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# Formulation of Newton’s Second Law of Motion

## Newton’s Second Law of Motion – An overview

Last updated date: 24th Mar 2023
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Isaac Newton provided us with many laws and discoveries. One of his laws talks about motion and the forces it attains.

Starting with his first law, also known as the law of inertia tells us that if an object is moving or going in a specific direction or a straight line, its state won’t change until and unless an external force acts towards it. Then comes Newton’s second law of motion, which tells us that the time of change of any object is equal to its magnitude as well as its direction of imposition. This law is the most important and most talked-about law of the three laws of motion.

### Formula of Newton’s Second Law of Motion

The Newton’s Second Law of Motion’s formula says that the force is equal to the product of the mass of the object and its acceleration.

• Going further to Newton's third law, which states that to every reaction, there is

• supposed to be an equal and opposite reaction.

### Mathematical Formulation of Second Law of Motion

The second law of motion tells us about the relationship between force and acceleration. We can measure a lot of things with this law, including the force related to the mass and acceleration of the object. In simpler terms, this law conveys that any form of acceleration is the result of some form of force acting on or towards it. The force is also considered to be directly proportional to the direction of the object.

Equation describing the Newton’s second law of motion:

F = m*a,

Or a = $\frac {F(net)}{m}$

(Here, F = force m = mass a = acceleration)

Where, an ∝ f

And a ∝ $\frac {1}{m}$

Newton’s second law of motion is applied when starting with a simple example of the second law of motion if you push a chair and a bed with the same force. The chair will move and the bed might not. Since the chair has lesser volume and weight as compared to the bed, it will tend to attain more Acceleration. We can also take the example of a bicycle. Whenever you push the paddles of a cycle, it tends to move forward. This is a clear result of the second law of motion.

### Application of Newton’s Second Law of Motion

• An example of Newton’s second law of motion formula is pushing a car and truck by applying the same force. Since the car has a smaller mass, it will gain more acceleration than a truck which has a much larger mass.

• Riding a bicycle is another instance of Newton’s Second Law of Motion formula at work. Here, the bike is the mass, and the rider pushing the paddles with his or her leg is the force.

• Another instance of Newton’s Second law of motion formula can be observed in the cricket field. A fielder while catching a cricket ball pulls his or her hand back. It is done to delay the momentum of the ball, which is moving at an incredible speed. If the velocity is not reduced, then the ball which is moving at high speed will exert a considerable force on the player’s hand leading to serious injury.

• You must have noticed that during athletic sports like long jumps, high jumps, a bed of sand or cushioned bed is placed at the place where the sportsperson is going to land. It is because, when the sportsperson lands after completing a long jump or high jump, his/her momentum becomes zero.

However, when momentum becomes zero very quickly, it results in the creation of a great force that may cause injury to the person, which is why a soft bed or bed of sand is placed to slow down the momentum of the sportsperson to prevent an accident. It is a practical application of Newton’s Second law Formula.

### Do It Yourself

1. A force of 70 Newton was exerted on an object whose mass is equal to 30 kilograms. Calculate the acceleration of the said object according to the second law of motion formula.

2. An object has a mass of 12 kilograms. After applying force, it accelerates at 15 m/s2. Determine the value of force that was applied using Newton’s 2nd law formula.

3. Based on your understanding, derive the mathematical formula of the second law of motion.

## FAQs on Formulation of Newton’s Second Law of Motion

1. What are the different types of Motion?

The different types of motion include Translational Motion, Rotational Motion, Periodic Motion, and Non-periodic Motion.

In translational motion, all parts of the object cover the same distance in a given time. It can be further categorised into two types – Rectilinear and Curvilinear motion.

On the other hand, when an object moves in a circular motion on an axis, it is known as rotational motion. A type of movement which repeats itself after equal intervals of time is known as periodic motion. A motion that is found to not repeat at a fixed interval, or does not take place at all is known as non-periodic motion.

2. What are the applications of Newton’s Third Law of Motion?

Application of Newton’s Third Law of Motion can be observed when a rocket or other projectiles are launched in the air. In this case, the engines of the projectile exert a large force in the air. The air too pushes back with an equal amount of force that propels the rocket forward into space.

3. What is the difference between Mass and Weight?

Mass can be defined as a measure of how much matter is present in an object. In contrast, weight is the measure of the force of gravity being exerted on a body.

Apart from this, one of the main differences between mass and weight is that the mass of a body will stay the same regardless of the location. On the other hand, since weight is dependent on gravity, an object’s weight changes when it moves from a region of strong gravity towards weak gravity or vice versa.

4. What are the different types of motion according to Newton?

According to Newton, there are four types of motion -

• Translational motion - in this motion, an object covers all the given same distance in a given time.
• Rotational motion - as the name of this motion suggests, the object revolves on-axis in this motion.
• Periodic motion - this motion means that the object repeats its motion after an equal interval of time.
• Non-periodic motion - this motion is of periodic motion, in this object repeats its motion but not on an equal interval of time.

5. Suggest the applications for the third law of motion suggested by Newton.

The third law of Newton’s theory is easily exemplified, it can be seen when a rocket or any other projectile is launched in the air. The thrust they leave behind helps them to move upward the engines connect at the end of the projectile leave a string force to move in the air, and if the thrust is disabled then the projectile will not be able to move.

6. Suggest the applications for the second law of motion suggested by Newton.

Newton’s second law of motion, tells us that the time of change of any object is equal to its magnitude as well as its direction of imposition. An example is a moving car. This law is the most important and most talked-about law of the three laws of motion. Its formula says that the force is equal to the product of the mass of the object and its acceleration.

7. In the second law of Newton’s theory what relationship is talked about?

The second law conveys that any form of acceleration is the result of some form of fforce acting on or towards it. The force is also considered to be directly proportional to the direction of the object. The second law of motion tells us about the relationship between force and acceleration. We can measure a lot of things with this law, including the force related to the mass and acceleration of the object.

8. What is Mass and what is weight, describe the difference.

To define mass, one should understand the quantity of matter present in an object. Mass is the matter and area covered by an object. Mass can be seen with the naked eye and it is a third-dimensional object. Whereas weight is the force of gravity exerted on the body. It can be felt but can’t be seen. Weight is directly proportional to the force of gravity. Weight different planet by planet.