Help with Hooke's law and elastic potential energy

[Bruzzix]

I've been stuck on this question and can't understand why I'm wrong:
"Springs A and B are compressed so that they hold equal amounts of elastic potential energy. Calculate the value of the ratio of the compression of A to that of B".
Spring A has a force constant of 20000N/m and spring B's force constant is 10000N/m
My answer was a ratio 0f 2:1, but the book gives an answer of 0.71.

Below is an attachment of what the graph looks like. The y-axis is force in N and the x-axis is compression in cm. Blue is A and red is B.

Thanks.

[bobisnotmyname]

I've been stuck on this question and can't understand why I'm wrong:
"Springs A and B are compressed so that they hold equal amounts of elastic potential energy. Calculate the value of the ratio of the compression of A to that of B".
Spring A has a force constant of 20000N/m and spring B's force constant is 10000N/m
My answer was a ratio 0f 2:1, but the book gives an answer of 0.71.

Below is an attachment of what the graph looks like. The y-axis is force in N and the x-axis is compression in cm. Blue is A and red is B.

Thanks.

Very good question
your problem is your not doing the ratio with the elastic potential energy. remember Ek=0.5*k*x^2
lets let both the sprinks have a elastic potential energy of 10000J.
so, 10000=0.5 *20000*x^2 for spring a, so solve for x. x=1
10000=0.5*10000*x^2 for spring b, solve for x. x=square root of 2
then 1/square root of 2=0.70710678...
hence your answer

[alchemy]

1/2 k_A x^2 = 1/2 k_B y^2
10000x^2=5000y^2
2x^2=y^2
sqrt(2) x = y
x/y=1/sqrt(2)=0.71.

Slightly different way of doing it than bobisnotmyname, in case you'd like to know...

[Bruzzix]

Thanks bob and alchemy