The Relation Between Newtons and Kilograms

Newton and kilograms are the SI units of force and mass. There is a directly proportional relation between newtons and kilograms. It means that any change in mass (Kg) will cause a change in force (N) while acceleration remains constant. Under the gravity of the Earth, 1 kilogram of mass experiences a force of 9.81 newtons. 

In this blog, you will learn about the kilogram and pounds, their mathematical relationship, and how to convert kg to newtons and vice versa. 

First, we will learn about the Kilograms and Newtons

Kilogram

The kilogram is the basic unit of mass in the International System of Units. It is equal to one thousand grams. The kilogram is abbreviated as ‘kg’. 

Newton 

Newton, abbreviated as ‘N’, is the unit of measuring force in the International System of Units (SI). One newton is the amount of force required to accelerate a 1kg mass at a rate of one meter per second squared. 

Mathematical Relation Between Kg and Newton

The relationship between kilograms (kg) and Newtons (N) is defined by Newton's second law of motion. It states that force (F) equals mass (m) times acceleration (a). Mathematically, this relationship is expressed as;

F = ma

In terms of units, it is represented as;

In which,

• ‘N’ is the unit of force in Newton.
• ‘kg’ is the mass in kilograms.
• ‘m’ represents the distance travelled in metres.
• ‘s’ is the time spent in seconds.

Thus, one Newton is a force required to accelerate a mass of one kilogram at a rate of one meter per second squared. In simpler terms, one Newton is the force needed to make a 1 kg object speed up by 1 m/s every second. 

Relationship Between Weight(N), Mass (Kg), and Gravity (g) 

Weight is defined as the force exerted on an object due to gravity. When dealing with weight, the acceleration is due to gravity, denoted as 'g'. Its value is approximately 9.81 m/s² on Earth. 

The relationship between weight, mass, and gravity is defined by the formula Weight (W) = mass (m) x gravitational acceleration (g)

Where,

• Weight is measured in Newtons (N), 
• Mass is measured in kilograms (kg),  
• Gravitational acceleration in meters per second squared

So, the equation becomes;

Thus, one Newton is a force exerted on a mass of one Kilogram due to gravitational force. 

Weight is the force exerted on an object due to gravity, and it is directly proportional to both the mass of the object and the gravitational field strength. 

How to Convert Kg to Newtons 

Kilograms can be converted into Newtons by using the below given equation. 

To convert any value of kg, we can multiply it by 9.81. 

Let’s look at some of the examples. 

Example 1

Convert 10 kg to Newtons. 

Using the equation.

Thus, 10 kg is equal to 98.1 N.

Example 2

Convert 80 kilograms into Newtons.

Using the equation.

Thus, 80 kg is equal to 784.8 N.

Converting Newtons to Kg

Newton can be converted to Kg by dividing the value of Newton by the gravitational force. The formula to convert Newtons to kilograms is given as;

Let’s look at the examples.

Example 1

Convert 20 N to Kg

According to the formula

Substituting the value in the formula

Thus, 20 Newton is equal to 2.04 kg. 

Example 2

Convert 100 Newtons to Kg

We will use the formula.

Substitute the values in the formula. 

So, 100 N is equal to 10.204 kg.

Conclusion

In the International System of Units (SI), a Newton (N) is the unit of force, while a kilogram (kg) is the unit of mass. The relationship between them is defined by Newton's second law of motion. One Kg is equal to 9.81 Newtons, and one Newton is equal to 0.10197 kg.