F = m × a | Newton's Second Law of Motion | Free Physics Tool
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📝 Step-by-step solution
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💡 Force F in Newtons (N) | Mass m in kilograms (kg) | Acceleration a in m/s² | 1 N = 1 kg·m/s²
📖 How to Use This Force Calculator
1
Select what you want to calculate - Force (F), Mass (m), or Acceleration (a).
2
Enter the known values - For force: enter mass and acceleration. For mass: enter force and acceleration. For acceleration: enter force and mass.
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⚡ Newton's Second Law of Motion
Newton's second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This fundamental principle of classical mechanics is expressed by the equation: F = ma
Where F is the net force in Newtons (N), m is the mass in kilograms (kg), and a is the acceleration in meters per second squared (m/s²). This law explains how objects move when forces are applied.
📊 Force Formulas
Force (F): F = m × a Mass (m): m = F / a Acceleration (a): a = F / m
Force is measured in Newtons (N). 1 Newton = 1 kg·m/s² = force needed to accelerate 1 kg at 1 m/s².
🔬 Real-World Examples of Force
Gravity: Weight = mass × g (g = 9.81 m/s²). A 10 kg object weighs 98.1 N.
Car Acceleration: 1000 kg car accelerating at 5 m/s² requires 5000 N of force.
Kicking a Ball: Force applied determines how fast the ball accelerates.
Braking: Negative acceleration (deceleration) requires force opposite to motion.
Lifting: You must apply upward force greater than weight to lift an object.
💡 Types of Forces
Contact Forces: Friction, tension, normal force, air resistance, applied force
Net Force: Vector sum of all forces acting on an object
Balanced Forces: Net force = 0 → object at rest or constant velocity
Unbalanced Forces: Net force ≠ 0 → object accelerates
❓ Frequently Asked Questions (FAQ)
What is a Newton of force?
One Newton (N) is the force required to accelerate a 1 kg mass at 1 m/s². It's roughly the weight of a small apple (≈ 100g). For reference, a 50 kg person weighs about 490 N on Earth.
Why does acceleration decrease as mass increases?
According to Newton's second law, acceleration = F/m. For the same force, a larger mass results in smaller acceleration because more mass has more inertia (resistance to change in motion).
What is the difference between mass and weight?
Mass is the amount of matter in an object (kg). Weight is the force of gravity acting on that mass (N). Weight = mass × g. On the Moon, mass stays the same but weight is about 1/6 of Earth weight.
Can force be negative?
Force is a vector quantity, so it has direction. Negative sign indicates force acting in the opposite direction of the chosen coordinate axis. Negative acceleration (deceleration) results from force opposite to motion.
What is Newton's first law of motion?
Newton's first law (law of inertia) states that an object at rest stays at rest, and an object in motion stays in motion with constant velocity, unless acted upon by an unbalanced external force.
How do I calculate net force?
Net force is the vector sum of all forces acting on an object. If forces act in the same direction, add them. If they oppose, subtract. The net force determines acceleration according to F_net = ma.