What is the maximum length of the spring?

AI Thread Summary
The discussion centers on determining the maximum length of a spring while considering gravitational effects and energy conservation. The initial formula proposed involves spring potential energy and kinetic energy but lacks clarity on its application. Participants emphasize the need to incorporate gravitational potential energy along with kinetic and spring potential energy in calculations. A more comprehensive approach is suggested to accurately assess the spring's behavior under these conditions. Overall, understanding the interplay of these energy types is crucial for solving the problem effectively.
annnnnw
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New member has been reminded to always show lots of work in their schoolwork thereads.
Homework Statement
A mass of 0.4 kg hangs motionless from a vertical spring whose length is 0.95 m and whose unstretched length is 0.65 m. Next, the mass is pulled down to where the spring has a length of 1.20 m and given an initial speed upwards of 1.6 m/s. What is the maximum length of the spring during the motion that follows?
Relevant Equations
Spring Stiffness F=kx
Conservation of energy
I know gravity needs to be taken into account and that I can find the stiffness but generally I'm pretty lost
 
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Any conservation laws that you can apply?
 
I tried
1/2(k_s)(s_f)^2 = 1/2(m)(v_i)^2 + 1/2(k_s)(s_i)^2

But I'm not really sure it's the best for what going on here
 
Thread paused for Moderation...
 
annnnnw said:
I tried
1/2(k_s)(s_f)^2 = 1/2(m)(v_i)^2 + 1/2(k_s)(s_i)^2

But I'm not really sure it's the best for what going on here
Thread is reopened provisionally.

@annnnnw -- Please show more effort in your replies in this thread. There are several types of energy involved in this question, including gravitational potential energy (GPE), kinetic energy (KE) and the spring's potential energy (PE) based on how extended it is from its resting postion. Please include all of these in your calculations. Thank you.
 
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