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- 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?