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Explain work doneby a constant force . |
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Answer» Solution :Constant force : The magnitude and direction offorce actingon the body remains constant during the motion of body , then such type of force is known as constant force . DEFINITION of work on a trial basis is as under : Work : " The product of magnitude of force and dispalcement during which te force is acts is called work " . ` :. `Work = Force F `xx` Displacementd ...(1) where F is the forceactingon the bodyand d isthe displacementin the direction of force . Work is denotedby thedot product of force `vec(F)`and displacement in the direction of force . It is not necessary that the displacementof a body is always in the direction of force of force applied . If the displacement`vec(d)` It is not necessary that thedisplacement of a body is always in the dirction of force applied . If the displacement of bodyis not in the direction of force applied then the definition of work is given as under by two ways . (1) Work= Force `xx` Component of displacement in the direction of force (2) Work = Component of force in the direction of displacement `xx` displacement...(3) Understanding these by following figure (a) a body UNDERGOES a displacement `vec(d)`under the influence of the force `vec(F)` on the bodywith `theta `ALONG the horizontal direction .  Force is not fully responsible for displacement `vec(d)` for this take the componentof force as shown in figure . (i) The componentof force in the horizontal ( displacement `vec(d)` is not ) direction is `F cos theta ` (II) Perpendicular component `f sin theta ` to the displacement `vec(d)`is not responsible for horizontaldispalcement .  ` :. ` From the equation (3) of definition of work `W = |vec(F)| cos theta xx |vec(d)|` ` :. W = F cos theta.d` ` [ :. |vec(F)| = F and |vec(d) |=d]` The perpendicular components of displacement `vec(d)`in the directionof forceas shown in figure (b) are , (1) Component `dcos theta `in the direction of force `vec(F)` (2) Component `dsin theta ` in the perpendiculardirection of force `vec(F)` ` :. ` From the equation(2) of definition of work , `W = |vec(F)| xx|vec(d)| cos theta` ` :. W = F d cos theta ""`...(5) ` [ :.|vec(F ) |= F and |vec(d) | = d.|` From equation (4) and (5) , the result obtained by two different definition of work is same . If `theta = 0^(0), cos 0^(0)=1 :. ` Work in general `W = d cos theta ""....(5)` ` [ :. |vec(F)|=F and |vec(d)| = d]` From equation (4) and (5) , the result obtained by two different definition of work is same . If `theta =0^(0) ,cos0^(0)=1 :. ` Work in general W = Fdwhich is as equation (1) . The work obtained by the force acting on the body for definite displacement is proportional to the magnitude of force . |
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