## Forces

A push or pull that accelerates an object having some mass is known as force. It is considered a vector quantity as it has both direction and magnitude.

The SI unit of force is known as Newton (N). It is kg m/s^{2}.

a) Two skaters pushing the third skater in different directions with forces F_{1} and F_{2}. The resultant force F_{total }is in the direction shown.

b) A free-body diagram representing the resultant force

Net force:

It is the sum of the forces acting on the object to obtain a resultant force.

Forces can be of two types:

- Contact forces
- Non-contact forces.

**1. Contact forces**– These are the forces that are exerted on an object after coming in contact with it.

These are further classified as:

- Spring force- This force is the reactive force exerted by the molecules of an object when a force is exerted to change its shape. It works like that in spring.
- Applied force- This is the type of force that is exerted by the muscles of our body.
- Air resistance force- It is the force exerted by air/gas present in the atmosphere in the direction opposite to the movement of an object. When an object has to move faster, the streamlined design of the object helps it to move faster. This is because the streamlined design helps objects reduce the air resistance force or air drag.
- Normal force- This is the force acting at the contact point in the direction perpendicular to the surface. When a box is kept on a table, the table’s surface will exert this force in an upward direction.
- Tension force- The force present in the ropes and strings attached to an object is called tension force. Tension force is always a pull force.
- Frictional force- This is the force exerted by the surface due to its roughness. This roughness leads to a type of force that decelerates the moving object. The force is called frictional force.

**2. Non-contact forces** – These are the forces that can be exerted on an object, from a distance without being in actual contact with it.

These are further classified as:

- Electromagnetic force- These are the forces associated with electric and magnetic fields. These are responsible for the binding of atoms and molecules to form the atomic structure.
- Gravitational force- This is the attractive force between 2 objects with mass, especially the earth and another object. Every object in the universe attracts other bodies towards it due to a force called gravitational force.
- Nuclear force- This is the force acting between the protons and neutrons of the atoms. This force is responsible for the bonding of the nucleus.

## Newton’s laws

There are three physical laws of a motion introduced by *Isaac Newton,* which relate the forces acting on an object and its motion. These three laws are the foundation of basic mechanics.

### Newton’s First law:

This law says that, if a body is in motion or is at rest, it will continue to be in motion or will be at rest unless an external net force is applied. This postulate is called the __law of inertia. __

__Inertia__:

Inertia is the property of a body by which it resists the change in its velocity. If the object is at rest, it has a tendency to remain at rest. If it is moving, it tends to keep moving at a constant velocity.

When an object moves at a constant velocity, then resultant forces acting in a particular direction on it must be zero. If the resultant force is not zero, then the object will show movement in the direction of the net force.

Daily life examples:

- Consider the experience when we are on a train. When the train suddenly stops, we tend to go forward. This is because our body “tends to do whatever it was doing” and tends to be in motion, due to inertia. Similarly, when a train at rest accelerates suddenly, we tend to move backwards. This is because our body tends to be at rest. So, from the point of view of a person on the train, we would look to go forward after applying sudden brakes and move backwards after sudden acceleration.

- Consider an object sliding on a table. Initially, it is at rest, and then a person pushed it to move it with a velocity of 5 m/s. After the initial push, the person did not exert any force. Will the object continue to slide on the table or will it come to a halt?

Answer:

Based on the first law, the object must continue to slide if no external force is applied. However, here even when the person is not exerting any force, the frictional force of the table exists. So, this works as the resistance force, which stops the object after sliding to a distance.

Also, when the surface of the table is lubricated to reduce its roughness. It will decrease the frictional force; the object will slide to a longer distance.

So, Frictional force is the coefficient of friction ‘μ’, multiplied with the resultant force ‘R’.

μR=F

For an object to move in the direction of the force ‘F’ applied, the frictional force must be lesser than the force applied.

μR<F

### Newton’s second law

According to newton’s second law, the rate of change of the momentum is directly proportional to the net force on the object with a constant mass.

Momemtum = mass x velocity

So,

The second law of motion is the relation between the force, mass, and acceleration of a body. It states that the acceleration produced in an object by a net force is directly proportional to the force and indirectly proportional to the mass of the object.

As v/t equals to the acceleration (a) so, it can be said that force acting on a body can be calculated by its mass multiplied by its acceleration.

F = m x a

Example: Take two boxes A and B with a mass of 5 Kg and 10 Kg respectively. If we have to move them at the same acceleration, then which box requires more force to be moved?

We know that Force= mass x acceleration. So, for the same acceleration, the heavier box B will require more force to be moved from one place to the other.

In the first law of motion, we saw that an object requires an external force to change its state of motion, the second law of motion is the mathematical concept to calculate the force or acceleration of an object having mass.

Daily life example:

Consider a kid sitting in a cart and two kids are pushing it from behind. The two kids are acting forces F1 and F2 to move the cart at an acceleration of ‘a’ and frictional resistance force ‘f’ is also acting.

Note: According to the first law, only external forces affect the motion. So, we need to determine the boundaries of the system. Here, the kid and cart make one system with weight ‘w’.

From the above situation, we understand that the acceleration is directly proportional to the net force acting on a body in the direction of motion.

a∝ F

Now, to understand the relation between the force and mass of an object on which the force is acting, see the below picture.

Here, a person is applying the same amount of force F on a ball and a car. The weight of the car is higher than that of the ball. Therefore the acceleration produced by force on the car will be very low as compared to that of the ball (neglecting the frictional resistance by the car’s wheels).

So, for the same force, we can say that the acceleration is inversely proportional to the mass of the object.

a ∝

### Application of Newton’s second law during freefall

Consider an elephant with mass M is falling with a gravitational force F and a mouse with mass m is falling with a gravitational force m. It is obvious that the elephant has more mass than the mouse. Still, the acceleration of both during freefall is the same. We may think that the elephant will have more acceleration due to its high mass, but the acceleration depends on both force and mass and not just on mass. The mass of the elephant also increases the force of gravity with which it is falling.

Hence, F/M for the elephant is equal to the f/m of the mouse.

### Newton’s third law of motion:

This states that when two bodies come in contact with each other, they exert equal forces on each other in the opposite direction. Also, we can say that for every action, there is an equal and opposite reaction.

The third law is essential to understand and analyse the forces.

Consider a swimmer pushing the wall by her feet. The wall pushes her back in the opposite direction that causes movement of the swimmer forwards.

Daily life examples:

[a] When we are standing on a floor, our body is exerting a downward force on the floor, and the floor is exerting an upward force on the body. Here, the force exerted by the floor is equal to the downward force exerted by our body. These opposite forces are called as the action and reaction forces.

So, it means that an object cannot exert a force on other bodies without experiencing a reaction force on itself.

[b] Without an external force in an upward or downward direction, a box kept on a table will remain ideal at rest as the equal, and opposite forces on the box have net resultant force zero. However, if the box is being made heavier by adding materials in it, then it can break the table on which it was kept. Does it mean that the third law of motion fails here? No, the third law does not fail here. Here, when the box exerted the downward force on the table, forces occurred in the atoms and molecules. Here, the table behaves like a spring. With force, the table bends to exert opposite force on the box. However, the table’s molecules can withstand the force up to a certain limit, and after reaching the limit, the downward force breaks the molecular bond. It eventually leads to a hole in the table. So, Newton’s third law was applied in the whole process, even when the table breaks.

[c] Similarly, when a water balloon is thrown on a moving car, the force exerted by both the car and the balloon is the same on each other. However, the balloon bursts because it is small mass cannot withstand the force at the acceleration. Also, the balloons have a property to burst.

Note: Newton’s third law does not mean that the objects are indestructible.

To understand the point where the reaction force will be acting, we need to define the system of interest.

Consider a student pushing a cart with some equipment on it as shown in the picture below. Here, two systems can be considered, system 1 when we have to analyse the forces by the entire group of the student and equipment. System 2 can be considered when we have to analyse the reaction force by equipment only. So, the site of the reaction force varies with the system of interest.

## Summary

- Force is a push or pull that changes the velocity of an object.
- Contact force and the non-contact force are the two fundamental types of forces.
- Newton’s first law is based on the law of inertia.
- Only the external forces can change the motion of an object.
- Due to the inertia of our body, we go forward when a bus suddenly stops and we move backwards when the bus suddenly accelerates forward.
- Newton’s second law gives Force= mass x acceleration. It is based on the rate of change in the momentum of an object.
- For the same/constant force, acceleration and mass are inversely proportional.
- Newton’s third law states that forces come in pair.
- If a body exerts a force on another body, then it will also experience reaction force from it.