Building a Marble Catapult

[bananamanz]

TL;DR Summary: I'm trying to solve how far to compress a spring to launch a marble 2-2.5m

I currently have a catapult built with a total height of 10 3/8 inches. The catapult tube is angled at 42 degrees and when the set spring inside the catapult is compressed by 1 inch the marble is launched 71 inches in 0.76 seconds. I am trying to find out how far back to compress the spring to get my desired distance of 2-2.5 meters.

 

[DaveE]

Is this a homework problem?
You've done one experiment, perhaps you could do some more to collect a data set to examine.

 

[Ibix]

Agree. This is probably not an ideal system, and you don't know how to model the losses in your actual system, which are probably considerable.

That said, you could compute the increase in compression you need in the ideal case. That would be a lower bound on what you need in reality, so you might be able to determine if it's probably impossible with your existing spring.

 

[Baluncore]

I am trying to find out how far back to compress the spring to get my desired distance of 2-2.5 meters.

The energy needed to cover that distance must come from the spring.
The marble will have a parabolic trajectory, beginning and ending with your preset launch angle. (I assume takeoff and landing are at the same height).
The horizontal velocity component is fixed at launch.
The vertical velocity is changed by gravity during the flight.
How long in time must the marble fly?
What height must the marble reach to remain airborne for that distance?
How much energy is stored in a spring as it is compressed? Is energy proportional to length, or to length squared?

Why 42°, I would have chosen a 45° launch angle to get more consistent range results and make the arithmetic simple.