# WORK DONE BY A CONSTANT AND VARIABLE FORCE.pdf - Work Done...

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Work Done by aConstant andVariable Force
Objectives: After completing thislecture, you should be able to:Define thespring constantand calculatethe work done by a varying spring force.
Graph of Force vs. DisplacementAssume that a constant force F actsthrough a parallel displacementDx.Force, FDisplacement, xFx1x2Theareaunder thecurve is equal to thework done.Work = F(x2-x1)WorkFx=DArea
Example for Constant ForceWhat work is done by a constant force of40 Nmoving a block from x =1 mto x =4 m?Work = F(x2-x1)WorkFx=D40 NForce, FDisplacement, x1 m4 mAreaWork =(40 N)(4 m-1 m)Work =120 J
Work of a Varying ForceOur definition of work applies only for aconstantforce or anaverageforce.What if the forcevarieswith displacement aswith stretching a spring or rubber band?FxFx
Hooke’s LawWhen a spring is stretched, there is arestoringforce that is proportional to the displacement.F = -kxThe spring constantkis a propertyof the spring given by:K =DFDxFxm

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