Calculating Work for an Elastic Spring with Two Connected Springs

[kimjh]

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.

 

[learningphysics]

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..