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56 PHYSICS A large force acting for a short time to produce a Thus, according to Newtonian mechanics, finite change in momentum is called an impulsive force never occurs singly in nature. Force is the force.Inthehistoryofscience,impulsiveforceswere mutual interaction between two bodies. Forces put in a conceptually different category from always occur in pairs. Further, the mutual forces ordinaryforces. Newtonianmechanicshasnosuch between two bodies are always equal and distinction. Impulsiveforceislikeanyotherforce– opposite. This idea was expressed by Newton in except that it is large and acts for a short time. the form of the third law of motion. ⊳ To every action, there is always an equal and Example 4.4 A batsman hits back a ball opposite reaction. straightinthedirectionofthebowlerwithout changing its initial speed of 12 m s . Newton’s wording of the third law is so crisp and If the mass of the ball is 0.15 kg, determine beautiful that it has become a part of common the impulse imparted to the ball. (Assume language. For the same reason perhaps, misconceptions about the third law abound. Let linear motion of the ball) us note some important points about the third Answer Change in momentum law, particularly in regard to the usage of the terms : action and reaction. = 0.15 × 12–(–0.15×12) 1. The terms action and reaction in the third law = 3.6 N s, mean nothing else but ‘force’. Using different Impulse = 3.6 N s, terms for the same physical concept in the direction from the batsman to the bowler. can sometimes be confusing. A simple and clear way of stating the third law is as This is an example where the force on the ball follows: by the batsman and the time of contact of the ball and the bat are difficult to know, but the Forces always occur in pairs. Force on a impulse is readily calculated. ⊳ body A by B is equal and opposite to the 4.6 NEWTON’S THIRD LAW OF MOTION force on the body B by A. The second law relates the external force on a 2. The terms action and reaction in the third law body to its acceleration. What is the origin of the may give a wrong impression that action comes before reaction i.e action is the cause external force on the body ? What agency and reaction the effect. There is no cause- provides the external force ? The simple answer effect relation implied in the third law. The in Newtonian mechanics is that the external force on a body always arises due to some other force on A by B and the force on B by A act at the same instant. By the same reasoning, body. Consider a pair of bodies A and B. B gives any one of them may be called action and the rise to an external force on A. A natural question other reaction. is: Does A in turn give rise to an external force 3. Action and reaction forces act on different on B ? In some examples, the answer seems bodies, not on the same body. Consider a pair clear. If you press a coiled spring, the spring is of bodies A and B. According to the third law, compressed by the force of your hand. The compressed spring in turn exerts a force on your F AB = – F BA (4.8) (force on A by B) = – (force on B by A) hand and you can feel it. But what if the bodies are not in contact? The earth pulls a stone Thus if we are considering the motion of any downwards due to gravity. Does the stone exert one body (A or B), only one of the two forces is a force on the Earth? The answer is not obvious relevant. It is an error to add up the two forces since we hardly see the effect of the stone on the and claim that the net force is zero. earth. The answer according to Newton is: Yes, However, if you are considering the system the stone does exert an equal and opposite force of two bodies as a whole, F and F are AB BA on the Earth. We do not notice it since the earth internal forces of the system (A + B). They add is very massive and the effect of a small force on up to give a null force. Internal forces in a its motion is negligible. body or a system of particles thus cancel away Reprint 2026-27