# Newton's Second Law: what it consists of, formula and examples

## The second law of Newton

Newton's second law, called the fundamental law or fundamental principle of dynamics, states that a body accelerates if a force is applied to it, understanding force as a maneuver such as pulling or pushing a body.

To better understand the fundamental law it is necessary to clarify two basic concepts:

• The force applied to the body is called the net force.
• The change in speed experienced by the moving body is called acceleration.

In other words, the acceleration of a body is proportional to the net force applied to it. That is, if we apply a greater force, the body increases its acceleration.

This principle is part of Newton's laws or laws of motion, which were published for the first time in 1687 by the English physicist and mathematician Isaac Newton in his work Principia Mathematica, and are key to understanding the movement of bodies.

## Newton's second law formula

Newton's second law is expressed in the following formula:

F = ma

Where:

• Fis the net force. It is expressed in Newton (N)
• m is the mass of the body. It is expressed in kilograms (Kg.).
• a is the acceleration acquired by the body. It is expressed in meters per second squared (m/s 2 ).

A simple example to understand this formula would be the calculation of the force that must be applied to a 0.4 kg soccer ball to kick it with an acceleration of 3.5 m/s 2. In this case, the formula would be:

F = ma

F = 0.4kg. 3.5m/ s2

F = 1.4N

## Examples of Newton's second law

The fundamental law of dynamics can be described in the following examples:

1. ### Two children and a swing

Two children are sitting on a swing. One of them swings applying little force and its acceleration is slower. The second boy swings harder and his acceleration is greater.

1. ### The two boxes

We have two boxes: one of 15 kg. and another of 50 kg. If we apply the same amount of force to move them, the first box will move faster. But if we want the two boxes to move at the same speed, we will have to apply more force to the heavier box.

1. ### Kick the ball

If we have a tennis ball and a soccer ball and we kick them, the tennis ball will have a greater acceleration, since it is the body with less mass. While the soccer ball will have a lower acceleration because it has more mass.

1. ### Push the car

A moving car stalls in the middle of the street and the driver must push it to get it to safety. While the driver uses his own strength, the car moves slowly, but when other people help the driver to push the car, it moves faster, since the greater the force, the greater the acceleration.

1. ### The supermarket cart

If the shopping cart is empty, its acceleration is greater even though not as much force is applied when pushing it. On the other hand, if it is full, its acceleration is less and more force is required to move it forward.

1. ### Open the doors

To open an armored door requires more force than it takes to open a common wooden door, which is lighter.

1. ### The golf ball

In order for the golf ball to reach the desired hole, a certain amount of force must be applied to it. If little force is applied, the acceleration of the ball will be less and it will travel slowly, and if the force applied is greater, the acceleration will be greater and the ball will travel faster.

1. ### The bike

Newton's second law applies when we ride a bicycle. Pedaling is force, mass is the bike, and our body weight and acceleration is how fast it moves.

1. ### Shot Put

The shot put is an Olympic sport in which the athlete must propel a very heavy metallic sphere, called a bullet. The greater the force applied, the greater the acceleration the bullet will acquire and the further it will go.

1. ### The Bowling Ball

The force applied to the ball increases its acceleration and causes it to travel down the lane, knocking over the pins.

1. ### The truck and the car

For a car to run, it is necessary for the engine to generate the force to increase the acceleration of the car. The bigger the car, the more force you need to accelerate. Therefore, a truck requires more force than an ordinary car.

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