 #1
LCSphysicist
 636
 153
 Homework Statement:

A mass of 10 kg falls 50 cm onto the platform of a spring scale,
and sticks. The platform eventually comes to rest 10 cm below its initial
position. The mass of the platform is 2 kg. Find the spring constant.
 Relevant Equations:
 All below
This is my scope of the question, i could think to solve it by two steps, but before, let's give name to the things.
X is positive down direction.
X = 0 at the initial position o the platform
Mass of the falling block is m1
Mass of the platform, m2
Spring constant k
Δx is the initial stretched length of the spring
h1 is the height of the block
h2 is the final distance (0,1m) of the origin
vb is the block speed
vc is the both bodies speed
vb² = 2gh1
m1*vb = (m1+m2)*vc
(m1+m2)*vc²/2 + kΔx²/2 = (m1+m2)*g*h2 + k(Δx + h2)²/2
Δx = m2*g/k
That is a system possible and determined, but why this is wrong?
I see we could apply kx before and in the final scenario, but why the first attempt is wrong?