Calculating Work for an Elastic Spring with Two Connected Springs

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To calculate the work necessary to stretch two connected springs with coefficients k1 = 1,476 N/m and k2 = 3,271 N/m for a total stretch of 10 cm, the energy stored in each spring must be determined using the formula E = 0.5 * k * x^2. The relationship between the stretches of the two springs, x1 and x2, is established by the equation x1 + x2 = 0.1 m, with the net force at their contact point being zero. By solving for x1 and x2, the individual energies can be calculated, leading to the total work done, which is confirmed to be 5.09 J according to the professor's notes. This approach highlights the importance of understanding the interaction between connected springs in calculating work.
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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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