 # Common Forces in Mechanics

Common Force in Mechanics: In the study of mechanics, you will deal with a wide range of forces. These forces can be broadly divided into two types, contact and non-contact forces. Some non-contact forces are the gravitational force, electrical and magnetic forces between charged and magnetic bodies. In this article, we will focus on the contact forces which are common forces in mechanics.

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As mentioned, there are a variety of force that exists in the universe. Let’s study the most common forces among them in detail:

## I. Contact Force

A contact force arises when an object is in contact with some other object. Whenever two objects are in contact with each other, mutual contact forces exist which satisfy Newton’s Third Law of Motion. The component of the contact force normal to the contact surfaces is called ‘Normal Reaction’.

Also, the component parallel to the surfaces is called ‘Friction’. A contact force can arise even when solids are in contact with liquids. Some examples of contact forces are buoyant force experienced by a solid immersed in a liquid, air resistance, viscous force, etc. The tension in a string and the force due to a spring are two other common forces of mechanics. What happens when you compress or extend a spring using an external force? A restoring force proportional to the compression or elongation is generated, right? It goes back into its original form. T

his restoring force can be represented as F = –kx, where x is the displacement and k is the force constant. The negative sign simply means that the restoring force is opposite to the external force. In case of an inextensible string, the force constant is very high. The restoring force is called ‘Tension’.

## II. Electrical Force – the foundation of contact forces

You already know that there are four fundamental forces in nature –

• Gravitational force
• Electromagnetic force
• Weak nuclear force
• Strong nuclear force.

Of these, only the first two are relevant in our study of mechanics. What if we told you that all the contact forces mentioned above arise from electrical forces? A little difficult to believe since mechanics deals with uncharged and non-magnetic bodies.

However, since all bodies are made up of charged nuclei and electrons (at the microscopic level), all contact forces can be traced back to the electrical forces between the charged constituents of the bodies.

## III. Friction

Imagine a body with mass ‘m’ at rest on a horizontal table. The body is at rest because the force of gravity (mg) is being canceled by the Normal Reaction Force (N) of the table.

What happens if we apply a horizontal force ‘F’ to the body? Ideally, the body should move with the acceleration F/m, provided there is no other external force on the body. However, we observe that if the force is too small, then the body does not move at all. This implies that there is some force which nullifies the small horizontal force, resulting in a zero displacement.

This force, parallel to the surface of the body in contact with the table is called frictional force or friction. It is denoted as fs, where the sub-script ‘s’ represents static friction. Remember, static friction comes into existence only when an external force (F) is applied. As F increases, fs increases too. fs is equal and opposite to the applied force F. It increases up to a certain limit, keeping the body at rest. The purpose of this force is to oppose the impending motion and is called Static Friction.

Now, we also know that as we increase the applied force, after a certain limit the body begins to move. This limiting value of static friction (fs)max is independent of the area of contact and is related to the Normal Force (N) as follows:

(fs)max = μsN  …… (1)

Where μs is a constant of proportionality and is called the coefficient of static friction. It depends only on the nature of the surfaces in contact. Therefore, the law of static friction is written as:

fs ≤ μsN   …… (2)

### Kinetic Friction

When F exceeds (fs)max, the body starts sliding on the surface. As this motion starts, the frictional force fs starts decreasing from its maximum value and another type of frictional force is formed – Kinetic or Sliding Friction, denoted by fk, which is also independent of the area of contact and also of the velocity. The law of kinetic friction is written as:

fk = μkN … (3)

Where μk is the coefficient of kinetic friction which depends only on the surfaces in contact. It has been proved experimentally that μk is less than μs.

Once the relative motion starts, the acceleration of the body is (F-fk)/m … according to Newton’s Second Law of Motion. Hence, for a body moving with a constant velocity F=fk. Also, once the applied force is removed, the acceleration is –fk/m which brings the body to an eventual halt.

### Static Friction

While understanding frictional force, it is important to note that it only opposes the relative motion and not all kinds of motion. Let’s understand with the help of an example:

Imagine a box on the floor of an accelerating train. Now, the box is stationary with respect to the train. However, for an observer outside the train, the box is accelerating with a speed equal to that of the train. What forces do you think, cause the box to accelerate?

Clearly, it is the force of static friction between the box and the train. If there was no friction, then the box would remain at its initial position when the train accelerates and would hit the back of the train. This impending relative motion is opposed by the static friction (fs). fs allows the box to accelerate with the train keeping it stationary with respect to the train.

### Rolling friction

Ideally, a circular object, like a ring or a sphere, should not suffer any friction when it rolls over a horizontal plane. The reason being that at every instance, there is only one point of contact between the body and the plane and this point has no relative motion to the plane. Hence, the kinetic or static friction should be zero leading to the body rolling with a constant velocity.

But, this does not happen. We know that in order to keep a body rolling, we will need to apply some force to counter the resistance to motion (rolling friction). If we take a body having the same weight as the circular body, then we find that the static friction is much larger than the rolling friction. In other words, a lesser force is needed to keep the ball rolling.

When a body is rolling, the surfaces in contact get momentarily deformed. This results in a finite area (not a point) of the body being in contact with the surface. The effect – the component of the contact force parallel to the surface opposes the motion.

## The Pros and Cons of Friction

In machines with different moving parts, friction plays a negative role in opposing the relative motion and dissipating energy in the form of heat. However, there are many ways of reducing friction (kinetic) in a machine. The use of lubricants, ball-bearings between moving parts, or a thin cushion of air between solid surfaces in relative motion are some examples.

On the other hand, friction is highly important in our daily lives. We can walk because of the friction between our feet and the ground. If you have ever been to an ice-rink you will understand how difficult it is to walk when there is little/no friction. Kinetic friction is used by brakes in machines and automobiles.

## Solved Examples for You

Q1. The figure below shows a man standing stationary with respect to a horizontal conveyor belt that is accelerating at 1 m/s2. What is the net force on the man? If the coefficient of static friction between the man’s shoes and the belt is 0.2, up to what acceleration of the belt can the man continue to be stationary relative to the belt? (Mass of the man = 65 kg.) Solution: We know that,

Mass of the man = m = 65 kg
Acceleration of the belt = a = 1 m/s2
Coefficient of static friction = μs = 0.2

Hence, using Newton’s Second Law of Motion, the net force acting on the man (F) is

F = ma = 65N

Now, the man can continue to be stationary with respect to the conveyer belt till such time that the net force exerted on the man is less than or equal to the frictional force between him and the belt (fs). Therefore,

(fs)max = fs
mamax = μsN = μsmg
∴ amax = μsg = 0.2 x 10 = 2 m/s2
Therefore, the maximum acceleration of the belt up to which the man can stand stationary is 2m/s2.

This concludes our discussion on the topic of common forces in mechanics.

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