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74 PHYSICS The work done by the force is defined to be Table 5.1 Alternative Units of Work/Energy in J the product of component of the force in the direction of the displacement and the magnitude of this displacement. Thus W = (F cos )d = F.d (5.4) We see that if there is no displacement, there is no work done even if the force is large. Thus, when you push hard against a rigid brick wall, the force you exert on the wall does no work. Yet ⊳ Example 5.3 A cyclist comes to a skidding your muscles are alternatively contracting and stop in 10 m. During this process, the force relaxing and internal energy is being used up on the cycle due to the road is 200 N and and you do get tired. Thus, the meaning of work is directly opposed to the motion. (a) How in physics is different from its usage in everyday much work does the road do on the cycle ? language. (b) How much work does the cycle do on the road ? No work is done if : (i) the displacement is zero as seen in the example above. A weightlifter holding a 150 Answer Work done on the cycle by the road is kg mass steadily on his shoulder for 30 s the work done by the stopping (frictional) force does no work on the load during this time. on the cycle due to the road. (ii) the force is zero. A block moving on a smooth (a) Thestoppingforceandthedisplacementmake o horizontal table is not acted upon by a an angle of 180 ( rad) with each other. horizontalforce(sincethereisnofriction),but Thus, work done by the road, may undergo a large displacement. W r Fd cos (iii) the force and displacement are mutually = 200 10 cos perpendicular. This is so since, for = /2 rad (= 90 ), cos ( 2) = 0. For the block = – 2000 J moving on a smooth horizontal table, the It is this negative work that brings the cycle to a halt in accordance with WE theorem. gravitational force mg does no work since it acts at right angles to the displacement. (b) From Newton’s Third Law an equal and If we assume that the moon’s orbit around opposite force acts on the road due to the cycle. Its magnitude is 200 N. However, the the earth is perfectly circular then the earth’s gravitational force does no work. road undergoes no displacement. Thus, The moon’s instantaneous displacement is workdonebycycleontheroadiszero. ⊳ tangential while the earth’s force is The lesson of Example 5.3 is that though the radially inwards and = /2. force on a body A exerted by the body B is always Work can be both positive and negative. If is equal and opposite to that on B by A (Newton’s o o between 0 and 90 , cos in Eq. (5.4) is positive. Third Law); the work done on A by B is not If is between 90 and 180 , cos is negative. necessarily equal and opposite to the work done In many examples the frictional force opposes on B by A. o displacement and = 180 . Then the work done 5.4 KINETIC ENERGY by friction is negative (cos 180 = –1). As noted earlier, if an object of mass m has From Eq. (5.4) it is clear that work and energy velocity v, its kinetic energy K is have the same dimensions, [ML T ]. The SI unit oftheseisjoule(J),namedafterthefamousBritish   2 physicistJamesPrescottJoule (1811-1869).Since K  m v.v   mv (5.5) work and energy are so widely used as physical concepts, alternative units abound and some of Kinetic energy is a scalar quantity. The kinetic thesearelistedinTable5.1. energy of an object is a measure of the work an Reprint 2026-27