Spring compression -- Ball colliding with a spring-mounted platform

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The discussion focuses on the complexities of modeling the collision between a ball and a spring-mounted platform using energy equations. The user attempts to establish a system of equations that equates the spring's potential energy with gravitational potential and kinetic energy, but encounters difficulties leading to a quadratic equation that does not yield expected results. There is also a request for clarification on the implications of an elastic collision between the ball and the platform. Additionally, the user seeks insight into how the value of the platform's velocity (vp) was determined. The conversation highlights the challenges in applying physics principles to this specific scenario.
dge
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Homework Statement
What is the lowest position attained by the platform after it collides elastically with a ball.
Relevant Equations
1/2mv^2=KE
1/2kx^2=Us
mgx=Ug
1639430782496.png

I've tried establishing a systems of equations with -(1/2)kx^2+mpgx+(1/2)mpvp^2=0, but this leads to an annoying quadratic that when solved does not give one of the listed answers. My thought was that the spring's potential energy is going to be equal to the gravitational potential energy and kinetic energy.
 
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dge said:
I've tried establishing a systems of equations
Don't let us guess. Show your work !
Also: what does it mean that the ball collides elastically with the platform ?

##\ ##
 
dge said:
-(1/2)kx^2+mpgx+(1/2)mpvp^2=0
How did you get the value of ##v_p##?
 

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