How to Convert Kilograms to Newtons: Formula, Steps & Examples
Every physical quantity in Physics is measured using specific units. Two of the most commonly used units are the kilogram (kg) for mass and the newton (N) for force. Understanding the relation between kilogram and newton is essential for solving problems in mechanics and related topics.
The kilogram (kg) is the fundamental SI unit for mass. One kilogram equals 1,000 grams. It quantifies the amount of matter present in an object and remains unchanged regardless of location.
Newton (N) is the SI unit of force. By definition, a force of one newton can accelerate a mass of one kilogram at a rate of one meter per second squared (1 m/s2). This relationship is rooted in Newton’s Second Law of Motion.
Fundamental Relationship Between kg and Newton
According to Newton’s Second Law of Motion, force is given by:
Where F is force (in newtons), m is mass (in kilograms), and a is acceleration (in m/s2).
On Earth’s surface, the acceleration due to gravity (g) is approximately 9.8 m/s2. Using this, the weight (force) of an object in newtons is:
W = m × g
Therefore, 1 kg mass exerts a force of 9.8 N (rounded off) due to gravity.
Key Conversion Formulas
| Physical Quantity | Unit | Relation |
|---|---|---|
| Mass | kilogram (kg) | — |
| Force | newton (N) | F = m × a |
| Weight | newton (N) | W = m × g (g ≈ 9.8 m/s2) |
Direct Relation:
1 kg × 9.8 m/s2 = 9.8 N
So, a mass of 1 kilogram has a weight of approximately 9.8 newtons on Earth.
Step-by-Step: Converting Kilograms to Newtons
| Step | Action | Example |
|---|---|---|
| 1 | Write the given mass in kg | m = 5 kg |
| 2 | Multiply by 9.8 m/s2 (value of g) | 5 × 9.8 = 49 |
| 3 | Express the answer in newtons | 49 N |
Similarly, to convert from newtons to kilograms:
1 N ≈ 0.102 kg (since 1 N = 1 kg × 1 m/s2 and g ≈ 9.8 m/s2)
Concept Examples
- How many newtons is 5 kg?
Weight = 5 × 9.81 = 49.05 N
- If weight of an object is 40 N, what is its mass?
Mass = 40 / 9.81 ≈ 4.08 kg
- Why is 1 kgf (kilogram-force) = 9.8 N?
1 kgf is defined as the force exerted by 1 kg mass under gravity, so 1 kgf = 1 kg × 9.8 m/s2 = 9.8 N
Comparison Table: kg, kgf, and Newton
| Parameter | kg | kgf | Newton (N) |
|---|---|---|---|
| Physical Quantity | Mass | Force | Force |
| SI Unit? | Yes | No | Yes |
| Definition | Amount of matter | Force due to 1 kg under gravity | Force required to accelerate 1 kg by 1 m/s² |
| Relation | — | 1 kgf = 9.8 N | — |
Quick Facts and Tips
- We often round 1 kg as 10 N for estimation, but use 9.8 N for accuracy in calculations.
- kg and newton are not interchangeable; one is mass, the other is force.
- Conversion is valid only when considering acceleration (usually gravity).
- g varies slightly by location, so standard value 9.8 m/s2 is used in most calculations.
Practice and Further Learning
- Revise the difference between mass and weight.
- Understand calculation of weight and force in Physics.
- Refer to Laws of Motion for detailed derivations and examples.
- Solve problems using unit of force and unit of weight.
- For advanced topics, review gravity and Newton’s law of gravity.
Summary Table: From kg to Newton – At a Glance
| Given Mass (kg) | Calculation | Weight (N) |
|---|---|---|
| 1 kg | 1 × 9.8 | 9.8 |
| 5 kg | 5 × 9.8 | 49 |
| 10 kg | 10 × 9.8 | 98 |
Conclusion & Next Steps
Mastering the relation between kg and newton will help you solve a variety of Physics numerical problems accurately.
Focus on using the correct formula and understanding the underlying concept of mass versus force. Practice converting values and applying these relations in different scenarios for deeper learning.
Continue your study using Vedantu’s Physics resources, including detailed guides, concept explanations, and regular practice through solved examples and exercises.
FAQs on Relation Between Kilogram (kg) and Newton (N) in Physics
1. What is the fundamental relationship between a kilogram (kg) and a Newton (N)?
The kilogram (kg) is the SI unit of mass, while the Newton (N) is the SI unit of force. Their relationship is defined by Newton's Second Law (F = m × a):
- 1 Newton is the force needed to accelerate a 1 kg mass by 1 m/s².
- Therefore, 1 N = 1 kg × 1 m/s².
2. How do you convert a mass in kilograms (kg) to its weight in Newtons (N)?
To convert mass to weight on Earth's surface, use:
Weight (N) = Mass (kg) × Acceleration due to Gravity (g)
- Standard value for g is 9.8 m/s².
- Example: For 5 kg, Weight = 5 × 9.8 = 49 N.
3. Are mass (in kg) and weight (in N) the same thing? Explain the key differences.
No, mass and weight are different physical quantities:
- Mass (kg): Measures the amount of matter, scalar, does not change with location.
- Weight (N): Measures the gravitational force on a mass, vector, changes with gravity.
- Formula: Weight = Mass × Gravity (W = m × g).
4. Why do we often approximate 1 kg as 10 N in calculations?
Approximating 1 kg as 10 N simplifies mental math because:
- Acceleration due to gravity (g) ≈ 9.8 m/s², but rounded to 10 m/s² for quick calculations.
- This estimation helps speed up problem-solving, but use 9.8 N/kg for accurate results.
5. How is the relation between kg and Newton derived from Newton's Second Law of Motion?
The relation comes from Newton’s Second Law:
- Formula: Force (F) = Mass (m) × Acceleration (a)
- 1 Newton (N) is defined as the force needed for 1 kg of mass to accelerate at 1 m/s² (→ 1 N = 1 kg × 1 m/s²).
6. What does 'kilogram-force' (kgf) mean, and how does it relate to the Newton?
Kilogram-force (kgf) is a non-SI unit of force:
- 1 kgf is the force exerted by 1 kg of mass under standard gravity.
- Relation: 1 kgf = 9.8 N (using g = 9.8 m/s²)
- Newton is the SI unit; kgf is used for gravitational force calculations.
7. How many kilograms are there in 1 Newton?
To find the mass (kg) for 1 Newton of weight:
- Use the formula: Mass = Force / Acceleration due to gravity
- Mass = 1 N / 9.8 m/s² = 0.102 kg
- So, 1 Newton is the weight of approximately 102 grams (0.102 kg).
8. Is 1 kg equal to 10 newtons?
1 kg is not exactly equal to 10 Newtons.
- 1 kg mass on Earth weighs about 9.8 N (using g = 9.8 m/s²).
- 1 kg ≈ 10 N is an estimation for easier math, but precise calculations use 9.8 N.
9. How can you convert weight from newtons to kilograms?
To convert weight (N) to mass (kg):
- Use the formula: Mass = Weight ÷ Acceleration due to gravity
- Mass (kg) = Weight (N) / 9.8 (m/s²)
- Example: 49 N / 9.8 = 5 kg.
10. What are the main differences between kg, kgf, and Newton?
Differences:
- Kilogram (kg): SI unit of mass, measures amount of matter
- Kilogram-force (kgf): Non-SI unit of force, force by 1 kg under gravity; 1 kgf = 9.8 N
- Newton (N): SI unit of force, force required for 1 kg to accelerate at 1 m/s²
11. What formula do you use to calculate the weight of an object on Earth's surface?
The standard formula is:
Weight (N) = Mass (kg) × Gravity (9.8 m/s²)
- This relates the mass of any object to its gravitational force (weight) on Earth.
12. Why is understanding the relation between kg and Newton important for Physics exams?
Understanding the relation:
- Helps solve numerical problems involving force, mass, and weight
- Prevents unit confusion in MCQs and derivations
- Essential for competitive exams like JEE and NEET
