# Newton's Second Law Calculator

Created by Davide Borchia
Last updated: Sep 05, 2022
Table of contents:

Newton, scientist, and measurement unit: learn why we use his name to measure forces with our calculator for Newton's second law of motion.

In this accessible article, we will guide you in a short but thorough exploration of kinematics. We will start with the definition of a force, then introduce Newton's law of motion. We will celebrate the formula for Newton's second law of motion, and analyze its simple equation. To continue, we will give you some examples of Newton's second law, how to find acceleration and how to find newtons.

## What is a force?

Force is a fundamental concept in physics. We call every influence capable of changing the state of motion of an object "force". From this definition, you can see how lift, drag, friction, gravity, and even electromagnetic force are all forces.

Physicists measure forces in newtons, a measure of the ability of a force to change the state of motion. In the next section, we will understand why: first, we need to meet the scientist who gifted his name to this measurement unit and introduce the formula for Newton's second law of motion.

## Newton's second law: how to find acceleration from a force, and vice versa

In his own words, Newton "had seen further [...] by standing on the shoulders of giants". Isaac, if you can hear us, you are a giant! Newton's groundbreaking works paved the road to modern science, with many of his discoveries still of fundamental importance in most fields of physics, and not only.

Even though we remember him primarily for his work on gravity (by the way, the apple is a myth), Newton also left outstanding contributions to kinematics, with three laws bearing his name.

• Newton's first law of motion: every body continues in its state of rest, or of uniform motion in a straight line, unless it is compelled to change that state by forces impressed upon it. With these words, Newton finally gave a solid definition to the concept of inertia. However, we begin and end right there: inertia is .
• Newton's second law of motion: the change of motion of an object is proportional to the force impressed; and is made in the direction of the straight line in which the force is impressed. Thanks, Isaac: this is a mathematical formulation. We will see the equation for Newton's second law of motion in a moment.
• Newton's third law of motion: to every action there is always opposed an equal reaction; or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts. In this short line, Newton explains why the wall pushes back on us when we push on a wall. But not why, when we stare into the abyss, the abyss gazes back at us. Go ask Nietzsche.

🙋 We made a calculator dedicated to a particular case of Newton's third law: check our normal force calculator!

The first and third laws are "laws". You have to respect them, physics has to respect them, but the story ends there. However, we can define a neat formula for Newton's second law of motion:

$\vec{F} = m \cdot \vec{a}$

Where:

• $\vec{F}$ — The force, measured in newtons;
• $m$ — The mass, measured in kilograms; and
• $\vec{a}$ — The acceleration, measured in meters per second squared.

That's how you find newtons, and also the reason we measure forces in $(\text{kg}\cdot\text{m} / \text{s} ^2)$.

🙋 Why vectors? Because motion has a direction. You can skip them if the direction is not relevant to your problem, but whenever forces sum (as we show in the net force calculator) and you are not sure if they are collinear.

Inverting this equation gives you the acceleration of a body as a function of the applied force and mass:

$\vec{a} = \frac{\vec{F}}{m}$

If you are not metricated, calculating Newton's second law of motion may require you to use different measurement units. The usual triad for the US customary system is:

• The pound-force for the force;
• The pound for the mass and
• The foot per square second for the acceleration.

Let's go on and find out how to use our implementation of Newton's second law equation.

## How to use our Newton's second law calculator

Our Newton's second law calculator is more than just $F=ma$. If you are wondering how to find acceleration from Newton's second law, you can use our calculator in reverse: simply input the force and the mass, and we'll do the rest.

We can also help you calculate the parameters of the acceleration. From initial and final speed to elapsed time, you don't need to know everything; we can calculate it!

## Examples of applications of the equation of Newton's second law of motion

It's time to talk about elephants. But before elephants, we need to speak about Italians, and in particular about Galileo Galilei. The astronomer, physicist, and heretics died one year before the birth of his pal Newton and greatly influenced the latter with his works.

Here we will talk about free-fall: Galileo showed us that the mass of an object doesn't affect the final velocity after a fall. But why do elephants explode, then?

🙋 We are a bit obsessed with it: we made the free fall calculator, the terminal velocity calculator, and the g-force calculator about this concept! But forgive us: it's so interesting.

Free-fall suggests that — in the absence of air resistance and other forces — every object falls at the same speed, regardless of the mass. Take then an elephant, a duck, and a mouse. Take a dog instead of a duck. Bring them on top of a building and let them fall. While all of them will fall with roughly the same acceleration (allow us to neglect some real-life effects), the force acting on them varies greatly. Consider their masses:

• Our small house mouse has a mass of $0.019\ \text{kg}$;
• The adorable dog is an Akita Inu, with mass $35\ \text{kg}$; and
• The elephant has a mass of $2,500\ \text{kg}$.

Calculate the forces acting on those poor animals with our Newton's second law calculator, using an acceleration of $9.81\ \text{m}/\text{s}^2$:

• The force acting on the mouse is $0.19\ \text{N}$;
• The force acting on the dog is $343.35\ \text{N}$; and
• The force acting on the elephant is $24.52\ \text{kN}$.

Since there is a direct relationship between force and energy, you can imagine that the impact has way worse consequences for the pachyderm than for the rodent!

Davide Borchia
Mass
lb
Initial velocity
mph
Final velocity
mph
Time difference
sec
Acceleration
ft/s²
Force
N
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