Contraction of spring colliding with balls

[devanlevin]

on a vertical spring (k=100n/m) there is a box with a mass of 5kg, a ball of 1kg is dropped into it from a height of 1m what is the maximum contraction of the spring if the collosion is plastic.

i hope that my terminology is correct as i am not studying this in english and am translating

what i did was find the velcocity of the colision, ie the velocity of the ball after falling 1m, came to 4.27[m/s]

then using momentum and collision laws

m1v1+m2v2=(m1+m2)U

M1-the ball
M2-the box

m2v2=0(stationary object)

U=m1v1/(m1+m2)
U=(1*4.27)/6=0.7378[m/s]

then what i did was, using energy i said the energy is conserved from after the impact till the springs maximum contraction so:

E=0.5(m1+m2)U^2=0.5Kx^2
3*0.7378^2=50x^2

x=0.18m

then onto that i added another0.49m which is the original contraction from the weight of the box, and i get
x=0.67m

but the answer in the book is 0.79m and i just can't see how they got it

 

[Winzer]

Hello devinlevin!
I would agree with your attack until your energy equation:E=0.5(m1+m2)U^2=0.5Kx^2
3*0.7378^2=50x^2- specifically the left side.

First try setting up a general equation, not plugging in numbers and tell me what you get.