A spring of force constant k is stretched by a small length x. Find the work done in stretching it further by a small length y.

A spring of force constant k is stretched by a small length x. Find th

1.	A spring of force constant k is stretched by a small length x. Find the work done in stretching it further by a small length y.
Answer» Solution :Let `W_(1)` is the work done in stretching a spring of force CONSTANT .K. through a length ..X... Then `W_(1)=(1)/(2)Kx^(2)` Let `..W_(2)..` is the workdone in stretching the spring through a length `(x+y)`. Then `W_(2)=(1)/(2)K(x+y)^(2)` `THEREFORE` Additional work done, to increase the elongation by ..y.. is `W=W_(2)-W_(1)` `W=(1)/(2)K(x+y)^(2)-(1)/(2)Kx^(2)` `therefore W=(1)/(2)Ky (y+2x)`