Solve Spring Problem: 97.6g Ball Dropped from 58.7cm

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SUMMARY

The problem involves a 97.6 g ball dropped from a height of 58.7 cm, compressing a spring to a maximum displacement of 4.60282 cm. The gravitational acceleration is 9.8 m/s². The correct approach utilizes the energy conservation equation mgh = 0.5k(deltax)². The correct calculation reveals that the spring constant k is 530 N/m after adjusting the height to include the spring compression, which was initially overlooked.

PREREQUISITES
  • Understanding of gravitational potential energy (mgh)
  • Familiarity with Hooke's Law and spring constant (k)
  • Ability to convert units (grams to kilograms, centimeters to meters)
  • Basic knowledge of energy conservation principles
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  • Review energy conservation in mechanical systems
  • Study Hooke's Law in detail
  • Practice unit conversion techniques for physics problems
  • Explore more complex spring-mass systems and their dynamics
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Homework Statement


A(n) 97.6 g ball is dropped from a height of
58.7 cm above a spring of negligible mass.
The ball compresses the spring to a maximum
displacement of 4.60282 cm.
The acceleration of gravity is 9.8 m/s2 :


Homework Equations


mgh
.5k(deltax)^2


The Attempt at a Solution


I first converted all grams to kg, and cm to m:
97.6g=.0976kg
58.7cm=.587m
4.60282cm=.0460282m
then:
mgh=.5k(deltax)^2
(.0976g)(9.8m/s^2)(.587m)=.5k(.0460282m)^2
k=530N/m

I really don't see what i could've done wrong, but this isn't the right answer, according to my homework service
 
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Hint: you took the wrong h.
 
lol, i forgot to add deltax to h
 

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