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Work, Energy, and Simple Machines 117 7.1WorkDonebyaConstantForce Work = 3 W Let us begin by doing some thinking based F on our experience of lifting objects to a s = 3 m height. 3 m Consider a wheat bag of mass 5 kg kept mg on the floor (Fig. 7.2a). Gravitational force mg Work = W Work = 3 W Work = 3 W acts downwards on the bag, where m is the 2 m mass of the bag and g is the acceleration due F F F F 3F to gravity. To lift the bag slowly to a height of s = 1 m 1 m, you must apply an upward force equal 1 m to mg. The force applied by you acts upwards mg mg mg mg 3mg on the bag as the bag is displaced through a distance of 1 m in the direction of the force. 0 m In everyday language, you would say that you (a) (b) (c) (d) did some work. Fig. 7.2: Lifting bags to a height If you lift 3 such bags one after the other to the same height (Fig. 7.2b), you would have done 3 times more work than to lift 1 bag. If the bag is lifted to the same height by a machine using some fuel, it will require 3 times more fuel to lift 3 bags. Now, suppose you lift all the 3 bags together to the same height (Fig. 7.2c). You would need to apply a force 3 times larger than that Note required for a single bag. Since, you have done the same task as in Fig. 7.2b, the work done by you would be 3 times the work required to While lift 1 bag. This shows that applying a larger force over the same distance describing the work done, it allows you to proportionally do more work. Next, consider lifting a single 5 kg bag of wheat but to a height of 3 m is important to (Fig. 7.2d). You would have carried out 3 times more work as compared specify the force (or agency) to the work required to lift the same bag by 1 m. Or if the same machine doing the work is used three times in succession to lift the bag by 1 m each time, it would and the object require 3 times more fuel. Thus, applying the same force over a larger on which the distance allows you to proportionally do more work. work is done. The scientific definition of work done by a force is based on the above observations. The work done by a constant force acting on an object in bringing about a certain displacement can be defined as: workdoneonanobjectbyaconstantforce=forceapplied×displacementinthe direction of the force (7.1) In the example that we discussed, the displacement was in the vertical direction, however, Eq. (7.1) can be used even if the force and displacement, both are in a horizontal direction, or any other direction for that matter. s s F For example, consider an object upon which F a constant force F is acting, and it undergoes a displacement s in the direction of force (Fig. 7.3). Then, the work done W by the force on the object is (a) (b) Fig. 7.3: Work done by a force while displacing W = F × s (7.2) an object in (a) horizontal direction, and (b) vertical direction