Calculate Spring Extension for Horizontal Projectile Launcher

[Dunno03]

I've built a horizontal spring launcher, and i need to calculate the extension needed in the spring in order to launch a projectile horizontally to a given distance.

The launcher consists of a striker connected to the spring... when the spring is pulled back and let go the strike moves forward and hit the projectile.

i have the vertical distance of the launch, the mass of both the launcher system (mass of spring + mass of striker), mass of the projectile, the distance the projectile needs to travel and also the spring constant (k),

so far... i have:

Kinetic Energy (launcher) + Elastic Potential Energy = Kinetic Energy (projectile)

problem i run into... is that i can't simplify the equation ... i get to:

Mlauncher*Vlauncher^2 + k*x^2 = Mprojectile*Vprojectile^2

Vprojectile = deltaX / time

time = SquareRoot[DeltaY/(g/2)] g = 9.8m/s^2

Vlauncher = (Mprojectile * Vprojectile) / Mlauncher

i need to make an equation that allows me to solve for x (spring extension)... but i just can't simplify it properly... If anyone could help me out, it would be greatly appreciated. Thanks.

By the way, is there a general formula to calibrate something like this?

 

[cristo]

You say in the first line that this is required to launch the spring a set horizontal distance. How do you change the range of your launcher- i.e. do you change the angle, or vertical height?

 

[Dunno03]

I don't launch the spring, but rather launch a projectile attached to the spring... n this will be done by pulling the spring back.

spring gets pulled back, striker attached to the back of the spring gets pulled back along with it, when i let go of the back of the spring, the striker moves forward and hits the projectile. So changing the extensions distance (x)

 

[Fermat]

Why don't you secure the launcher rigidly, so that it doesn't move. Then Vlauncher will be zero and your equation will reduce to,

k*x^2 = Mprojectile*Vprojectile^2

 

[Dunno03]

the vlauncher is the velocity of the striker. The mass of the striker and it's velocity must be taken into consideration because it's part of the system...right?

 

[Fermat]

The launcher is the entire apparatus for setting the projectile in motion. You should rename that velocity as Vstriker.

You only need the velocity of the striker if it is still going to be moving after impact with the projectile. If the striker were still to be moving after impact, then you would need to know the coefficient of restitution between the striker and the projectile.

If this is just a basic projectile launcher, then you should be able to ignore the striker and simply equate the compressed spring energy (kx²) with the kinectic energy of the projectile. Assume that the striker has zero velocity after impact.

In a basic project like this you would make assumptions and approximations.
For example, you are not going to be worrying about air resistance, projectile spin, or resitance within the launch tube (if you have one). The spring itself has mass and will be moving, and will have kinetic energy. But normally you would ignore that.

 

[Dunno03]

Our physics teacher told us that if our spring has any sort of mass attached to it, then that mass needs to be taken into consideration. The only way I could think of to sort of integrated the mass of the striker into the equation was to add that kinetic energy. Any other ways to add the mass of the striker into the equation? And restitution... is that sort of like friction?