Spring and Hanging Mass
A block of mass 4 kg hangs vertically from a spring with constant k = 100 N/m which is attached to the ceiling and initially is not stretched or compressed. The block is initially held at rest by an external force. The block is then released and falls under the combined forces of gravity and the spring.
What is the speed of the block when it has dropped a vertical distance 0.4 m?
(Quick note: I defined down as positive and up as negative)
F (spring) = -k*x
F (weight) = m*g
F (net) = F (spring) + F (weight) = m*a
a = ω^2*x
v = ω*r
OR I could go this direction
PE (elastic) = 1/2*k*x^2
KE = 1/2*m*v^2
PE = KE (by conservation of energy)
The Attempt at a Solution
I followed the first set of equations, finding the net force on the spring in motion and then finding acceleration to get angular and then linear velocity.
Then I followed the second set of equations using conservation of energy (assuming all of the PE at rest is converted to KE in motion).
I got two similar, but different answers. Which way is the right way? Have I done anything right at all??