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# Formulation of Newton’s Second Law of Motion

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

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Law of Motion formulated by Isaac Newton, an English Mathematician and physicist around 1686 examines and explains the relationship between an object in motion and forces acting on it.

For instance, his first law or law of inertia states that an object which is moving in a particular direction in a straight line or is at rest will continue doing so unless an external force acts on it. Newton’s third law of motion proposes that for every action, there will be an equal and opposite reaction. However, his second law of motion formula is one of the essential laws in the world of mechanics.

### Mathematical Formulation of Second Law of Motion

While the first law defines inertia, the second law of motion formula explains the relationship between acceleration and force. We can also measure force concerning mass and acceleration based on this law.

The second law of motion states that any acceleration in an object or body as a result of a force acting on it is directly proportional to the magnitude and direction of the said force.

The equation for Newton’s second law is as follows -

F = m*a,

Or

a = F (net)/ m,

[Here, F = force

m = mass

a = acceleration]

Where, a ∝ f

And a ∝ 1/m

### 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.

1. What are the different types of Motion?

Ans. 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 which 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?

Ans. 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 the equal amount of force that propels the rocket forward into space.

3. What is the difference between Mass and Weight?

Ans. 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.