Question

A block of mass m is pushed against a spring of spring constant k. The spring is compressed by a distance d, the block is then released. It is launched by the spring along a horizontal frictionless surface with a final speed v. A second block, this one having mass 9m is pushed against the same spring and released, gaining a final speed 3v. By what distance was the spring compressed in the second case?

Answer 1

in first case,mass is m ,distance of compression d.

spring force,F=-kd

acceleration given by spring,a=kd/m

final velocity,v=(kd/m)*t

in second case,3v=(kd'/9m)t

so,1/3=9d/d'*

d'=27d