[Physics Class Notes] on Formulation of Newton’s Second Law of Motion Pdf for Exam

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 2^nd law formula.

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