Easy Energy Conservation Problem causing me trouble

AI Thread Summary
The discussion focuses on a physics problem involving a block dropped onto a spring, requiring the calculation of the block's speed at a specific spring compression. The user initially calculated the elastic energy at two compression points but neglected to account for gravitational potential energy in their energy balance. They realized that not all elastic energy converts to kinetic energy, as some remains as potential energy in the spring. The correct approach involves incorporating gravitational potential energy to accurately determine the block's speed. The user seeks clarification on their calculations and acknowledges the need to consider all forms of energy involved.
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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