Elastic Energy and Conservation of Energy

[HelloMotto]

Homework Statement

A horizontal spring of force constant 12 N/m, is mounted at the edge of a lab bench to shoot marbles at targets on the floor 93.0cm below. A marble of mass 8.3 x 10^-3 kg is shot from the spring, which is initially compressed a distance of 4.0 cm. how far does the marble travel horizontally?

i can see how i can calculate this, but I am not sure what the energy statement is in this question

originally i stated that

Eelastic + Eg = Ek

but that didnt work

I tried Eelastic = Ek
and that worked.

but it dosent make sense why Eelastic + Eg = Ek dosent work.
initially the ball is off on a table. so there should be gravitational potential energy...but why dosent it work with calculation?

 

[Kurdt]

The following page may help you.

http://hyperphysics.phy-astr.gsu.edu/Hbase/pespr.html

 

[baba89]

The conservation of energy principle states that energy cannot be created or destroyed, only transferred from one form to another. In this case, the elastic potential energy in the spring is converted into kinetic energy when the marble is shot out. The equation Eelastic + Eg = Ek does not work because the marble does not have any gravitational potential energy when it is on the table, as it is not yet in motion. Therefore, the equation Eelastic = Ek is correct, as all of the initial elastic potential energy is converted into kinetic energy when the marble is shot out. To calculate the distance traveled by the marble horizontally, you can use the equation Ek = 1/2mv^2, where m is the mass of the marble and v is its velocity. You can also use the conservation of energy equation to find the velocity of the marble at the moment it leaves the spring, and then use this value to calculate the distance traveled horizontally.