Force

Force Formula

The equation for force is given by Newton's 2^nd 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 2^nd law can be represented as follows:

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

it can also be written as

Or in words

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

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.

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.

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.

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.

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 3^rd law. Newton's 3^rd 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

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 1^st 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

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

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.

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.