Question

two blocks each of mass m are connected to a spring of spring constant k. if both are given velocity v in opposite directions then the maximum elongation of spring is

Answer 1

total kinetic energy of blocks = total potential energy of two blocks

given, mass of each block is m and velocity v in opposite directions .

so, total kinetic energy = 1/2 mv² + 1/2mv²

spring constant is k , let maximum elongation is done by each block is x

then, total potential energy = 1/2 kx² + 1/2kx²

so, 1/2 mv² + 1/2mv² = 1/2kx² + 1/2kx²

or, mv² = kx²

or, x² = mv²/k

or, x = v√{m/k}

so, maximum elongation of spring = x + x = 2x
= 2v√{m/k}