A 250 g mass is placed on the spring with spring constant of 25.0 N/m. Assuming that the spring is pointed straight up, to what height could the spring propel the object?

Explanation:

It depends on how far the spring is compressed.

Let's assume it is an ideal spring following Hooke's Law and that friction is negligible.

Let the amount of compression be "x" meters.

The spring potential energy will be converted to gravity potential energy.

  PE = PS

mgh = ½kx²

     h = kx²/2mg

     h = 25.0x² / (2(0.250)(9.81))

     h = 5.096839...x²

     h = 5.10x²

this "h" value will be measured from the lowest position or maximum spring compression point.

The height above the uncompressed length of spring would be h - x