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| © Eugene Brennan |
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.
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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.
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| One N is equivalent to about 100g or 3.5 ounces, a little more than a pack of playing cards. © Eugene Brennan |
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| 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.
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| 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.
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| 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.
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| 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.
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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
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| 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.
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| 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.
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| Newton's three laws of motion. © Eugene Brennan |
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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
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