Block attached to spring - calculate how far it will move

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Homework Help Overview

The problem involves a block attached to a vertically suspended spring, where participants are tasked with determining how far the block will move before coming to a stop. The context includes concepts from mechanics, particularly involving spring forces and energy conservation.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss various approaches, including using force equations and energy conservation principles. Some question the validity of equating forces and speeds at the moment of stopping, while others explore the relationship between gravitational potential energy and spring potential energy.

Discussion Status

The discussion is active, with participants sharing different methods and questioning the assumptions behind their approaches. Some guidance has been offered regarding the energy conservation perspective, and there is acknowledgment of a potentially correct approach, though understanding of the underlying principles remains a point of emphasis.

Contextual Notes

Participants are navigating through the implications of their assumptions about forces and energy in the context of the problem, with some noting discrepancies in their initial calculations.

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Homework Statement


A spring with spring constant 200 N/m is suspended vertically with its upper end fixed to the ceiling and its lower end at position y = 0. A block of weight 20 N is attached to the lower end, held still for a moment, and then released. How far will the block move before coming momentarily to a stop?

Homework Equations


mg = -kx
mg = 0.5kx^2

The Attempt at a Solution


I tried using the first equation and got x = 0.1m as my ans. which was wrong. I then tried using the second equation instead and still got an incorrect answer. Where am I going wrong? The ans. is 0.2 m.

Thanks in advance!
 
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You need to look at this problem from an energy conservation standpoint.
 
The block comes to a stop when its speed is zero. Your approach is invalid because the speed of the block is not necessarily zero when the net force acting on the block is zero.
 
Hmm ok would it be something like this? mgh = 0.5kx^2 and the x and the h are the same? Cuz then solving for h I get (2mg)/k and when I subbed in the number I got 0.2. Is this the right way of doing this problem?
 
Looks like a good way to get the answer!
 
Your answer is correct; however, it is important you understand why the approach is valid. Do you?
 

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