Calculating Work for an Elastic Spring with Two Connected Springs

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SUMMARY

The discussion focuses on calculating the work required to stretch a system of two connected elastic springs with spring constants k1 = 1.476 N/m and k2 = 3.271 N/m over a distance of x = 10 cm. The correct solution for the work done, as noted by the professor, is 5.09 Joules. The relationship between the stretches of the two springs, x1 and x2, is established through the equation x1 + x2 = 0.1 m, allowing for the calculation of energy stored in the springs using the formula E = 0.5 * k * x².

PREREQUISITES
  • Understanding of Hooke's Law and spring constants
  • Familiarity with energy equations for elastic potential energy
  • Basic algebra for solving simultaneous equations
  • Knowledge of unit conversions (meters to centimeters)
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  • Study the derivation of energy stored in springs using E = 0.5 * k * x²
  • Learn about systems of springs in series and parallel configurations
  • Explore advanced topics in mechanics related to elastic materials
  • Practice problems involving multiple springs and energy calculations
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Students in physics or engineering courses, particularly those studying mechanics and elasticity, as well as educators looking for examples of spring systems in problem-solving contexts.

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Please help this urgent problem!~

Homework Statement



An elastic spring is made of two springs connected one after the other. The coefficients of the springs are k 1 = 1,476 N/m and k 2 = 3,271 N/m. Calculate the work necessary to strech the spring for x=10cm.



Homework Equations



E=0.5 * k * x^^2

k= spring constant
x= distance



The Attempt at a Solution



correct solution is 5.09 <-- this is from professor's note but I still find how this value became.. please help me out.
 
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The net force acting on the point of contact of the 2 springs is zero... what is the force due to spring 1 on the point of contact... what is the force due to spring 2 on the point of contact...

this gives a relationship between x1 (amount spring 1 stretches) and x2(amount spring 2 stretches)

along with x1 + x2 = 0.1m

you can solve for x1 and x2. then you get energy stored in the springs..
 

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