# Force

**Historical Development of Force Concepts:**

- Philosophers in antiquity explored force in the study of objects and machines.
- Aristotle, Archimedes, Galileo Galilei, Isaac Newton, and Einstein contributed to the understanding of force.
- Pre-Newtonian concepts included simple machines, buoyant forces, and natural vs. forced motion.
- Newtonian mechanics revolutionized the description of forces in physics.
- Early 17th-century concepts like Leibniz’s “vis viva” and Newton’s “vis motrix” influenced the concept of force.

**Newton’s Laws of Motion:**

- Newton’s first law states objects at rest remain at rest, and moving objects continue at a constant speed.
- The second law explains the relationship between force, mass, and acceleration.
- The third law states that for every action, there is an equal and opposite reaction.
- Newton’s laws have dominated the description of forces in physics.
- Efforts have been made to define the concept of force explicitly based on Newton’s laws.

**Vector Nature of Forces:**

- Forces are vector quantities with direction and magnitude.
- Resultant forces are determined by vector addition using the parallelogram rule.
- Free body diagrams help track and resolve forces acting on a system.
- Forces can be combined and resolved into independent components using vector addition.
- The additive properties of forces are demonstrated in static equilibrium experiments.

**Equilibrium in Mechanics:**

- Equilibrium occurs when all forces acting on an object are balanced.
- Static equilibrium involves no acceleration and being at rest.
- Dynamic equilibrium entails constant speed in a straight line.
- Equilibrium is achieved when the resultant force on a point particle is zero.
- Net torque must be zero for equilibrium in extended bodies.

**Forces in Classical Mechanics:**

- Idealized models provide insight into forces in classical mechanics.
- Gravitational forces, solid objects as rigid bodies, and models simplifying interactions are common in classical mechanics.
- Gravity was identified as a universal force by Isaac Newton.
- Acceleration due to gravity on Earth is approximately 9.81 m/s¬≤.
- Newton’s law of gravity unified celestial and falling motions.

In physics, a **force** is an influence that can cause an object to change its velocity, i.e., to accelerate, meaning a change in speed or direction, unless counterbalanced by other forces. The concept of force makes the everyday notion of pushing or pulling mathematically precise. Because the magnitude and direction of a force are both important, force is a vector quantity. The SI unit of force is the newton (N), and force is often represented by the symbol **F**.

Force | |
---|---|

Common symbols | , F, F |

SI unit | newton (N) |

Other units | dyne, pound-force, poundal, kip, kilopond |

In SI base units | kg·m·s^{−2} |

Derivations from other quantities | F = ma |

Dimension |

Force plays a central role in classical mechanics, figuring in all three of Newton's laws of motion, which specify that the force on an object with an unchanging mass is equal to the product of the object's mass and the acceleration that it undergoes. Types of forces often encountered in classical mechanics include elastic, frictional, contact or "normal" forces, and gravitational. The rotational version of force is torque, which produces changes in the rotational speed of an object. In an extended body, each part often applies forces on the adjacent parts; the distribution of such forces through the body is the internal mechanical stress. In equilibrium these stresses cause no acceleration of the body as the forces balance one another. If these are not in equilibrium they can cause deformation of solid materials, or flow in fluids.

In modern physics, which includes relativity and quantum mechanics, the laws governing motion are revised to rely on fundamental interactions as the ultimate origin of force. However, the understanding of force provided by classical mechanics is useful for practical purposes.

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