy through controlled deformation. This reminds us that both momentum and energy ideas are needed for a full explanation of a collision.

Protective Equipment in Sport

The same principle is used in:

• cycling helmets
• climbing mats
• boxing gloves
• shin pads
• cricket pads
• horse-riding body protectors
• padded goalposts
• running shoes

Padding compresses and increases the stopping time. This reduces the peak force on the body.

A helmet does not prevent the head’s momentum from changing. Instead, it aims to make that change happen over a slightly longer time while distributing the force over a wider area.

Even a few additional milliseconds can make an important difference.

Using Impulse to Produce Motion

Impulse is not only about stopping objects. It is equally important when setting objects in motion.

A sprinter pushes backwards and downwards on the starting blocks. The blocks exert an equal and opposite force on the athlete.

The longer and more strongly the athlete pushes, the greater the impulse and the greater the change in forward momentum.

The same idea applies when:

• a swimmer pushes away from the wall
• a rower drives the blade through the water
• a footballer kicks a ball
• a golfer strikes a golf ball
• a high jumper pushes against the ground
• a rocket engine produces thrust
• a propeller accelerates water backwards

To change an object’s momentum, a resultant force must act for a period of time.

Impulse in Rowing and Sailing

Impulse also has applications on the water.

A rower applies force to the water through the blade. The water is pushed backwards, and the boat gains forward momentum.

A short, violent stroke may produce a large peak force but may not always give the most controlled or effective motion. A well-timed stroke delivers force through an appropriate part of the movement.

In sailing, changes in momentum occur when:

• a boat accelerates after a tack
• a gust increases the force on the sail
• a boat collides with a wave
• a crew member moves suddenly
• a boat is brought alongside a pontoon
• a safety boat takes up the tension in a tow line

A tow line should not become tight with a sudden jerk. A sharp change in momentum over a very short time creates a large force that may damage fittings or destabilise the boats.

Allowing the force to build more gradually increases the time and reduces the peak load.

Impulse and Rockets

A rocket engine produces thrust by ejecting gas backwards at high speed.

The exhaust gases gain backward momentum. The rocket gains an equal amount of forward momentum.

Even a relatively small force can create a large change in momentum if it acts for long enough.

This is particularly important in space, where engines or thrusters may operate for extended periods. Small thrusters can gradually alter a spacecraft’s velocity, orientation or orbit.

Impulse is often used when describing rocket engines. The total impulse of an engine is the thrust multiplied by the time for which it operates.

Specific impulse is another quantity used in rocket science, although it has a specialised definition related to how effectively the engine uses propellant.

Does Impulse Improve Efficiency?

Impulse can help us analyse how effectively a force changes motion, but impulse is not the same as energy efficiency.

A system can produce the required impulse while wasting considerable energy as:

• heat
• sound
• vibration
• unwanted deformation
• turbulence
• movement in the wrong direction

For example, a tennis player may produce a large impulse, but an inefficient technique may also create unnecessary body movement, vibration and strain.

Similarly, a propeller may create thrust, but some energy may be lost in turbulence.

Efficiency is normally calculated using:

Efficiency = useful energy output ÷ total energy input

or:

Efficiency = useful power output ÷ total power input

Impulse answers the question:

“How much did the momentum change?”

Efficiency answers the question:

“How much of the input energy produced the useful result?”

The two ideas are related in practical situations, but they should not be confused.

Improving the Application of Force

In sport and engineering, we often want force to be applied:

• in the correct direction
• at the correct time
• for an appropriate duration
• without excessive peak forces
• with minimal unwanted motion
• with as little wasted energy as possible

A rower who applies force at the wrong point in the stroke may waste energy.

A tennis player who strikes the ball away from the racket’s effective hitting region may produce more vibration and less useful ball speed.

A runner whose foot lands too far ahead of their body may experience a braking impulse before producing a forward-driving impulse.

Impulse analysis can therefore help coaches and engineers understand not only whether motion changed, but how that change was produced.

My Experience of Teaching Impulse

Impulse is one of those topics that can appear rather dry when it is introduced only as:

J = FΔt

Students may learn the equation, substitute a few numbers and assume that the topic is finished.

The understanding changes when they see a real force–time graph.

A collision that looks instantaneous suddenly has a structure. The force rises, reaches a peak and falls again. Changing the bumper changes the graph. A bouncing object produces a different momentum change from one that simply stops.

Tennis is particularly useful because students already understand that the racket changes the motion of the ball. Physics gives them the language to describe exactly what has happened.

The most important step is often getting students to include direction.

A ball that reverses direction does not merely change its speed. Its velocity and momentum have changed sign. Missing that point can completely change the answer to a calculation.

Impulse also brings several parts of the A Level course together:

• Newton’s laws
• momentum
• vectors
• graphs
• collisions
• materials
• energy
• experimental data

That makes it far more than a single equation to memorise.

Common Mistakes to Avoid

Students commonly lose marks by:

• ignoring the direction of velocity
• using speed instead of velocity
• forgetting that momentum is a vector
• calculating mv − mu incorrectly when u is negative
• using the maximum force instead of the average force
• treating every force–time graph as a rectangle
• confusing impulse with energy
• assuming a longer stopping time reduces the total impulse
• forgetting that a rebound creates a larger momentum change

A reliable method is:

  1. Choose a positive direction.

  2. Write each velocity with its correct sign.

  3. Calculate the initial momentum.

  4. Calculate the final momentum.

  5. Find final momentum minus initial momentum.

  6. Use impulse = change in momentum.

  7. Use the contact time to calculate average force if required.

Conclusion: A Small Time with a Large Effect

Impulse allows us to understand events that happen in fractions of a second.

It explains why a tennis ball can reverse direction almost instantly, why a player moves their hands backwards when catching, why airbags save lives and why padding reduces injuries.

It also helps us investigate how forces create motion in running, rowing, swimming, vehicles and spacecraft.

The central idea is simple:

Impulse = change in momentum

Yet behind that simple equation lies a powerful way of thinking.

We cannot always avoid a change in momentum. A ball must be stopped, a passenger must be restrained and an athlete must push against the ground.

What we can control is how the force is applied, how long it acts and in which direction it acts.

That is where impulse becomes more than an examination equation. It becomes a practical tool for understanding sport, safety, motion and engineering.

13 July 2026

Is the River Thames at Bourne End Clean? Why We Need Evidence, Not Opinions

 


Is the River Thames at Bourne End Clean? Why We Need Evidence, Not Opinions

The River Thames at Bourne End can look beautiful.

On a calm summer morning, the water reflects the trees, sailing boats move quietly across the reach and insects hover around the marginal plants. It is tempting to look at the scene and conclude that the river must be clean and healthy.

Equally, after heavy rain, when the water becomes brown and turbid or pieces of debris float downstream, it is easy to decide that the river is badly polluted.

Neither conclusion is properly scientific.

A river cannot simply be described as “good” or “bad”. Water quality is a collection of physical, chemical and biological measurements, all of which can change with the weather, the season, the flow of the river, the time of day and the precise location at which a sample is taken.

To understand the water quality of the Thames at Bourne End, we need evidence.

That is where A Level Biology becomes particularly valuable.

What Does the Official Evidence Tell Us?

The reach containing Bourne End forms part of the Environment Agency’s Thames “Reading to Cookham” water body.

The Environment Agency currently classifies this wider stretch as having moderate ecological status. However, the detail behind that single word is much more interesting. The biological quality elements were classed as good, the invertebrate classification was good and the macrophyte—or aquatic plant—classification was high. Dissolved oxygen was rated high, while phosphate and temperature were only moderate. The classification history also records concerns involving persistent chemical pollutants.

That already demonstrates the problem with asking whether the river is simply clean or dirty.

Some indicators suggest a river capable of supporting a healthy biological community. Others reveal nutrient, temperature, physical modification or chemical pressures.

More importantly, an Environment Agency classification for a 38-kilometre water body cannot tell us the exact condition of the water beside a particular pontoon at Bourne End on a particular morning.

For that, we need local measurements.

A River Is Constantly Changing

Water quality is not fixed.

A sample collected at 9 am may produce different results from one collected at 4 pm. A sample taken after several dry days may differ considerably from one taken after a thunderstorm. Water beside dense aquatic vegetation may contain different concentrations of dissolved gases from water in the centre of the channel.

Temperature, river flow, rainfall, photosynthesis, respiration, agricultural runoff and discharges into the river can all affect the results.

Thames Water provides a near-real-time map showing monitored storm-overflow activity, including the time and duration of recorded discharges. This is useful contextual evidence, although it does not replace direct sampling at Bourne End.

The scientific question should therefore not be:

“Is the Thames at Bourne End clean?”

A better question would be:

“How do the physical, chemical and biological indicators of water quality vary at Bourne End with location, depth, season, time of day and recent rainfall?”

That is a much more interesting investigation.



Dissolved Oxygen: Can Aquatic Organisms Breathe?

Dissolved oxygen is one of the most important measurements.

Fish, freshwater shrimp, insect larvae and many microorganisms need oxygen dissolved in the water for aerobic respiration. A river may look clear but still have an oxygen problem.

Oxygen enters the water through contact with the atmosphere, especially where the water is disturbed at weirs or around obstructions. Aquatic plants and algae also release oxygen during photosynthesis.

At the same time, respiration by plants, animals and microorganisms removes oxygen. Decomposers can consume particularly large quantities when breaking down sewage, dead algae or other organic material.

The Environment Agency’s real-time water-quality monitoring systems commonly measure dissolved oxygen alongside temperature, conductivity, pH, turbidity, ammonium, chlorophyll and nitrate.

For an A Level investigation, dissolved oxygen could be measured:

  • near the bank and towards the main channel;

  • beside dense plant growth and in more open water;

  • at the surface and, where it can be done safely, at greater depth;

  • early in the morning and later in the afternoon;

  • before and after a period of heavy rain.

Morning and afternoon comparisons would be particularly interesting. Plants respire throughout the night but cannot photosynthesise without light, so dissolved oxygen may be lower around dawn. During a sunny day, photosynthesis may increase the oxygen concentration.

Temperature must be recorded at the same time because warm water holds less dissolved oxygen than cooler water.

One isolated dissolved-oxygen reading would tell us very little. A repeated pattern would be much more valuable.

Carbon Dioxide, pH and Photosynthesis

Carbon dioxide is closely linked to oxygen.

Respiration releases carbon dioxide, while photosynthesis removes it. As dissolved carbon dioxide increases, it can affect the pH of the water.

Directly measuring dissolved carbon dioxide in the field can be more difficult than measuring oxygen, but students could combine suitable dissolved-gas tests with pH measurements and observations of plant density.

The most useful investigation might compare:

  • heavily vegetated water with open water;

  • shaded areas with sunny areas;

  • morning readings with afternoon readings;

  • flowing water with sheltered areas near the bank.

This provides an excellent opportunity to connect ecology with the familiar A Level Biology equations:

carbon dioxide + water → glucose + oxygen

and

glucose + oxygen → carbon dioxide + water + energy

The equations are simple. Seeing their effects in an actual river makes them meaningful.

Turbidity: How Much Light Can Pass Through the Water?

Turbidity measures the cloudiness of water caused by suspended particles.

These particles may include clay, silt, organic matter, algae and microorganisms. Turbidity is normally measured using a turbidity meter in nephelometric turbidity units, although a turbidity tube can provide a simpler comparative measurement.

Heavy rainfall may wash soil and other material into the river. Boat movements, increased flow or disturbance of the riverbed may also raise suspended sediment.

High turbidity matters because it reduces the amount of light reaching submerged plants. This may lower photosynthesis and eventually affect dissolved oxygen.

Suspended particles can also settle on leaves, eggs and riverbed habitats.

However, cloudy water is not automatically polluted water, just as clear water is not automatically safe water. Turbidity is one piece of evidence that must be interpreted alongside the other results.

Temperature at Different Locations and Depths

Water temperature affects almost every part of a river ecosystem.

It affects metabolic rate, respiration, photosynthesis and the amount of oxygen that can remain dissolved in the water. It can also determine which species can survive in a particular habitat.

Students could lower a temperature probe to several depths, provided this can be done safely from a pontoon or boat. In a shallow, fast-moving section, the water may be well mixed and the differences small. In deeper or more sheltered areas, a temperature gradient may be found.

Measurements should also be taken:

  • in sunlight and shade;

  • near the bank and in the main channel;

  • close to incoming streams or drainage channels;

  • at several times during the day.

The result would be a temperature profile rather than one apparently precise but unrepresentative number.

Flow Rate: The Variable That Changes Everything

Flow rate influences nearly every other result.

Fast-flowing water is usually better aerated, while slow-moving water allows sediment to settle. Increased flow after rain may dilute some substances while simultaneously bringing additional sediment, nutrients, bacteria and organic material into the river.

A simple surface-flow investigation can be carried out by timing a floating object over a measured distance. Several repeats are needed, and the float must be recovered so that nothing is left in the river.

A flow meter would provide better local velocity measurements.

For a more ambitious investigation, students could measure the approximate cross-sectional area of the channel and combine this with average velocity:

discharge = cross-sectional area × mean velocity

At Bourne End, however, safety must take priority. There is no need for students to enter deep or fast-moving water merely to obtain another measurement. Sampling from the bank, pontoon or a properly supervised boat is much more appropriate.

Aquatic Plants and Marginal Vegetation

The plants growing in and beside the Thames are not merely scenery.

Aquatic plants provide habitats, refuge from predators, surfaces for eggs and feeding areas for many organisms. Their photosynthesis can also influence oxygen and carbon dioxide concentrations.

Students could establish a transect along the bank and record:

  • the plant species present;

  • percentage cover;

  • water depth;

  • distance from the bank;

  • degree of shading;

  • sediment type;

  • evidence of grazing or physical disturbance.

Quadrats could be used for marginal plants, while photographs would create a permanent record that could be analysed later in the classroom.

Repeated photographs from the same points would reveal seasonal change much more effectively than a single visit.

The investigation should also distinguish between native plants, invasive species and filamentous algal growth. A large quantity of green material does not necessarily indicate a healthy ecosystem. Excessive nutrient concentrations can encourage rapid algal growth, which may later create an oxygen demand as the algae die and decompose.

Invertebrates: The River’s Living Record

Chemical measurements show the condition of the river at the moment the sample is taken. Invertebrates can reveal what conditions have been like over a longer period.

Some freshwater invertebrates are relatively tolerant of pollution or low oxygen. Others require well-oxygenated water and are much more sensitive.

A carefully controlled sweep or kick sample might reveal freshwater shrimp, snails, leeches, caddisfly larvae, mayfly nymphs, beetle larvae and other organisms.

Riverfly monitoring uses the types and numbers of freshwater invertebrates as an indicator of river health. It complements chemical testing because the organisms reflect the ecological effect of water conditions rather than merely the concentration of a substance on one day.

Students could calculate:

  • species richness;

  • total abundance;

  • the relative abundance of indicator groups;

  • a diversity index;

  • differences between habitats.

Finding many organisms is not enough. A sample containing hundreds of individuals from one pollution-tolerant species may indicate a less balanced community than a smaller sample containing a wide variety of sensitive species.

Microbial Content: Clear Water Can Still Contain Bacteria

Microbiology is one of the most important—and most easily overlooked—parts of water-quality testing.

The water may appear completely clear while still containing microorganisms associated with faecal contamination.

For designated bathing waters, the Environment Agency tests for E. coli and intestinal enterococci. These are used as indicators of faecal pollution.

A proper microbial investigation at Bourne End would require carefully collected sterile samples and an appropriate laboratory method. Results should be expressed quantitatively, normally as the number of organisms or colony-forming units in a stated volume of water.

This work also requires particularly careful risk assessment.

Unknown environmental microorganisms should not be treated as harmless. School or tuition investigations should use approved procedures, sealed test systems or an accredited laboratory. Incubated cultures should not be reopened, and student results should never be used to declare the river safe for swimming.

The most revealing comparisons might be:

  • after prolonged dry weather;

  • after heavy rain;

  • upstream and downstream of potential inputs;

  • beside the bank and in the main flow;

  • across several months.

One sample cannot establish microbial safety. Repeated, professionally controlled testing is needed.

Nutrients and Other Chemical Measurements

Although oxygen, carbon dioxide and turbidity are important, a fuller survey should include additional chemical variables.

Phosphate and nitrate are particularly relevant because they can stimulate excessive plant and algal growth. Ammonium may indicate organic pollution, while conductivity can reveal changes in the concentration of dissolved ions.

Useful measurements could include:

  • pH;

  • nitrate;

  • phosphate;

  • ammonium;

  • conductivity;

  • alkalinity;

  • dissolved oxygen;

  • water temperature.

These should not be investigated as unrelated numbers. Students should look for relationships.

Does turbidity increase after rain?

Does phosphate concentration rise at the same time?

Are warmer areas associated with lower dissolved oxygen?

Do areas with more aquatic plants show larger differences between morning and afternoon oxygen readings?

Does invertebrate diversity change between habitats?

These questions turn data collection into scientific analysis.

Designing a Reliable Bourne End Investigation

A credible study needs more than an impressive box of sensors.

To do an accurate investigation we need three sampling locations: one upstream, one beside the main area of interest at Bourne End and one farther downstream. Each location needs a clear description, photographs and, where appropriate, a grid reference.

At every location, the same measurements should be taken using the same method.

Each measurement should be repeated. Equipment should be calibrated, sampling containers labelled and the time, weather and recent rainfall recorded.

The investigation should also be repeated across the year. A river in February is not the same ecosystem as a river in August.

A useful programme might include:

  • monthly baseline testing;

  • morning and afternoon comparisons;

  • additional sampling after heavy rainfall;

  • seasonal plant surveys;

  • regular invertebrate monitoring;

  • occasional accredited microbial analysis.

This would gradually create a genuine local dataset.

What A Level Biology Students Would Learn

The value of this work extends far beyond learning how to operate a dissolved-oxygen probe.

Students would have to consider:

  • independent, dependent and control variables;

  • random and systematic error;

  • repeatability and reproducibility;

  • representative sampling;

  • uncertainty;

  • correlation and causation;

  • risk assessment;

  • statistical significance;

  • ethical treatment of organisms;

  • the limitations of their conclusions.

They would also discover that real biological data are rarely neat.

A sensor may drift. A sample may become contaminated. One site may be inaccessible. A plant may be difficult to identify. Results may contradict the original hypothesis.

That is not failed science.

That is science.

My View of the River Has Changed

When I look across the Thames at Bourne End, I see sailing water, a working navigation channel and an attractive part of the local landscape.

A biological investigation encourages me to see much more.

The river is a moving system of organisms, gases, nutrients, microorganisms, sediment, temperature changes and human influences. Every insect larva, patch of weed and dissolved-oxygen reading contributes another piece of evidence.

The official evidence suggests a mixed picture: a river supporting valuable biological communities but still affected by nutrient, chemical and physical pressures.

Our local measurements could reveal how that wider picture appears at Bourne End—and how it changes from one day to the next.

Conclusion: Replace Assumptions with Evidence

So, what is the water quality of the River Thames at Bourne End?

The honest answer is that it cannot be reduced to one word.

The wider Environment Agency classification is moderate, but several biological indicators are good or high. Other indicators reveal continuing pressures. Conditions at one precise location may also change rapidly with rainfall, temperature, river flow, plant activity and pollution events.

The only scientifically defensible approach is to measure, repeat, compare and analyse.

That is why this could become such a powerful A Level Biology project.

Students would not simply learn about ecosystems from a textbook. They would investigate a real river, collect evidence about their local environment and begin constructing a long-term record of its health.

The Thames may look peaceful from the bank.

The science beneath the surface is far more complicated—and far more interesting.

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