A MASSLESS SPRING IS BETWEEN A 1-KILOGRAM MASS AND A3-KILOGRAM MASS, BUT IS NOT

Question

A MASSLESS SPRING IS BETWEEN A 1-KILOGRAM MASS AND A3-KILOGRAM MASS, BUT IS NOT ATTACHED TO EITHER MASS. BOTHMASSES ARE ON A HORIZONTAL FRICTIONLESS TABLE. IN ANEXPERIMENT, THE 1-KILOGRAM MASS IS HELD IN PLACE, AND THESPRING IS COMPRESSED BY PUSHING ON THE 3-KILOGRAM MASS. THE3-KILOGRAM MASS IS THEN RELEASED AND MOVES OFF WITHA SPEED OF 10METERS PER SECOND. A) DETERMINE THE MINIMUM WORK NEEDED TO COMPRESS THE SPRING INTHIS EXPERIMENT. THE SPRING IS COMPRESSED AGAIN EXACTLY, BUTTHIS TIME BOTH MASSES ARE LEASED SIMULTANEOUSLY. B) DETERMINE THE FINAL VELOCITY OF EACH MASS RELATIVE TO THETABLE AFTER THE MASSES ARE RELEASED. A MASSLESS SPRING IS BETWEEN A 1-KILOGRAM MASS AND A3-KILOGRAM MASS, BUT IS NOT ATTACHED TO EITHER MASS. BOTHMASSES ARE ON A HORIZONTAL FRICTIONLESS TABLE. IN ANEXPERIMENT, THE 1-KILOGRAM MASS IS HELD IN PLACE, AND THESPRING IS COMPRESSED BY PUSHING ON THE 3-KILOGRAM MASS. THE3-KILOGRAM MASS IS THEN RELEASED AND MOVES OFF WITHA SPEED OF 10METERS PER SECOND. A) DETERMINE THE MINIMUM WORK NEEDED TO COMPRESS THE SPRING INTHIS EXPERIMENT. THE SPRING IS COMPRESSED AGAIN EXACTLY, BUTTHIS TIME BOTH MASSES ARE LEASED SIMULTANEOUSLY. B) DETERMINE THE FINAL VELOCITY OF EACH MASS RELATIVE TO THETABLE AFTER THE MASSES ARE RELEASED.

Explanation / Answer

when one kg mass was heldstationary , and 3kg mass is compressed aganist it       if x bethe compression in the spring and            potential energy of the spring = kinetic energy of 3kg afterrelease                         kx^2 /2 = mv^2 /2 k,x = force constant and springcpompression m,v = are the mass and velcotiy ofthe 3kg body if both the masses are releasedsymultaneously , then conservation of energydemands           mv =m'v ' ......eq1            v = m'v' / m and enrgy conservation of thesysterm gives         mv^2/2 + m'v'^2 /2 = kx^2 /2...........eq2 pluggin eq1 in eq2 for v we cansolve for v'.

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