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In physics, a force is action which can cause an object with mass to accelerate.[1] Force has both magnitude and direction, making it a vector quantity. According to Newton's second law, an object with constant mass will accelerate in proportion to the net force acting upon it and in inverse proportion to its mass. An equivalent formulation is that the net force on an object is equal to the rate of change of momentum it experiences.[2] Forces acting on three-dimensional objects may also cause them to rotate or deform, or result in a change in pressure. The tendency of a force to cause angular acceleration about an axis is termed torque. Deformation and pressure are the result of stress forces within an object.[3][4]

Since antiquity, scientists have used the concept of force in the study of stationary and moving objects. These studies culminated with the descriptions made by the third century BC philosopher Archimedes of how simple machines functioned. The rules Archimedes determined for how forces interact in simple machines are still a part of physics.[5] Earlier descriptions of forces by Aristotle incorporated fundamental misunderstandings which would not be corrected until the seventeenth century by Isaac Newton.[4] Newtonian descriptions of forces remained unchanged for nearly three hundred years.

Current understanding of quantum mechanics and the standard model of particle physics associates forces with the fundamental interactions accompanying the emission or absorption of gauge bosons. Only four fundamental interactions are known in order of decreasing strength, they are strong, electromagnetic, weak, and gravitational.[3] High-energy particle physics observations made during the 1970s and 1980s confirmed that the weak and electromagnetic forces are expressions of a unified electroweak interaction.[6] Einstein in his theory of general relativity explained that gravity is an attribute of the curvature of space-time.

Since antiquity, the concept of force has been recognized as integral to the functioning of each of the simple machines. The mechanical advantage given by a simple machine allowed for less force to be used in exchange for that force acting over a greater distance. Analysis of the characteristics of forces ultimately culminated in the work of Archimedes who was especially famous for formulating a treatment of buoyant forces inherent in fluids.[5]

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