Calculating the Maximum Compression of a Spring

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Homework Help Overview

The problem involves a block of mass dropped onto a spring, requiring the calculation of the maximum compression of the spring. The subject area includes concepts of energy conservation, specifically gravitational potential energy and elastic potential energy.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of energy conservation principles, questioning the initial setup and the inclusion of gravitational potential energy during spring compression. There is an exploration of the relationship between potential energy and spring compression.

Discussion Status

Some participants have provided guidance on modifying the energy equation to include the additional distance the block moves down the spring. Multiple interpretations of the problem are being explored, with different participants arriving at varying values for the maximum compression.

Contextual Notes

There is a noted discrepancy in the calculated values for spring compression, with participants indicating different results based on their interpretations of the energy equations. The original poster's initial answer was deemed incorrect, leading to further discussion on the correct approach.

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Homework Statement



A block of mass m = 3.4 kg is dropped from height h = 44 cm onto a spring of spring constant k = 1920 N/m (Fig. 8-38). Find the maximum distance the spring is compressed.

[PLAIN]http://edugen.wiley.com/edugen/courses/crs1650/art/qb/qu/c08/fig08_36.gif



Homework Equations



Ep=mgh

Ep=1/2kx^2



The Attempt at a Solution





Ok so I found the Potential Energy Ep=mgh. That energy should equal to 1/2kx^2.

So I set mgh = 1/2kx^2 to solve for x but my answer was wrong?
 
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Your choice to use kinetic and potential energy is correct, but you are missing one small thing.

The distance the block moves down along the spring (that is, the distance the spring is displaced x) still counts as gravitational potential energy for the block. So modifying the equation you have to take this into account will yield:

mg(h+x) = .5kx^2

From here you can solve for x, the displacement of the spring. Since it is a quadratic, you will get 2 different answers, but it should be clear which one is the correct answer.
 
What was your answer for x, I got 0.1236m.
 
Gorz said:
What was your answer for x, I got 0.1236m.



that's what I got to the first time, but it was wrong...
 
if you try what I mentioned you will get x=.142m which I believe is the correct answer.
 

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