Math Calculators
Force Calculator

# Force Calculator

Easy to use force calculator helps determine the unknown variable in the force equation (F = ma). Force = mass × acceleration.

There was an error with your calculation. A force calculator is an easy-to-use tool that helps you find the missing variable in a physics force formula F = ma. In this force equation, F is the force, m is the object's mass, and a is its acceleration.

The force calculator determines the force required to accelerate an object. This equation is known as Newton's second law of motion and is a fundamental principle of physics.

The force equation F = ma states that force is equal to the product of an object's mass and acceleration.

You can use it in any variation. Knowing the mass and acceleration, you can calculate the force (F = ma). If you know the mass and the force, you can calculate the acceleration (a = F/m). Finally, you have information about acceleration and force. In that case, you can enter the variables you know and calculate the object's mass (m = F/a).

To use the force calculator, enter the values of the two variables, and the calculator will find the value of the third variable.

The Newton force calculator uses the most popular mass, acceleration, and force measurements. You will most likely find among them the ones you need.

## Force Calculator Applications

First, the force mass acceleration calculator helps students, teachers, and professionals who need to calculate force quickly and accurately to solve problems in school or at work.

Engineers can use the f = ma calculator to determine the force required to move a load or to calculate the force acting on a machine. Such information is essential in designing and constructing bridges, buildings, and appliances.

Scientists can use the Newton’s second law calculator to figure out how liquids and gases behave and how gravity affects things in space.

Physicists can use the calculator to perform calculations related to energy and thermodynamics. They can calculate an object's potential and kinetic energy.

## Newton's Laws

Isaac Newton made monumental contributions to the field of classical mechanics through his formulation of the three laws of motion. His most renowned work, "Philosophiæ Naturalis Principia Mathematica," commonly known as the Principia, was first published in 1687. In this groundbreaking treatise, Newton laid the foundations for classical mechanics, introducing his laws of motion and the law of universal gravitation.

In the Principia, Newton built upon the insights of his predecessors, such as Galileo and Kepler, while introducing revolutionary concepts that would fundamentally change the understanding of physical phenomena. One of his key contributions, known as Newton's first law or the law of inertia, states that an object at rest will stay at rest, and an object in motion will stay in motion at a constant velocity along a straight line, unless acted upon by an external force. This principle applies universally, whether on Earth or in space. On Earth, external forces such as friction and air resistance often play a significant role, but the law itself is universally applicable.

Let us give a brief formulation of all three laws and then take a closer look at the second law used in our online calculator.

### Newton's First Law

A body remains at rest, or in motion at a constant speed in a straight line, unless acted upon by a force.

Newton's first law is also called the law of inertia. A simple illustration of this would be a hockey puck on a frozen lake. If the puck is at rest, it will remain at rest until a force, such as a hockey stick, pushes it. If the puck is in motion, it will continue to move in a straight line across the ice, until a force such as friction from the ice or a collision with another puck causes it to change direction or speed.

### Newton's Second Law

When a body is acted upon by a force, the time rate of change of its momentum equals the force.

We can often observe the effects of Newton's second law in life. One way to visualize this is through an illustration of a person pushing a heavy box across the floor. If the person applies a small force to the box, the box may not move at all, or may only move very slowly. However, if the person applies a larger force to the box, it will accelerate (move faster) across the floor. Additionally, if the box is more massive, it will be harder to accelerate and will require more force to move it.

### Newton's Third Law

If two bodies exert forces on each other, these forces have the same magnitude but opposite directions.

Imagine two people pushing against each other. If one person pushes harder, the other person will push back with an equal force. This is the principle behind how rocket engines work; the hot gases expelled out of the back of the rocket create a reaction force that propels the rocket forward.

## Newton's Second Law in Details

With the discovery of Newton's second law, his name became associated with the physical concept of force. And the second law itself is closely related to the concepts of force, velocity, acceleration, and mass.

What is a force in physics? Force is a physical quantity that must have a direction (vector), and it is a measure of activity on the body. The letter F stands for force.

You can measure the magnitude of the force, for example, using a special device - a dynamometer. It usually consists of a spring connected to an arrow pointer. If the spring is stretched, the arrow will deflect, showing the quantitative characteristic of the force F.

The way the velocity changes over time is called acceleration (it is usually denoted by the letter a). In practice, in real life, all bodies move with acceleration. If the velocity increases or decreases uniformly, then such motion is called equilibrium acceleration.

This formula can calculate acceleration:

a = (V - V₀) / t

Where a is acceleration, V is the speed at the final moment, V₀ is the speed at the initial moment, and t is the time during which this acceleration occurred.

An example of motion with acceleration would be anybody or anything falling. It will fall with the same acceleration caused by the Earth's gravity.

And finally, the characteristic of the motion of any body is affected by its mass, which is commonly denoted by the letter m. In physics, mass is often a measure of the inertia of a body. That is, the greater the mass of a body, the harder it is to move it. However, having already moved it, it is also harder to stop.

The second law describes what happens to a physical body under the influence of external forces. This law says that the greater the sum of external forces applied to the body, the greater the acceleration of the body.

Newton's first law once tried to explain how celestial mechanics work, how the planets continuously move around the Sun. In contrast, the second law is more down-to-earth in this respect. It explains the motion of bodies here on Earth. The second law is often used to describe the motion of objects in everyday life, such as the motion of a car on a road or the motion of a ball thrown in the air.

It is the fundamental law of dynamics as well as the fundamental law of physical nature.

There are several classical definitions of Newton's second law. The first says that the force acting on a body is equal to the product of the body's mass times the acceleration imparted by the force.

The second definition comes not from the force but from acceleration; it states that the acceleration of a body is directly proportional to the force applied to it and inversely proportional to its mass.

## Newton's Second Law Formulas

The classical force equation represents the first definition we gave you:

F = ma

F is the force acting on the body, m is its mass, and a is the acceleration.

For the second definition, the equation would be as follows:

a = F/m

The greater the force acting on the body, the greater its acceleration. The greater the body's mass, the less its acceleration will be.

It is sufficient to know the magnitude and direction of all the forces acting in a mechanical system and the mass of the material bodies of which it is composed. One can calculate its behavior in time with complete accuracy.

The second law is closely related to the concept of inertia, which is the tendency of an object to resist changes in its motion. According to the second law, the greater an object's mass, the greater the force needed to accelerate it, and the greater its inertia.

## The Examples of Newton's Second Law

A good example is hitting the ball. When we kick a ball, we apply a force that sets its direction and acceleration. The harder the impact, the faster the ball will fly.

Pushing a shopping cart in a supermarket. Try pushing an empty and a loaded cart. In the second case, it would take a much greater force to give the cart the same acceleration as in the first case. This is an excellent example to demonstrate how weight affects Newtonian regularity.

A golf or baseball game is a good example of Newton's law in action. Take a baseball bat and a ball. Suppose you hit the ball with the bat, and the impact is stronger than all the other forces. In that case, the ball will acquire an acceleration equal to the ratio of the resultant forces to its mass.

## Calculation Examples

Let's look at a few calculations that can be done with our force calculator. To measure force, we will take the standard force formula F = ma.

To calculate mass, we will take its variant: m = F/a. And accordingly, to determine the acceleration, we will use the formula a = F / m.

### Force calculation

A car with a mass of 2 tons increased its speed from 10 m/s to 16 m/s for 5 minutes (300 seconds). Determine the force transmitting the acceleration.

First determine the acceleration by the formula

a = (V - V₀) / t

a = (V - V₀) / t = (16 - 10) / 300 = 0.02 = m/s²

Now we now know the car's acceleration, namely 0.02 = m/s². We know the mass: 2000 kilograms. So we can substitute the data we have in the equation for force and calculate the force:

F = ma = 2000 × 0.02 = 40 Newtons

Thus, the force that gives the acceleration is equal to 40 Newtons.

### Acceleration Calculation

What acceleration will a stone weighing 2 kilograms develop if a force equal to 20 Newtons is applied to it?

In this problem, we know the mass and the force. Therefore, we can substitute two known variables into the formula and calculate the acceleration:

a = F / m = 20 / 2 = 10 m/s²

As a result, we've found that the rock will develop an acceleration of 10 m/s².

### Mass Calculation

A construction crane applies a force of 1000 Newtons to lift a concrete block, and the block has an acceleration of 0.5 m/s². To calculate the mass of the block, we can use the formula:

m = F / a

We substitute in the formula the data we have and the force and acceleration, and we get:

m = F / a = 1000 / 0.5 = 2000 kg

Thus, the mass of the block is equal to 2000 kg.

## Conclusion

The force calculator is a valuable tool for anyone studying physics or working in physics and engineering. It is a simple and efficient calculator for solving problems involving force, mass, and acceleration that is based on Newton's second law of motion.

Newton's second law of motion is the cornerstone of classical mechanics. It serves as the basis for the design of rockets and other vehicles, the study of fluid dynamics, and the analysis of structures and materials.

With the force calculator, you can easily find the missing variable in the equation F = ma and use it to solve problems in various fields. Whether you are a student, physics teacher, engineer or scientist, this force calculator will make your calculations more accurate and efficient.