Calculating the Height of a Block Launched from a Compressed Spring

[Suraj M]

Homework Statement

A block of mass 250 g is kept on a vertical spring with spring constant 100N/m fixed from below.
The spring is now compressed to have a length 10 cm shorter than its natural length and is released. How high does the block rise?g = 10m/s

Homework Equations

E=½kx²
and other basic equations

The Attempt at a Solution

So I found out initial energy imparted,
$$E_1 = ½kx² = 0.5 J$$
then equated to change in potential and new spring energy.
$$E_2 = mgh + ½k(x-h)²$$ where h is the height required
solving E₁= E₂, I get an awkward answer. the answer given is 20 cm. How?

 

[Tanya Sharma]

Your E2 is incorrect .

Why do you think spring would have elastic potential energy when the block leaves it ?

 

[Suraj M]

Oh so you're assuming the block is not attached to the spring, huh, didn't consider that!
Oh i get the right answer then, its just a regular launch. thank you Tanya!