Two blocks are connected by a light string that passes over a frictionless pulley. The block of mass m$1$

$=4$ kg lies on a horizontal surface and is connected to a spring of force constant k $=20$ N$/$m$.$ The system is released from rest when the spring is unstretched. The mass of the second block is m$2=$

$2$ kg $($Take g$=9\mathrm{.}81$ m$/$s$2.)$

A$)$ Calculate the distance, h$,$ the hanging block of mass m$2$ falls before coming to rest, if there is no friction between the block of mass m$1$ and the surface. Provide your answer in meters.

B$)$ What is the value of the potential energy stored on the spring after the block of mass m$2$ is hung? Provide your answer in Joules. $($Assume there is no friction between the block of mass m$1$

and the surface, and the blocks move the same distance, h$,$ as in part A$.)$

C$)$ Calculate the distance, h$,$ the hanging block of mass m$2$

falls before coming to rest, if the coefficient of kinetic friction between the block of mass m$1$

and the horizontal surface is $0\mathrm{.}2.$ Provide your answer in meters.

D$)$ What is the magnitude of the work done by friction? Provide your answer in Joules. $($Assume the coefficient of kinetic friction between the block of mass m$1$

and the horizontal surface is $0\mathrm{.}2$ and the blocks move the same distance, h$,$ as in part C$.)$