A spring with spring constant k = 55 N/m and unstretched length of L0 is attached to the ceiling. A block of mass m = 3 kg is hung gently on the end of the spring.
a) How far does the spring stretch?
----------ANSWER: .53509 m
This is the hard part...
**Now the block is pulled down until the total amount the spring is stretched is twice the amount found in part (a). The block is then pushed upward with an initial speed vi = 2 m/s.
KE = (1/2) mv^2
KE = (1/2) kx^2
KE + PE = 0
The Attempt at a Solution
I tried simply doubling the distance found in part a to get x=1.07018, and then plugged that into the formula KE = 1/2 kx^2 to get KE = 31.495.
I then used that value in KE = 1/2 mv^2 and solved for v to get v=4.58, which is wrong. I also tried to add 2 to that to get v=6.58, but thats wrong too.
How do I incorporate the Vi = 2 into this?