How much do the bed springs stretch when a person jumps on them?

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SUMMARY

The discussion focuses on calculating the stretch of 20 vertical springs in an innerspring mattress when a 48 kg person jumps onto it from a height of 1.95 m. Each spring has a spring constant of 5000 N/m, and the gravitational acceleration is 9.8 m/s². The conservation of mechanical energy principle is applied, using the equation 1/2 kx² to determine the stretch. Participants express confusion regarding the correct setup of the energy equation and whether to multiply or divide the spring constant by the number of springs.

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  • Understanding of conservation of mechanical energy
  • Familiarity with Hooke's Law and spring constants
  • Basic algebra skills for solving equations
  • Knowledge of gravitational acceleration and its effects on mass
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  • Review the principles of conservation of mechanical energy in physics
  • Study Hooke's Law and its application in real-world scenarios
  • Practice solving quadratic equations, particularly in the context of physical problems
  • Explore the effects of multiple springs on force distribution and energy absorption
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Students studying physics, particularly those focusing on mechanics and energy conservation, as well as educators seeking to clarify concepts related to spring systems and energy equations.

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Homework Statement


The innerspring mattress on your grandmother’s bed is held up by 20 vertical springs, each having a spring constant of 5000 N/m. A 48 kg person jumps from a 1.95 m platform onto the innersprings.
The acceleration of gravity is 9.8 m/s2 .
Assume: The springs were initially un- stretched and that they stretch equally (typical old fashioned bed).
Determine the stretch of each of the springs. Answer in units of m.


Homework Equations



consevation of mechanical energy using spring equation, 1/2kx2


The Attempt at a Solution



im not really sure how to setup the conservation of energy equation... if i have it right here then i should solve for y, but i don't see how to do that algebraically. i will always end up with a y on either side. unless I'm supposed to apply the quadratic formula... nope, still a wrong answer. am i setting up the conservation of energy equation right?

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should the spring constant be multiplied by 20 to compensate for the 20 springs, or should the answer be divided by 20?

i don't see where i went wrong in my math...
 
edited
 

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