Kilogram is the SI unit of mass that tells us how much matter is in an object. Newton, on the other hand, is the SI unit of force. It measures the push or pull on an object. There exists a straight proportionality between the kilogram and newton. The equivalent of one kilogram-force is 9.81 Newtons.
In this article, we will learn the relation between kg and newton in detail.
Table of Content
What is Kg?
Kilogram is used to measure the amount of matter in an object. A kilogram (kg) is a unit of mass. It is part of the metric system, which is used worldwide. The kilogram is the base unit of mass in the International System of Units (SI). It is commonly used in everyday contexts for measuring the weight of objects.
Kilograms connect to other units through various formulas. For example, in physics, mass relates to weight. Under Earth’s gravity, mass measured in kilograms can be converted into newtons to find an object’s weight.
What is Newton?
Newton is the standard unit of force in the International System of Units (SI). It is abbreviated as “N”. It measures the amount of force required to accelerate a one-kilogram mass at a rate of one meter per second squared. This unit is named after Sir Isaac Newton, who gave the laws of motion.
Newton quantifies the force applied to objects. This includes everything from pushing a cart to the force of gravity. A newton specifically measures how much force is needed to move mass in a particular way.
Relation Between kg and Newton
The relationship between kilograms (kg) and newtons (N) is defined by Newton’s second law of motion, which states that the force F acting on an object is equal to the mass m of the object multiplied by its acceleration a. Mathematically, it can be expressed as:
F = m × a
Here, ‘F’ is force in newtons, ‘m’ is mass in kilograms, and ‘a’ is acceleration in meters per second squared (m/s²).
To find the specific relationship between these units, we consider Earth’s gravity. The standard acceleration due to gravity on Earth is about 9.81 m/s².
By substituting Earth’s gravity for acceleration (i.e. 9.8m/s²) in the formula F = m × a, we get
Force = mass × 9.81 m/s²
Hence, to convert mass from kilograms to newtons, we multiply the mass by 9.81 and to determine mass from a force in newtons, divide the force by 9.81.
Let Force = 1 N and mass = 1 kg, then from above we can conclude that:
- One kilogram of mass applies a force of 9.81 newtons under the influence of gravity.
1N is Equal to How Many Kg?
A Newton is a unit of force in the International System of Units (SI). It measures the amount of force required to accelerate a mass of one kilogram at a rate of one meter per second squared. On the other hand, a kilogram is a unit of mass, not force.
To find out how many kilograms are equivalent to one Newton of force on Earth, we use the formula :
F = mg
m = F/g = 1 N/ 9.81 m/s2 = 0.101937 kg
Thus, 1 Newton is equivalent to approximately 0.10937 kilograms under Earth’s gravity. This means that the force of 1 Newton will accelerate a mass of approximately 0.101937 kg at 1 meter per second squared on Earth.
The table below shows the relation between kg and newton:
|
Kg to Newton |
1 kg = 9.81 N |
|---|---|
|
Newton to Kg |
1 N = 0.101937 kg |
Mathematical Relation between kg and Newton
To express the mathematical relation between kg and Newton, we will use the Newton’s Second law of motion by taking m = 1 kg and a = 1 m/s², we get:
F = 1 kg × 1 m/s²= 1 N
From the above expression, we can conclude that Newton is directly proportional to kg. So,
- If the object has negligible or significantly low mass, then the force required in Newtons will also be minimal.
- Iff the object is particularly heavy, then a greater force will be required.
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Solved Examples based on kg and Newton
Example 1:Convert 20 kg to Newtons on Earth.
Solution:
Using the formula: F = m × g
F = 20 kg × 9.81 m/s2
So, F = 196.2N
Thus, an object with a mass of 20 kg weighs 196.2 Newtons on Earth.
Example 2: What is the force in Newtons of a 1 kg feather on Earth?
Solution:
We know F = m × g
F = 1 kg × 9.81m/s2
F = 9.81N
Hence, the feather exerts a force of 9.81 Newtons due to Earth’s gravity.
Example 3: Calculate the weight in Newtons for an 80 kg person.
Solution:
We know F = m × g
F = 80kg × 9.81m/s2
F = 784.8N
Hence, a 80 kg person has a weight of 784.8 Newtons on Earth.
Example 4: Calculate the total force exerted by three boxes on Earth with masses of 3 kg, 4 kg, and 5 kg, respectively.
Solution:
We will calculate the force for each box and then sum them:
F1 = 3 kg × 9.81 m/s2 = 29.43 N
F2 = 4kg × 9.81m/s2= 39.24N
F3 = 5kg × 9.81m/s2= 49.05N
Total force, F = 29.43 N + 39.24 N + 49.05 N = 117.72 N
The total force exerted by the boxes is 117.72 Newtons.
Example 5: A suitcase weighs 49.05 Newtons. What is its mass in kilograms?
Solution:
Using the formula, F = m × g, m = F/g
Here, F = 49.05N
So, m = 49.05N/ 9.81m/s2 ≈ 5kg
Hence, the mass of the suitcase is approximately 5 kilograms.
Conclusion
In conclusion, the relationship between kilograms and newtons is fundamental in physics. Kilograms measure mass, while newtons measure force. This connection is essential for understanding how objects interact with Earth’s gravitational pull.
FAQs on Relation Between Kg and Newton
What is a kilogram?
A kilogram is a unit of mass in the metric system, used globally to measure the mass of objects.
What is a newton?
A newton is a unit of force in the metric system. It measures the force needed to accelerate a mass.
How do kilograms relate to newtons?
Kilograms measure mass, while newtons measure force. The two are related through the acceleration due to gravity.
How do you convert kilograms to newtons?
To convert kilograms to newtons, multiply the mass in kilograms by 9.81 m/s², the standard gravity of Earth.
Why use newtons instead of kilograms for force?
Newtons are used for force to clearly distinguish between mass (kg) and the effect of gravity on that mass.
Do kilograms and newtons measure the same thing?
No, kilograms measure mass, and newtons measure force, which includes the effect of gravity on mass.