Mass
oz
Initial velocity
mph
Final velocity
mph
Time difference
sec
Force
N

# Newton's Second Law Calculator

By Miłosz Panfil, PhD and Dominik Czernia, PhD candidate

The Newton's second law calculator is a perfect tool that helps you understand the second law of motion due to Isaac Newton. Have you ever wondered what is Newton's second law of motion or how to calculate a force acting on an object? The following short article comprises all the answers.

Isaac Newton was an English mathematician, physicist, and astronomer who is mostly known for his law of universal gravitation. Legend says that Newton sat under an apple tree when suddenly an apple felt on his head made him realize that the fall of bodies to Earth and the movement of celestial bodies, is caused by the same force - gravity.

Newton laid also the foundation for the classical mechanics with his three laws of motion which describe the resulting movement of the object under the forces acting upon it:

• The first law of motion - an object will remain at rest or in uniform motion in a straight line unless acted upon by a non-zero net force,
• The second law of motion - this is what our Newton's second law calculator is about. For example, this law explains how to calculate force knowing the acceleration of the body.
• The third law of motion - when one body exerts a force on a second body, the second body exerts a force, that is equal in magnitude and opposite in direction, on the first body (to every action there is always opposed an equal reaction).

## What is Newton's second law of motion?

The Newton's second law of motion states that acceleration of an object is proportional to the net force `F` acting on it and inversely proportional to its mass `m`. It is expressed with the following equation

`a = F / m`,

where

• `a [m/s²]` is the acceleration of an object,
• `F [N]` is the force acting on an object,
• `m [kg]` is the mass of an object.

Above law says that objects accelerate due to force acting on them. The effect of the force, the acceleration, depends on objects inertia: the unwillingness to change the velocity. The larger the mass, the larger the inertia.

## How to calculate the force?

Now, when you know what is Newton's second law of motion, we can easily find a force acting on a body. Turning around this law, we find an expression for the force. In practice, it is difficult to determine the acceleration directly. Instead, we can refer to its definition. Acceleration is a ratio of a change of the velocity to the time it took to accelerate. Using this piece of information, we can rewrite the formula for the force as

`F = m * (v_f - v_i) / dt`.

The new symbols are

• `v_f [m/s]` - the final velocity
• `v_i [m/s]` - the initial velocity
• `dt [s]` - the time it took to change the velocity.

With this formula, you can compute force you were looking for. You can also turn the equation around and ask what is the change of the velocity if you subject an object of mass `m` to the force `F` for `dt` seconds.

There is a related concept to the force which is the impulse. Check the impulse and momentum calculator to learn more about it!

## Newton's second law calculator

Computing the force is very easy with our Newton's second law calculator. Let us calculate the force it takes to stop a moving car. The car weighs `3500 lb` (`1586 kg`) and moves with the speed of `60 mph` (`97 km/h`). To stop it in `20 s` you need a force of `-2129 N` (check force converter for different measures of force). The minus sign signals that the force is acting opposite to the motion of the car: it's stopping the vehicle.

If you're interested in the physics of cars, check what happens during a car crash. Wondering where the car's center of mass might be? You don't have to wonder anymore! There is our car center of the mass calculator.

Miłosz Panfil, PhD and Dominik Czernia, PhD candidate

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