Newton's Second Law
Newton's Second Law of Motion states that the net force acting on an object equals the product of its mass and acceleration. It is the most quantitative of the three laws and provides the mathematical relationship between force, mass, and motion. This law is used in virtually every engineering and physics calculation involving dynamics, from designing car brakes to launching spacecraft.
Key Formula
F_net = m × a
LaTeX: F_{\text{net}} = ma
| Symbol | Meaning | Unit |
|---|---|---|
| F_net | Net force acting on the object | Newton (N) |
| m | Mass of the object | kilogram (kg) |
| a | Acceleration of the object | metre per second squared (m/s²) |
Worked Example
Problem
A box of mass 10 kg is pushed across a frictionless surface by a net force of 30 N. What is the acceleration of the box?
Solution
Using F_net = m × a, rearrange for acceleration: a = F_net / m. Substituting values: a = 30 N / 10 kg = 3 m/s².
Answer
The acceleration of the box is 3 m/s².
Effect of Force and Mass on Acceleration (Newton's Second Law)
| Mass (kg) | Net Force (N) | Acceleration (m/s²) | Example |
|---|---|---|---|
| 1 | 10 | 10 | Small ball pushed hard |
| 5 | 10 | 2 | Book pushed on desk |
| 10 | 10 | 1 | Backpack dragged slowly |
| 10 | 30 | 3 | Backpack pushed firmly |
| 50 | 100 | 2 | Heavy box on wheels |
| 1000 | 5000 | 5 | Car accelerating from rest |
Interactive Tools
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Related Terms
Newton's First Law
Newton's First Law of Motion states that an object at rest remains at rest, and an object in motion continues in motion at constant velocity, unless acted upon by a net external force. This principle is also known as the Law of Inertia and forms the conceptual foundation of classical mechanics. It explains why passengers lurch forward when a bus brakes suddenly, or why a hockey puck slides indefinitely on a frictionless ice surface.
Mass
Mass is a fundamental scalar quantity that measures the amount of matter in an object and determines its resistance to acceleration (inertia). Unlike weight, mass does not depend on gravitational field strength and remains constant regardless of location in the universe. Mass is measured in kilograms (kg) in the SI system and plays a central role in Newton's Second Law, gravitational force calculations, and energy equations.
Weight
Weight is the gravitational force exerted on an object due to a gravitational field, typically Earth's. It is a vector quantity directed toward the centre of the gravitational body and varies depending on the local gravitational acceleration. A person who weighs 686 N on Earth would weigh only about 114 N on the Moon, because the Moon's gravitational acceleration is approximately one-sixth that of Earth.
Formulated by Sir Isaac Newton and published in 'Principia Mathematica' (1687). The word 'force' comes from Latin 'fortia' meaning strength. 'Acceleration' derives from Latin 'accelerare' — to hasten, from 'ad-' (toward) + 'celer' (swift).