Calculating the spring constant involving energy

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SUMMARY

The discussion focuses on calculating the spring constant (K) for a 142 g ball dropped from a height of 62.2 cm, which compresses a spring by 4.35501 cm. The correct approach involves using Hooke's Law and the potential energy formula, specifically PE = 1/2 kx^2, rather than equating energy and force terms directly. The final formula derived is K = -(2 * mg(h+x)) / x^2, where g is 9.8 m/s², h is the height, and x is the compression distance. Participants emphasized the importance of unit conversion from centimeters to meters for accurate calculations.

PREREQUISITES
  • Understanding of Hooke's Law and spring mechanics
  • Knowledge of potential energy concepts in physics
  • Ability to perform unit conversions, particularly from centimeters to meters
  • Familiarity with basic algebra for manipulating equations
NEXT STEPS
  • Study the derivation and application of Hooke's Law in various contexts
  • Learn about energy conservation principles in mechanical systems
  • Explore unit conversion techniques and their importance in physics calculations
  • Investigate the relationship between force, mass, and acceleration in gravitational contexts
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Students studying physics, particularly those focusing on mechanics and energy concepts, as well as educators seeking to clarify spring dynamics and energy conservation principles.

rbailey5
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Homework Statement


A 142 g ball is dropped from a height of 62.2 cm above a spring of negligible mass. The ball compresses the spring to a maximum displacement of 4.35501 cm. acceleration due to gravity is 9.8. Calculate the the spring force constant K.


Homework Equations



Hooke's law: F=-kx and the potential energy of the spring is given by mg(h+x) because total displacement involves the compression distance x as well as the height of the ball

The Attempt at a Solution


So I got mg(h+x)=-kx,
-mg(h+x)/x=k
(-.142*9.8*(.622+.435501))/.435501=k but I keep getting the wrong answer. What am I doing wrong am I supposed to use PE=1/2kx^2 instead?
 
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rbailey5 said:
So I got mg(h+x)=-kx,
You can't set an energy term equal to a force term.
What am I doing wrong am I supposed to use PE=1/2kx^2 instead?
Yes.
 
ok so you get -(mg(h+x)*2)/x^2=k,

-(2*.142*9.8*(.622+.435501)/.435501^2=k
 
rbailey5 said:
ok so you get -(mg(h+x)*2)/x^2=k,

-(2*.142*9.8*(.622+.435501)/.435501^2=k
Get rid of that minus sign. And be careful when converting cm to m: 4.35 cm = 0.0435 m.
 
sweet thanks!
 

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