Determine the distance that the spring is compressed

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SUMMARY

The discussion focuses on calculating the distance a spring is compressed when a 2 kg block is dropped from a height of 0.45 meters onto a spring with an elastic constant of 200 N/m. The conservation of energy principle is applied, where the gravitational potential energy of the block is converted into the elastic potential energy of the spring at maximum compression. The maximum compression can be determined using the formula 0.5mv^2 = 0.5kx^2, where the velocity of the block is zero at maximum compression. The discussion also touches on the significance of considering gravitational potential energy in this scenario.

PREREQUISITES
  • Understanding of conservation of energy principles
  • Familiarity with elastic potential energy calculations
  • Knowledge of gravitational potential energy concepts
  • Basic algebra and quadratic equations
NEXT STEPS
  • Study the conservation of mechanical energy in spring systems
  • Learn about the relationship between mass, height, and potential energy
  • Explore the concept of simple harmonic motion (SHM) and its amplitude calculations
  • Investigate the effects of varying spring constants on compression distances
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Physics students, mechanical engineers, and anyone interested in understanding the dynamics of spring systems and energy conservation principles.

waterfaire
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A 2 kilogram block is dropped from a height of .45 meter above an uncompressed spring. The spring has an elastic constant of 200 Newtons per meter and negligible mass. The block strikes the end of the spring and sticks to it.

A) Determine the distance that the spring is compressed
B) Determine the maximum compression of the spring
C) Determine the amplitude of the SHM

Mass = 2kg
Height = .45m
k = 200N/m

for A...I think I have to use conservation of energy, but I don't know what to put for the maxmium speed of the block.
 
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When the spring is compressed completely, how fast is the block moving?
 
robb_ said:
When the spring is compressed completely, how fast is the block moving?

the speed would be 0, right? at max. compression
 
yes, that is right
 
so...do i use

Ui + Ki = Uf + Kf
.5mv^2=.5kx^2
mv^2=kx^2...

? if i do, what's the velocity?
 
What other types of potential energy do you know of?
 
That would be true for a horizontal situation, but you have to take gravity into account for this problem. Dont be intimidated by the quadratic
 

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