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# Force

Force is a term we use in an everyday language all of the time. Sometimes people talk about 'The force of nature, and sometimes we refer to authorities such as the police force. Perhaps your parents are 'forcing' you to revise right now? We don't want to force the concept of force down your throat, but it would definitely be useful to know what we mean by force in physics for your exams! That's what we'll discuss in this article. First, we go through the definition of force and its units, then we talk about the types of forces and finally, we will go through a few examples of forces in our daily lives to improve our understanding of this useful concept.

Contents
Contents

## Definition of Force

Force is defined as any influence that can change the position, speed, and state of an object.

Force can also be defined as a push or pull that acts on an object. The force acting can stop a moving object, move an object from rest, or change the direction of its motion. This is based on Newton's 1st law of motion which states that an object continues to be in a state of rest or move with uniform velocity until an external force acts on it. Force is a vector quantity as it has direction and magnitude.

## Force Formula

The equation for force is given by Newton's 2nd law in which it is stated that the acceleration produced in a moving object is directly proportional to the force acting on it and inversely proportional to the mass of the object. Newton's 2nd law can be represented as follows:

$a=\frac{F}{m}$

it can also be written as

$F=ma$

Or in words

$\mathrm{Force}=\mathrm{mass}×\mathrm{acceleration}$

where$F$is the force in Newton$\left(\mathrm{N}\right)$, $m$is the mass of the object in$\mathrm{kg}$, and$a$is the acceleration of the body in$\mathrm{m}/{\mathrm{s}}^{2}$. In other words, as the force acting on an object increases, its acceleration will increase provided the mass remains constant.

What is the acceleration produced on an object with a mass of$10\mathrm{kg}$when a force of$13\mathrm{N}$is applied to it?

We know that,

$\mathrm{a}=\frac{\mathrm{F}}{\mathrm{m}}\phantom{\rule{0ex}{0ex}}\mathrm{a}=\frac{13\mathrm{N}}{10\mathrm{kg}}=\frac{13\frac{\overline{)\mathrm{kg}}\mathrm{m}}{{\mathrm{s}}^{2}}}{10\overline{)\mathrm{kg}}}\phantom{\rule{0ex}{0ex}}\mathrm{a}=1.3\frac{\mathrm{m}}{{\mathrm{s}}^{2}}$

The resultant force will produce an acceleration of$1.3\mathrm{m}/{\mathrm{s}}^{2}$on the object.

## Unit of Force in Physics

The SI unit of Force is Newtons and it is usually represented by the symbol$F$.$1\mathrm{N}$can be defined as a force that produces an acceleration of$1\mathrm{m}/{\mathrm{s}}^{2}$in an object of mass$1\mathrm{kg}$. Since forces are vectors their magnitudes can be added together based on their directions.

The resultant force is a single force that has the same effect as two or more independent forces.

Fig. 1 - Forces can be added together or taken away from each other in order to find the resultant force depending on whether the forces are acting in the same or opposite directions respectively

Take a look at the above image, if the forces act in opposite directions then the resultant force vector will be the difference between the two and in the direction of the force that has a greater magnitude. Two forces acting at a point in the same direction can be added together to produce a resultant force in the direction of the two forces.

What is the resultant force on an object when it has a force of$25\mathrm{N}$pushing it and a frictional force of$12\mathrm{N}$acting on it?

The frictional force will always be opposite to the direction of motion, therefore the resultant force is

$\mathrm{F}=25\mathrm{N}-12\mathrm{N}=13\mathrm{N}$

The resultant force acting on the object is$13\mathrm{N}$in the direction of motion of the body.

## Types of Force

We spoke about how a force can be defined as a push or pull. A push or pull can only happen when two or more objects interact with each other. But forces can also be experienced by an object without any direct contact between objects occurring. As such, forces can be classified into contact and non-contact forces.

### Contact Forces

These are forces that act when two or more objects come in contact with each other. Let us look at a few examples of contact forces.

#### Normal reaction force

The normal reaction force is the name given to the force that acts between two objects in contact with each other. The normal reaction force is responsible for the force we feel when we push on an object, and its the force that stops us from falling through the floor! The normal reaction force will always act normal to the surface, hence the reason its called the normal reaction force.

The normal reaction force is the force experienced by two objects in contact with each other and which acts perpendicularly to the surface of contact between the two objects. Its origin is due to the electrostatic repulsion between the atoms of the two objects in contact with each other.

Fig. 2 - We can determine the direction of the normal reaction force by considering the direction perpendicular to the surface of contact. The word normal is just another word for perpendicular or 'at right-angles'

The normal force on the box is equal to the normal force exerted by the box on the ground, this is a result of Newton's 3rd law. Newton's 3rd law states that for every force, there is an equal force acting in the opposite direction.

Because the object is stationary, we say that the box is in equilibrium. When an object is in equilibrium, we know that the total force acting on the object must be zero. Therefore, the force of gravity pulling the box towards the Earth's surface must be equal to the normal reaction force holding it from falling towards the centre of the Earth.

#### Frictional Force

The frictional force is the force that acts between two surfaces which are sliding or trying to slide against each other.

Even a seemingly smooth surface will experience some friction due to irregularities on the atomic level. Without friction opposing the motion, objects would continue to move with the same speed and in the same direction as stated by Newton's 1st law of motion. From simple things like walking to complex systems like the brakes on an automobile, most of our daily actions are possible only due to the existence of friction.

Fig. 3 - The frictional force on a moving object acts due to the roughness of the surface

### Non-contact forces

Non-contact forces act between objects even when they're not physically in contact with each other. Let's look at a few examples of non-contact forces.

#### Gravitational force

The attractive force experienced by all objects that have a mass in a gravitational field is called gravity. This gravitational force is always attractive and on the Earth, acts towards its centre. The average gravitational field strength of the earth is$9.8\mathrm{N}/\mathrm{kg}$. The weight of an object is the force it experiences due to gravity and is given by the following formula:

$F=mg$

Or in words

$\mathrm{Force}=\mathrm{mass}×\mathrm{gravitational}\mathrm{field}\mathrm{strength}$

Where $F$ is the weight of the object, $m$ is its mass and $g$ is the gravitational field strength at the Earth's surface. On the surface of the Earth, the gravitational field strength is approximately constant. We say that the gravitational field is uniform in a particular region when the gravitational field strength has a constant value. The value of the gravitational field strength at the surface of the Earth is equal to$9.81{\text{m/s}}^{2}$.

Fig. 4 - The gravitational force of the earth on the moon acts toward the centre of the Earth. This means that the moon will orbit in a nearly perfect circle, we say nearly perfect because the moon's orbit is actually slightly elliptical, like all orbiting bodies

#### Magnetic force

A magnetic force is the force of attraction between the like and unlike poles of a magnet. The north and south poles of a magnet have an attractive force while two similar poles have repulsive forces.

Fig. 5 - Magnetic force

Other examples of non-contact forces are nuclear forces, Ampere's force, and the electrostatic force experienced between charged objects.

## Examples of Forces

Let us look at a few example situations in which the forces we talked about in the previous sections come into play.

A book placed on a tabletop will experience a force called the normal reaction force which is normal to the surface that it sits on. This normal force is the reaction to the normal force of the book acting on the tabletop. (Newton's 3rd law). They are equal but opposite in direction.

Even when we're walking, the force of friction is constantly helping us push ourselves forward. The force of friction between the ground and the soles of our feet helps us get a grip while walking. If not for friction, moving around would have been a very difficult task. An object can only start moving when the external force overcomes the force of friction between the object and the surface on which it rests.

Fig. 6 - Frictional force while walking on different surfaces

The foot pushes along the surface, hence the force of friction here will be parallel to the surface of the floor. The weight is acting downwards and the normal reaction force acts opposite to the weight. In the second situation, it is difficult to walk on ice because of the small amount of friction acting between the soles of your feet and the ground which is why we slip.

A satellite re-entering the earth's atmosphere experiences a high magnitude of air resistance and friction. As it falls at thousands of kilometres per hour towards Earth, the heat from friction burns up the satellite.

Other examples of contact forces are air resistance and tension. Air resistance is the force of resistance that an object experiences as it moves through the air. Air resistance occurs due to collisions with air molecules. Tension is the force an object experiences when a material is stretched. Tension in climbing ropes is the force that acts to keep rock climbers from falling to the ground when they slip.

## Forces - Key Takeaways

• Force is defined as any influence that can change the position, speed, and state of an object.
• Force can also be defined as a push or pull that acts on an object.
• Newton's 1st law of motion states that an object continues to be in a state of rest or move with uniform velocity until an external force acts on it.
• Newton's 2nd law of motion states that the force acting on an object is equal to its mass multiplied by its acceleration.
• The SI unit of force is the Newton ($\mathrm{N}$) and it is given by $F=ma$, or in words,$\mathrm{Force}=\mathrm{mass}×\mathrm{acceleration}$.
• Newton's 3rd law of motion states that for every force there is an equal force acting in the opposite direction.
• Force is a vector quantity as it has direction and magnitude.
• We can categorise forces into contact and non-contact forces.
• Examples of contact forces are friction, reaction force, and tension.
• Examples of non-contact forces are gravitational force, magnetic force and electrostatic force.

#### Flashcards in Force 136

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What is force?

Force is defined as any influence that can bring about a change in the position, speed, and state of an object.

How is force calculated?

Force acting on an object is given by the following equation:

F=ma, where F is the force in Newton, M is the mass of the object in Kg, and a is the acceleration of the body in m/s2

What is the unit of force?

The SI unit of Force is the Newton (N).

What are the types of force?

There are many different ways of categorising forces. One such way is to split them into two types: contact and non-contact forces depending on whether they act locally or over some distance. Examples of contact forces are friction, reaction force, and tension. Examples of non-contact forces are gravitational force, magnetic force, electrostatic force, and so on.

What is an example of force?

An example of force is when an object placed on the ground will experience a force called the normal reaction force which is at right-angles to the ground.

## Test your knowledge with multiple choice flashcards

Which of these forces acts in the opposite direction to the direction of motion?

Force is a ...

The SI unit of force is ...

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