Newton's Second Law: Force, Mass, and Acceleration
Newton's Second Law of Motion states that force equals mass times acceleration: F = ma. This is one of the most fundamental and widely applied equations in physics. It explains why heavier objects require more force to accelerate, why rockets need powerful engines, and why crumple zones reduce crash forces. Any two of the three quantities can be used to find the third.
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Formula
Force Calculator (F = ma)
Calculate force, mass, or acceleration using Newton's second law F = ma.
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Worked Example
Given:
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FAQs
What is the unit of force?
The SI unit of force is the Newton (N), defined as 1 kg × 1 m/s² = 1 N. One Newton is approximately the force needed to hold a 100 g apple against gravity. The weight of a 1 kg object at Earth's surface is approximately 9.81 N (1 kg × 9.81 m/s² gravity).
What is the difference between mass and weight?
Mass is the amount of matter in an object (measured in kg) and does not change with location. Weight is the gravitational force on that mass (measured in Newtons): W = mg where g = 9.81 m/s². A person with 70 kg mass weighs 70 × 9.81 = 686.7 N on Earth, but only 113 N on the Moon.
How does Newton's second law apply to rockets?
Rocket thrust produces a force that accelerates the rocket. As fuel burns off, mass decreases, so the same thrust produces increasing acceleration (a = F/m). This is why rockets accelerate faster as they burn fuel. The opposite — greater mass needing more force — is why fuel efficiency in heavy vehicles is so challenging.