How Is Initial Velocity Calculated in a Spring Gun?

[ph4u]

A spring gun has a spring with a constant of 2.0 N/cm. If the spring is compressed 3.0cm and the gun is loaded with a .15 kg ball, what will be the initial velocity?



Equations such as E(k subscript)=0.5mv^2
E(p subscript)-mgh



3. i think that since kinetic energy is equall to potenial, i used the equation 0.5(m)(v)^2=mgh.
So the (m) crosses of from both sides and i solved for v^2.
Yeah that's as far as i got and I am confused as to what to do next or what to cross off next?

 

[juana_sm]

Kinetic energy of the ball is equal to potential energy of the spring, so:
mv^2/2=kx^2.
You don't need potential energy of the ball here.

 

[jmb88korean]

In this case, since the gun is told to be at a certain height, all the energy is potential, but its spring potential energy. Use E=(.5)kx^2 with k being the constant and x being the distance the spring is compressed. All this energy becomes linetic at the point of release so set it equal to the kinetic energy equation and solve for v using the given m.

If the gun was at a given height, then you would use the gravitational potential energy equation in the problem somehow, but since no height is given, you just use the ones I told you.