Calculating the max distance of compression of the spring HELP

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SUMMARY

The maximum distance of compression of a spring when a 2.0 kg block is dropped from a height of 40 cm onto a spring with a force constant of 1960 N/m can be calculated using the work-energy principle. The initial gravitational potential energy (W = mgh) is 7.84 J, which equals the elastic potential energy stored in the spring (W = 1/2 kx^2). The correct approach requires accounting for the total distance the block falls, which includes both the drop height and the spring compression. The final answer for maximum compression is 10 cm, indicating a miscalculation in the initial attempt.

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  • Familiarity with the concept of energy conservation
  • Basic algebra for solving equations
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Calculating the max distance of compression of the spring please HELP!

Homework Statement


A 2.0 kg block is dropped from a height of 40 cm onto a spring of force constant k = 1960 N/m. The maximum distance the spring is compressed is?


Homework Equations


I Used the equation W=mgh and W=1/2kx^2..


The Attempt at a Solution


i did..
W=2*9.8*0.4
=7.84
then i used
7.84=1/2*1960*x^2
from which i got x=0.0894427191
then i did
7.84*0.0894427191=0.7012309177
then i did
7.84-0.7012309177=7.13879

can anyone please help me tel where i went wrong? because the answer to this question is 10 but i don't know how to get it..please help=].
 
Physics news on Phys.org


There is extra gravitational potential energy from the distance through which the spring drops through while touching the spring. In other words, the total distance that the object drops is 40 cm plus however far the spring compresses.
 

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