Kilcullen Science and Engineering

Kilcullen Science and Engineering - Exploring Science, Engineering, and Technology

Monday, December 22, 2025

Work at Dunstown 400kV Substation

Satellite image of an electrical substation
Groundworks at Dunstown 400 kV Substation. Image © Airbus, Maxar Technologies.
On a section of land adjacent-to and SE of the existing substation.
Maybe extra transformer capacity being added or other electrical infrastructure. I'm going to have to visit Google Earth, rather than Google Maps, as the former has historical satellite imagery.
 
Edit: Possibly preliminary groundworks for this: The connection of a "a high-capacity 400 kV (kilovolt) underground electricity connection between Dunstown substation in Co Kildare and Woodland substation in Co Meath." This is part of the Kildare-Meath Grid Upgrade (or Capital Project 966).


Details of necessary works at Dunstown for this project are available here.


A solar farm has also been granted planning permission at Delamain, just before Dunstown and adjacent to the road, north of Carnalway Cross. On the plans for the development, a bay is shown at Dunstown 400 kV Substation for connection of the 220 kV underground line from the solar farm.
An Coimisiún Pleanála still haven't given a decision on the revised plans submitted for the proposed battery energy storage system (BESS) facility, as far as I understand it. However, the facility would be located NE of the substation. More information on the ACP site link below, and its status is "Live Case". According to an Irish Independent article of 30 August last year, a decision was supposed to have been made by December 2024. The article also said that:
"An Bord Pleanála, planning consultant Peter Thomson for the applicants has stated that since the grant of permission, there have been advances in BESS technology. He said the changes in the design and chemistry of batteries have allowed for enhanced safety. As a result, "the BESS will use lithium iron phosphate batteries instead of the initially proposed lithium ion batteries".

Friday, December 19, 2025

Microgeneration and Athgarvan Mill

19th century corn mill in Ireland
Athgarvan corn mill in 2001. © Eugene Brennan

I've added links below to a list of electrical power generating sites in Ireland in a Wikipedia article, and also written answers from a Dáil Éireann debate of Tuesday, 26 Jan 2010 on the Oireachtais.ie website. There may be sites that generate lower output, not listed in these resources. According to a list referred to by Minister Eamon Ryan and provided by EirGrid and ESB Networks, Athgarvan Grain Company Limited's installation in Athgarvan was generating 20 kW from its small hydro turbine. (The owner showed me this in 2001, but I can't remember anything about it). Also Silliot Hill was generating 1.255 MW from methane produced by the landfill. An installation at Celbridge Mills was listed as generating 55 kW.
 
19th century corn mill in Ireland
Athgarvan corn mill in 2001. © Eugene Brennan

I met Brian Byrne in the Valley Park this morning when out for a walk, and we were musing about how it would be great if there was a turbine that could generate electricity from the power of the Liffey. It wouldn't have to be a large device, and could power lights in the park and would be a wonderful demonstration of the power of water. The problem nowadays is that there's so much red tape implementing projects like this. Also, as far as I'm aware, land on both sides of a waterway needs to be owned to install a hydrogeneration system. However, this might only be the case for streams, when a "dam" has to be constructed, potentially flooding fields on the far bank.
 
 

Thursday, December 18, 2025

Let's Do Some Calculations: How Much Water?

Roman arch bridge with water flowing under it.
© Eugene Brennan
I know I'm getting nerdy about this and becoming somewhat obsessed, but let's do some calculations for the total amount of water which has been flowing through the town per day.

Releases of water from Golden Falls dam in Ballymore Eustace have been unusually high over the last week. Some of this water will have flowed through the penstocks (large diameter pipes) to power the alternator and generate electricity. If power from the hydroelectric station can't be accepted by the grid and water level is too high in the lake supplying the dam, it has to "overflow". It's released through "doors" known as sluices, which are raised by electric motors. It then flows down concrete spillways into the river. Flow rate can typically be up to 15 or 20 cubic metres per second (m³/s) during extended periods of rainfall, but over the last couple of days, the rate has peaked at 33 m³/s for periods during the mornings. The ESB provides hydrometric information on their website for several hydro power stations throughout the country. This information consists of head race levels in reservoirs feeding the dams, average daily flow rates and a single set of flow rate figures, which represent projected values at eight-hour intervals throughout the day. At the Golden Falls dam in Ballymore Eustace, average daily flow since 12th December has been 25 m³/s. That's a per second flow rate, but averaged over a whole day. So at times, it was higher than this and lower at other times. For instance, for Thursday 18th December, flow rates were forecast at 20.0, 33.0, 20.0 and 20.0 m³/s, at 00:00 (midnight), 08:00, 16:00 and 00:00 (midnight the next day) respectively.

So to calculate the quantity of water that has been passing through the town over a 24 hour period, simply multiply the flow rate per second by the number of seconds in a day:

Total flow in 24 hours = average flow rate in m³/s x number of seconds in a day

= 25 x 60 x 60 x 24

= 2,160,000 m³

To put that into perspective, it's the volume occupied by a cube with sides 129 m long; the distance from the crossroads in the town centre to Bardon's pub. 

Related Reading

Golden Falls Generator Assembly 

Golden Falls Dam and Ballymore 5 km Loop 

Hydroelectric dam with water being released down the spillways
Golden Falls dam in Ballymore Eustace. © Eugene Brennan

Examples of Forces in Everyday Life and How They Affect Things

Diagram showing a stickman pushing a box on a table, illustrating a force.
© Eugene Brennan
In this first part of a two-part tutorial, we'll learn the absolute basics about forces!

What's covered:

  • Definitions of force, mass, velocity, acceleration, weight
  • Vector diagrams
  • Adding and resolving vectors

What Is a Force?

We can think of a force of a force as a push or pull.

 



What Are Examples of Forces?

  • When you lift something off the ground, your arm is exerting a force upwards on the object. This is an example of an active force.
  • The Earth's gravity pulls down on an object, and this force is called weight.
  • A bulldozer can exert a huge force, pushing material along the ground.
  • A huge thrust is produced by the engines of a rocket lifting it up into orbit.
  • When you push against a wall, the wall pushes back. If you try to compress a spring, the spring tries to expand and pushes back against your hand. When you stand on the ground, it pushes up and supports you. All these are examples of reactive forces. They don't exist without an active force.
  • If the unlike poles of two magnets are brought together (N and S), the magnets will attract each other. However, if two like poles are moved close together (N and N or S and S), the magnets will repel.

Fundamental Quantities Used in Physics

Before we learn any more details about forces, we need to become familiar with the international system of units, abbreviated to SI from the French Système International d’Unités. It's the units system used for engineering and scientific calculations and is basically a standardization of the metric system.

3 of the 7 base quantities in the SI system are used in the study of mechanics (a branch of physics concerned with forces and motion). They are mass, length and time.

Mass

This is a property of a body (any object) and a measure of the body's resistance to motion known as inertia. It is constant and has the same value no matter where an object is located on Earth, on another planet or in space. The unit of mass in the SI system is the kilo (kg).

Length

In the context of mechanics, the distance travelled by an object. The unit of length or distance is the metre (m)

Time

The time taken for an object to travel a given distance. The unit of time is the second (s)

Derived Quantities

These quantities can be derived from mass, length and time. The basic derived quantities are:

Velocity

This is the speed of a body in a given direction and is measured in metres per second (m/s). Average velocity equals distance travelled (length) divided by time taken.

Acceleration

When a force is exerted on a mass, it accelerates. In other words, the velocity increases. This acceleration is greater for a greater force or for a smaller mass. Acceleration is measured in metres per second per second or metres per second squared (m/s²). Average acceleration equals change in velocity divided by the time the change occurred in.

Force

This can be thought of as a “push” or “pull.” A force can be active or reactive. Force equals mass multiplied by acceleration. The unit of force is the newton (N) (We’ll learn more about this later)

Note: In US English, metres is spelled “meters”.

What One Newton Feels Like

Force in the SI system of units is measured in newtons (N). A force of 1 newton is equivalent to a weight of about 3.5 ounces or 100 grams. It's also defined as the force that will give a mass of 1kg an acceleration of 1 metre per second per second. We'll discover more about this in the second part of this tutorial.

Diagram illustrating the concept of a force.
One N is equivalent to about 100g or 3.5 ounces, a little more than a pack of playing cards.    © Eugene Brennan

 
Pratt and Whitney jet engine from an F15 fighter jet,  fired-up upon a testbed
A Pratt & Whitney turbofan engine as used on the F15 fighter jet. This engine develops a thrust of 130 kN (equivalent to a weight of 13 tonnes). U.S. Air Force photo by Sue Sapp, public domain via Wikimedia Commons 

What Types of Forces Are There?

Effort, Thrust and Tractive Force

Different words are used depending on context to refer to the the force involved when a human or machine moves an object. Effort is often used to refer to the force applied to an object which may eventually cause it to move. For example, when you push or pull a lever, slide a piece of furniture, turn a nut with a wrench, or a bull dozer pushes a load of soil, the applied force is called an effort. When a vehicle is driven forwards by an engine, or carriages are pulled by a locomotive, the force which causes motion and overcomes friction and air drag is known as traction, tractive force or tractive effort. For rocket and jet engines, the term thrust is often used.

Weight

This is the force exerted by gravity on an object. It depends on the mass of the object and varies slightly depending on where it is located on the planet and the distance from the centre of the Earth. An object's weight is less on the Moon and this is why the Apollo astronauts seemed to bounce around a lot and could jump higher. However it could be greater on other planets. Weight is due to the gravitational force of attraction between two bodies. It is proportional to the mass of the bodies and inversely proportional to the square of the distance apart.

Tensile or Compressive Reaction

When you stretch a spring or pull on a rope, the material undergoes a strain or internal distortion that results in an equal reactive force pulling back in the opposite direction. This is known as tension and is due to stress caused by displacement of molecules in the material. If you try to compress an object such as a spring, sponge or gas, the object pushes back. Again this is due to strain and stress in the material. Working out the magnitude of these forces is important in engineering so that structures can be built with members which will withstand the forces involved, i.e they won't stretch and snap, or buckle under load.

Static Friction

Friction is a reactive force which opposes motion. Friction can have beneficial or detrimental consequences. When you try to push a piece of furniture along the floor, the force of friction pushes back and makes it difficult to slide the furniture. This is an example of a type of friction known as dry friction, static friction or stiction. Friction can also be a problem in machines and lubrication is necessary to reduce friction between moving parts.

Friction can be beneficial. Without it everything would slide and we wouldn't be able to walk along a pavement without slipping. Tools or utensils with handles would slide out of our hands, nails would pull out of timber and brakes on vehicles would slip and not be of much use. So we increase friction by putting treads with good grip on the soles of shoes and grips with knurls or ridges on the handles of tools. Brake blocks are made from rubber on bicycles. This has a high coefficient of friction to make them grip and slow down wheels when they make contact with the rims.

Viscous Friction or Drag

When a parachutist moves through the air or a vehicle moves on land, friction due to air resistance, slows them down. Air friction also acts against an aircraft as it flies, requiring extra effort from the engines. If you try to move your hand through water, the water exerts a resistance and the quicker you move your hand, the greater the resistance. The same thing happens as a ship moves through water. These reactive forces are known as viscous friction or drag.

Buoyancy Force

This is the force which pushes up on an object immersed in a fluid (a fluid can be a gas or liquid). So for instance when you push a ball down into water, you can feel the buoyancy force pushing it back upwards. You can read more about buoyancy and the Archimedes' principle in this tutorial:
Archimedes' Principle Experiments and Buoyant Force

Electrostatic and Magnetic Forces

Electrically charged objects can attract or repel each other, similar to how poles of a magnet will repel each other while opposite poles will attract. Electric forces are used in powder coating of metal and electric motors work on the principle of magnetic forces on electric conductors.

Pictogram illustrating the various types of forces
Types of forces. © Eugene Brennan

What Is a Load?

When a force is exerted on a structure or other object, this is known as a load. Examples are the weight of a roof on the walls of a building, the force of wind on a roof, or the weight pulling down on the cable of a crane when hoisting.

What Is a Vector?

A vector is a quantity with magnitude and direction. Some quantities such as mass don't have a direction and are known as scalars. However, velocity is a vector quantity because it has a magnitude called speed and also direction (i.e., the direction an object is travelling). Force is also a vector quantity. For example, a force acting down on an object is different from a force acting upwards on the underside.


Vectors are graphically represented on diagrams by an arrow, with the angle of the arrow wrt a reference line representing the angle of the vector. We can solve mechanics problems by drawing vectors to scale with the length of the arrow representing its magnitude and then adding the vectors to find unknown forces.

Graphical representation of a vector
Graphical representation of a vector. © Eugene Brennan 

Examples of Vectors and Scalars

Scalars

  • Temperature
  • Pressure
  • Voltage
  • Time
  • Mass

Vectors

  • Velocity
  • Force
  • Acceleration
  • Magnetic field strength
  • Weight

What Are Vector Diagrams?

In mechanics, we use free-body or force diagrams to describe and sketch the forces in a system. A force is usually represented by an arrow and its direction of action is indicated by the direction of the arrowhead. Rectangles or circles can be used to represent masses.

How to Add Vectors

As mentioned briefly above, a force or any other vector can be represented graphically by an arrow with a given direction known as a vector. If two or more forces are involved, problems in mechanics can be solved graphically by drawing the vectors as a vector diagram, the head of one vector ending at the tail of the 2nd vector and so on. The vectors are drawn to scale, the length representing the magnitude of a force and the angle being the angle of action of the a. The "Triangle of Forces" or "Parallelogram of Forces" is then a method for visualizing or finding the resultant of forces. The resultant vector from adding force vectors gives the magnitude and direction of two or more forces combined.

Vector Algebra: The Triangle of Forces

We can add forces graphically using a triangle of forces. When a body is under equilibrium of three forces acting at a point, the forces can be represented by the sides of a triangle taken in order.

Vector diagram showing triangle of forces
A vector diagram showing a triangle of forces. F3 is the sum of the two forces F1 and F2. © Eugene Brennan 

Vector Algebra: The Parallelogram of Forces

We can also sum forces using a parallelogram of forces. In the diagram below, one dotted side is drawn parallel to F1 and the other dotted side parallel to F2. A line is drawn joining the start of vectors F1 and F2 to where the two dotted sides intersect. This line represents the sum of the two forces F1 and F2.

Vector diagram illustrating adding of vectors using a parallelogram of forces.

Parallelogram of forces. F3 is the sum of the forces F1 and F2. © Eugene Brennan

Resolving Forces

We can also resolve or split up a force into two or more forces. This is like using the parallelogram of forces in reverse. In the diagram below, a mass rests on a slope. Using the parallelogram of forces in reverse, the weight force can be resolved into a force parallel to the slope and perpendicular to the slope. This is useful for these type of problems because it enables the normal reaction to be worked out (the reactive force exerted by the slope on the mass, due to the perpendicular component of the mass, F2, acting on the slope). F1 is the force acting down the slope. If the mass isn't moving, F1 is balanced by a static friction force acting up the slope.

Using the Parallelogram of Forces to Resolve Weight Into Normal and Tangential Forces

Freeform diagram showing forces on a mass on an inclined plane
Resolving forces for a mass on a slope. The red vector can be replaced by the two blue vectors. © Eugene Brennan

What Happens When a Force Acts on an Object?

Its velocity (which you'll remember is the same as speed, but in a certain direction) increases. We call an increase in speed, acceleration.


Freeform diagram showing force acting on a mass and accelerating it as per Newton's second law
A force causes a mass to accelerate. © Eugene Brennan

Newton's Three Laws of Motion

In the second part of this tutorial, we'll cover Newton's Three Laws of Motion for Beginners. This explains in more detail what happens to an object when a force acts on it.

Pictogram showing Newton's three laws of motion
Newton's three laws of motion. © Eugene Brennan

You May Also Like

 Newton's 3 Laws of Motion: Force, Mass and Acceleration

 

Recommended Books

Mechanics

Applied Mechanics by John Hannah and M.J. Hillier is a standard text book for students taking Diploma and Technician courses in engineering. It covers the basic concepts I briefly cover in this article as well as as other topics such as motion in a circle, periodic motion, statics and frameworks, impulse and momentum, stress and strain, bending of beams and fluid dynamics. Worked examples are included in each chapter in addition to set problems with answers provided.

Mathematics

Engineering Mathematics by K.A. Stroud and Dexter J. Booth is an excellent math textbook for both engineering students and anyone with an interest in the subject. The material has been written for part 1 of BSc. Engineering Degrees and Higher National Diploma courses.

A wide range of topics are covered including matrices, vectors, complex numbers, calculus, calculus applications, differential equations, series, probability theory, and statistics. The text is written in the style of a personal tutor, guiding the reader through the content, posing questions, and encouraging them to provide the answer.

This book basically makes learning mathematics fun!

References

Hannah, J. and Hillerr, M. J., (1971) Applied Mechanics (First metric ed. 1971) Pitman Books Ltd., London, England.

This article is accurate and true to the best of the author’s knowledge. Content is for informational or entertainment purposes only and does not substitute for personal counsel or professional advice in business, financial, legal, or technical matters.

© 2022 Eugene Brennan


Wednesday, December 17, 2025

Newton's 3 Laws of Motion: Force, Mass and Acceleration

An infographic explaining Newton's three laws of motion

An infographic explaining Newton's three laws of motion. © Eugene Brennan

Mechanics is a branch of physics which deals with forces, mass, and motion.
In this second part of a two part tutorial, you'll learn the absolute basics!
In the first tutorial, Examples of Forces in Everyday Life and How They Affect Things, we learned what force is and explored the various types of forces in the world around us.

What's Covered in This Guide?

  • Newton's three laws of motion and how an object behaves when a force is applied
  • Action and reaction
  • Friction
  • Kinematics equations of motion

A stick figure pushing a box on a table
From the article "Examples of Forces in Everyday Life and How They Affect Things". © Eugene Brennan

 

What Are Newton's Three Laws of Motion?

In the 17th century, the mathematician and scientist Isaac Newton came up with three laws of classical mechanics concerning motion of bodies in the Universe. These laws describe the relationship between the motion of an object and the forces acting on it. In physics, objects have a property called mass, measured in kg in the SI system (This stands for Système International d'Unités, the standard system of units used in science and engineering)

1. Newton's First Law of Motion: Rest or Uniform Motion

Basically, this means that if for instance a ball is lying on the ground, it will stay there. If you kick it into the air, it will keep moving. If there was no gravity, it would go on for ever. However, the external force, in this case, is gravity which causes the ball to follow a curve, reach a max altitude and fall back to the ground. Friction from air also slows it down.

Another example is when you put your foot down on the accelerator and your car increases in speed. When you take your foot off the accelerator, the car slows down, The reason for this is that friction at the wheels and friction from the air surrounding the vehicle (known as drag) causes it to slow down. If these forces were magically removed, the car would stay moving forever.
There are three scenarios for the first law: Two for when a body is at rest and one for when it's in motion.

Body at Rest

There are two scenarios for a body at rest:

Scenario 1: No forces acting on the body

In the example of a body floating in deep space, far from any planets or stars, where it isn't influenced by gravity, it will stay in this position at rest forever. In reality of course, it will always be influenced by gravity, even at huge distances, although the effect may be tiny. In the diagram below, the body is given the symbol m, representing its mass. The body doesn't have to be in space of course, but this is an extreme example of a body so remote, that there are extremely small forces acting on it.

Diagram illustrating Newton's first law of motion

No forces act on the body, so it stays at rest. © Eugene Brennan


Scenario 2: No net forces acting on the body.

In reality, there will always be forces acting on a body. If forces cancel out, there's no net force acting and again it stays at rest. An example is an object with mass m suspended from a rope. The force of gravity pulls down on the object. However the rope also pulls back up with a tension force. These forces cancel each other out and there's no net force.

Diagram illustrating Newton's first law of motion
Forces cancel out and since there's no net force, the body stays at rest. © Eugene Brennan

Body in motion

This is the 3rd scenario of Newton's 1st law. When a body is acted on by a net force, it accelerates and reaches a certain velocity. When that force is removed, it continues to travel at that velocity, unless another force acts on it. Again, the reason why we don't see this ideal behaviour happening in the real world and objects continuing to move without slowing down is because external forces act, usually friction and drag due to air. We see approximations though, so a spinning top will spin for a long time if it has a pointed foot that has little friction wit the surface on which it rests. Similarly a bowling ball or marble will roll a long way on a hard level surface without stopping.

Diagram illustrating Newton's first law of motion
Once a body is accelerated by a force, it continues in a state of uniform motion, unless another force acts on it. © Eugene Brennan

2. Newton's Second Law of Motion: Force and Acceleration

This means that if you have an object and you push it, the acceleration is greater for a greater force. So for example a 400 horse power engine in a sports car is going to create loads of thrust at the axle and accelerate the car to top speed much more rapidly than a regular engine would be capable of achieving with the same weight of car.

In the SI system of units, force is measured in Newtons (N), mass is measured in kilograms (kg) and acceleration is measured in metres per second per second (also known as metres per second squared) (m/s2)

So:

If F is the force in Newtons (N)

m is the mass in kilos (kg)

and a is the acceleration (m/s2)

Then we can write an equation for Newton's 2nd law:

F = ma

This tells us that the mass of a body multiplied by its acceleration equals the force applied to that body that gave it the acceleration a.

We can also rearrange the equation so

a = F / m

What does this equation tell us?

Acceleration is proportional to the applied force

So the acceleration is directly proportional to the applied force. Double the force F and a doubles. Triple the force F and a is tripled and so on.

Acceleration is inversely proportional to the mass

For larger masses, acceleration is smaller for the same force. So for example, In the equation above if we double m, a is halved.

Imagine in the example above that the sports car engine was placed into a heavy train locomotive and could drive the wheels. Because the mass of the locomotive is so large, the force creates much lower acceleration and the locomotive takes much longer to reach top speed (In the equation, F is the same, but m is below the line, so a is smaller).

Diagram illustrating Newton's second law of motion
A force accelerates an object with a mass m.© Eugene Brennan

Example: A force of 10 newtons is applied to a mass of 2 kilos. What is the acceleration?

F = ma

So a = F / m = 10 / 2 = 5 m/s2

The velocity increases by 5 m/s every second

Newton's second law: The equation Force = mass multiplied by acceleration. F = ma

Force = mass multiplied by acceleration. F = ma
 © Eugene Brennan

 

Weight as a Force

In this case, the acceleration is g, and is known as the acceleration due to gravity.
g is approximately 9.81 m/s2 in the SI system of units.

Again F = ma

So if the force F is replaced by a variable for weight we choose to be W, then substituting for F and a gives:

W = ma = mg

Example: What is the weight of a 10 kg mass?

W = mg = 10 x 9.81 = 98.1 newtons

Diagram showin how weight is a force due to a gravity and W = mg

Weight is the force on a mass due to gravity. The weight of a body of mass m equals mg, where g is the acceleration due to gravity. © Eugene Brennan

3. Newton's Third Law of Motion: Action and Reaction

This means that when a force is exerted on an object, the object pushes back.

Some examples:

  • When you push on a spring, the spring exerts a force back on your hand. If you push against a wall, the wall pushes back.
  • When you stand on the ground, the ground supports you and pushes back up. If you try to stand on water, the water cannot exert enough force and you sink.
  • Foundations of buildings must be able to support the weight of the construction. Columns, arches, trusses and suspension cables of bridges must exert enough reactive compressive or tensile force to support the weight of the bridge and what it carries.
  • When you try to slide a heavy piece of furniture along the floor, friction opposes your effort and makes it difficult to slide the object

 

Examples of active and reactive forces

Examples of active and reactive forces. © Eugene Brennan

What is Dry Friction or "Stiction"?

As we saw above, friction is an example of a force. When you attempt to slide a piece of furniture along a floor, friction opposes your effort and makes things more difficult. Friction is an example of a reactive force, and doesn't exist until you push the object (which is the active force). Initially, the reaction balances the applied force i.e. your effort pushing the furniture, and there is no movement. Eventually, as you push harder, the friction force reaches a maximum, known as the limiting force of friction. Once this value is exceeded by the applied force, the furniture will start to slide and accelerate. The friction force is still pushing back and this is what makes it so difficult to continue to slide the object. This is why wheels, bearings, and lubrication come in useful as they reduce friction between surfaces, and replace it by friction at an axle and leverage to overcome this friction. Friction is still necessary to stop a wheel sliding, but it doesn't oppose motion. Friction is detrimental as it can cause overheating and wear in machines resulting in premature wear. So engine oil is important in vehicles and other machines, and moving parts need to be lubricated.

diagram showing all the forces on a mass resting on a surface.

Forces acting on a mass when a force attempts to slide it along a surface. When the mass is just about to slide, the friction force Ff reaches a maximum value μRn. © Eugene Brennan

Dry static friction, also known as stiction (see above diagram)

If F is the applied force on a body

The mass of the body is m

Weight of the body is W = mg

μs is the coefficient of friction (low μ means the surfaces are slippery)

and Rn is the normal reaction. (the reaction force acting upwards at right angles to the surface due to the weight of the object acting downwards)

If the surface is horizontal, then

Reaction Rn = Weight W

Then

limiting friction force is Ff = μsRn = μsW = μsmg

Remember this is the limiting force of friction just before sliding takes place. Before that, the friction force equals the applied force F trying to slide the surfaces along each other, and can be anything from 0 up to μRn.

So the limiting friction is proportional to the weight of an object. This is intuitive since it is harder to get a heavy object sliding on a specific surface than a light object. The coefficient of friction μ depends on the surface. "Slippery" materials such as wet ice and Teflon have a low μ. Rough concrete and rubber have a high μ. Notice also that the limiting friction force is independent of the area of contact between surfaces (not always true in practice)

Kinetic Friction

Once an object starts to move, the opposing friction force becomes less than the applied force. The friction coefficient in this case is μk.

What Are Newton's Equations of Motion? (Kinematics Equations)

There are three basic equations which can be used to work out the distance travelled, time taken and final velocity of an accelerated object.

First let's pick some variable names:

u is the initial velocity

v is the final velocity

s is the distance covered

t is the time taken

and a is the acceleration produced by force F

As long as the force is applied and there are no other forces, the velocity u increases uniformly (linearly) to v after time t.

Diagram showing variables associated with a mass that has been accelerated by a force.

Acceleration of body. Force applied produces acceleration a over time t and distance s.© Eugene Brennan

So for uniform acceleration we have three equations:

v = u + at

s = ut + 1/2 at2

v2 = u2 + 2as

Examples:

(1) A force of 100 newtons accelerates a mass of 5 kg for 10 seconds. If the mass is initially at rest, calculate the final velocity.

Firstly it is necessary to calculate the acceleration.

F = 100 newtons

m = 5 kg

F = ma so a = F/m = 100/5 = 20 m/s2

Next work out the final velocity, knowing the acceleration:

Substitute for u, a and t:

u = initial velocity = 0 since the object is at rest

a = 20 m/s2

t = 10 s

v = u + at = 0 + 20 x 10 = 200 m/s

(2) A mass of 10 kg is dropped from the top of a building which is 100 metres tall. How long does it take to reach the ground?

In this example, in theory it doesn't make any difference what the value for the mass is, the acceleration due to gravity is g irrespective of the mass. Galileo demonstrated this when he dropped two balls of equal sizes but differing masses from the leaning tower of Pisa. However in reality, the drag force due to air resistance will slow down the falling mass, so a 10 kg sheet of timber would fall slower than a 10 kg lead weight. So assume there is no drag and the calculations apply to a weight falling in a vacuum.

We know s = 100 m

g = 9.81 m/s2

u = 0 m/s

We can use the equation s = ut + 1/2 at2

The acceleration a in this case is the acceleration due to gravity so a = g

Therefore substituting for u and g gives

s = 0t +1/2 gt2 s = 1/2gt2

Rearranging

t = √(2s/g) = √(2 x 100) / 9.81 = 4.5 seconds approx

Newton's equations of motion
Newton's equations of motion. © Eugene Brennan

The Hammer and Feather Experiment From Apollo 15

 

Related Reading 

Solving Projectile Motion Problems - Applying Newton's Equations of Motion to Ballistics

How Do Wheels Work? - The Mechanics of Axles and Wheels

 

Mechanics

Applied Mechanics by John Hannah and MJ Hillier is a standard text book for students taking Diploma and Technician courses in engineering. It covers the basic concepts I briefly cover in this article as well as as other topics such as motion in a circle, periodic motion, statics and frameworks, impulse and momentum, stress and strain, bending of beams and fluid dynamics. Worked examples are included in each chapter in addition to set problems with answers provided.

Mathematics

Engineering Mathematics by K.A. Stroud is an excellent math textbook for both engineering students and anyone with an interest in the subject. The material has been written for part 1 of BSc. Engineering Degrees and Higher National Diploma courses.

A wide range of topics are covered including matrices, vectors, complex numbers, calculus, calculus applications, differential equations, series, probability theory, and statistics. The text is written in the style of a personal tutor, guiding the reader through the content, posing questions, and encouraging them to provide the answer.

This book basically makes learning mathematics fun!

References

Hannah, J. and Hillerr, M. J., (1971) Applied Mechanics (First metric ed. 1971) Pitman Books Ltd., London, England.

If you liked this article, you may be interested in reading more articles about mechanics:

Solving Projectile Motion Problems - Applying Newton's Equations of Motion to Ballistics

How Do Wheels Work? - The Mechanics of Axles and Wheels

This content is accurate and true to the best of the author’s knowledge and is not meant to substitute for formal and individualized advice from a qualified professional.

© 2012 Eugene Brennan


Tuesday, December 16, 2025

Replica Gun Discussion on Liveline

Created by Grok.

A discussion on RTÉ Liveline today was about "Airsoft" type guns on public display in shops. Under the Firearms Acts 1925, revised to 2023, these guns must have a muzzle energy of less than 1 joule to avoid being classified as firearms requiring a license.

What's a joule?

It's the Système International (SI) unit of energy or work done.

Energy = power x time

So 1 watt for 1 second = 1 x 1 = 1 joule.

Think of a 1 watt bulb turned on for 1 second; that consumes 1 joule of energy.

Since energy can't be created or destroyed (except in nuclear reactions where there are mass-energy conversions), "consumes" doesn't mean the bulb destroys the energy, it's simply converted into another form of energy, light and heat. For an incandescent bulb, 95% of the energy is heat.

Another example of a joule is the work required to lift a weight. Work in physics has a very specific meaning. It's defined as something which occurs when a force moves a body through a distance. When an object is lifted off the ground, a force is required to counteract the force of gravity. 

The work done W when a force moves a mass m a distance h above the ground is defined as:

W = mgh

if m is 1 kilo and h is 10 cm (0.1 m)

and g is the acceleration due to gravity; approximately 9.81 metres per second per second

W = 1 x 9.81 x 0.1 = 0.981 or approximately 1 joule.

So that's the amount of energy an Airsoft pellet is limited to; the potential energy of a bag of sugar, raised 10 cm off the ground. (or 100 g, raised 1 m off the ground).
Contrast that with the energy of a rifle bullet, which is approximately the potential energy of a brick raised to the height of a chimney on a two story house. 

Wednesday, December 10, 2025

Big Picture Science Podcast: A Real Gas

Created by Grok

Did you know, some gasses have a colour (like chlorine), many are invisible and have have no taste or smell (such as oxygen and nitrogen), and yet others are totally unreactive—the noble gasses, such as neon, argon and xenon? Also steam is an invisible gas. The stuff we see coming out of a kettle is condensed steam, but close to 100 degrees Celsius.
In this episode, Mark Miodownik – Professor of materials and society at the University College London and the author of It’s a Gas: The Sublime and Elusive Elements That Expand Our World, talks with executive producer of BPS, Molly Bentley.

Monday, December 08, 2025

Items for Sale in Kilcullen, Circa 1900

Image courtesy The National Library of Ireland.


"Sides of pork, brooms, Cadbury chocolate and cocoa and The Freeman's Journal: some of the items for sale in Kilcullen circa 1900."
 
I've been examining photos from the Lawrence Collection again and zooming in to see whether I can spot any details I may have missed. The collection is available online on the National Library of Ireland's website. I first viewed the photographs on a visit to the NLI around 1982. In those days, before digitisation, photographic records were stored on rolls of microfilm and had to be viewed using optical microform readers.
The Lawrence Collection consists of approximately 40,000 glass plate negatives of buildings and scenes from life in Ireland, photographed between 1865 and 1914. The photographs were taken using large-format cameras and because of the size of the glass-plate negatives, resolution is quite high. There are 25 photographs of buildings and streetscapes in Kilcullen and its hinterland, and the collection became available to access online over 10 years ago.

You can view it here.

All images courtesy the National Library of Ireland.

The building at the corner of the entrance to the Valley Park, originally Andrew Maloney's premises.
 
Signs for "The Freeman's Journal" outside what is now Bardon's Pub. The premises was originally a hotel and then a pub and grocery.

A shop in Upper Main street which is now the premises of Dowling Property.

Near Centric Health.

Dublin House, now Woodbine Books. It was the premises of Denis Brennan, auctioneer, pub and drapers.

Tuesday, December 02, 2025

Leaky Schrader Valve

Hand truck tube. © Eugene Brennan

So being a member of 60 Facebook groups and squandering a lot of time nattering about all sorts of things, I try to get at least one useful thing done per day. Today was damp, so dealing with weeds in the driveway was out of the question. One of the items on my ever-growing-longer "to do" list I hadn't got around to was fixing the wheel on my hand truck which always seemed to be soft when I went to use the truck. I thought it might be a puncture caused by running over thorns (what usually happens with the bike). However doing a water test showed the Schrader valve was leaky. There's a special tool for taking the innards out of the valve casing, but I usually just use a needle-nose pliers. These valves have a conical part that sits into a conical seat, the cone being pressed against the seat by a spring. I blew out the valve with compressed air, gave the red ring that seals against the valve body a wipe and put the bits back together. This time there were no leaks whatsoever after the water test.

Removing the Valve innards. © Eugene Brennan

C
Check valve. © Eugene Brennan

© Eugene Brennan