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The idea of a reaction force comes from Newton's third law; "If object A exerts a force on object B ,then object B will exert an equal but opposite force back on A". In many problems some of the forces are considered as the "initiating" force or the applied force. When you consider a force as being applied, like a bulldoser pushing a rock, then the force which must act back , the rock pushing back on the doser, is called the reaction force. Sometimes you don't really have an initiating force but it still convienient to think of one force as the force of interest and the back force as the reaction force. There is no single formula for reaction force since it can apply to any force. For example, the earth attracts you with a force mg (your weight), then you can think of the reaction force as you attract the earth with a force -mg; equal but opposite.

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