Easy Energy Conservation Problem causing me trouble

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Homework Help Overview

The problem involves a block dropped onto a spring, focusing on energy conservation principles, specifically the conversion of gravitational potential energy to elastic potential energy and kinetic energy. The original poster attempts to find the speed of the block at a specific spring compression.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss calculating elastic energy at different spring compressions and relate it to kinetic energy. There is a suggestion to include gravitational potential energy in the calculations. Some participants question the assumptions about energy conversion during the spring's compression.

Discussion Status

The discussion is ongoing, with participants exploring different aspects of energy conservation. Some guidance has been offered regarding the inclusion of gravitational potential energy, and there is recognition of the complexities involved in energy conversion.

Contextual Notes

Participants are navigating the relationship between gravitational potential energy and elastic potential energy, noting that not all energy is converted to kinetic energy during the spring's compression.

motoxkx
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Problem:
A 3.30kg block is dropped from a height of 5.70m onto a spring of spring constant 3806 N/m. When the block is momentarily at rest, the spring has compressed by 32.0 cm. Find the speed of the block when the compression of the spring is 13.5cm.

How I approached it:
Calculate the the elastic energy when the spring is compressed 32.0cm. Then subtract the elastic energy when the spring is compressed 13.5cm. Then that energy would be the current kinetic energy, and I determined velocity from that. However, this is not giving me the correct answer.

Calculations:
Elastic Energy at 32.0cm
E = .5kx^2 = .5*3806*.32^2 = 194.8672 J

Elastic Energy at 13.5cm
E = .5kx^2 = .5*3806*.135^2 = 34.682 J

Subtract the potential energy remaining
194.8672 - 34.682 = 160.185 J

Find velocity
Ke = .5mv^2
160.185 = .5*3.30*v^2
v = 9.85 m/s

Where am I going wrong? Thanks in advance
 
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motoxkx said:
How I approached it:
Calculate the the elastic energy when the spring is compressed 32.0cm. Then subtract the elastic energy when the spring is compressed 13.5cm. Then that energy would be the current kinetic energy, and I determined velocity from that. However, this is not giving me the correct answer.
Don't forget to include gravitational PE in your energy calculations.
 
Doesn't all of the gravitational potential energy become elastic potential energy when the spring is compressed 25 cm?
 
Ah, never mind to my last post, I see where the potential energy comes into play because not all of the elastic energy is converted into kenitic energy, and some becomes potential energy. Thank you for the help.
 

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