Show thatthe law of conservation of mechanicalenergyis obeyedby pulling or compressingthe block tied at the end of a spring (a)

Show thatthe law of conservation of mechanicalenergyis obeyedby pullin

1.	Show thatthe law of conservation of mechanicalenergyis obeyedby pulling or compressingthe block tied at the end of a spring (a)
Answer» Solution :Infigure (a) block is in equilibrium ` :. X = 0 ` When a blockof mass m is pulled from its postionx = 0 UPTO `x_(m)` and itreleased then itmoves from `-x_(m)`to `x_(m)`. The total mechanicalenergyat any pointx = x it remainsconstant . `1/2 kx_(m)^(2) = 1/2 kx^(2) +1/2 mv^(2)` where v is velocity of BLOCKAT x . At originalpositionof block at x = 0 , the speed is maximu and hencekinetic energy is maximum . ` :. 1/2mv_(m)^(2) =1/2 kx_(m)^(2)` where `v_(m)` is maximum speed . ` :. v_(m)^(2) = k/m . x_(m)^(2)` `:. v_(m) = sqrt(k/m) .x_(m)` DIMENSIONAL formula of `sqrt(k/m) ` is `[T^(-2)]` hencedimensional formula of `v_(m)` is same as thedimensional formula of `sqrt(k/m).x_(m)` Hence, kineticenergy is converted into POTENTIAL energy and potential energyis convertedintokinetic energybut total mechanicalenergyremains constant .