Finding the Spring Constant of a Water-Balloon Launcher

[Minte]

Homework Statement

Find the average spring constant (k) of a water-balloon launcher, and use that to find the distance to pull back the launcher and launch a balloon of a certain weight a certain distance. I'm at the "finding k" part.

Diagram attached.

Known:
Weight of balloon (Fw, N), mass of balloon (m, kg)
Height of launcher (H, m)
Length of pullback (B, m)
Angle Theta (since tan Th = h/B)
Flight distance / range (x, m)

Unknown:
Spring constant of launcher (k, N/m)

Homework Equations

F=kx
U=kx^2/2
?

The Attempt at a Solution

I just can't find a place to start substituting equations. I tried converting spring energy to gravitational / kinetic energy, but the formulas got very complicated very quickly and lots of extra variables (such as velocity, time, and acceleration) were introduced. I don't think that I can use Fw for Fs, otherwise, why would the pullback distance matter?

I have a lot of data (a whole day on the baseball field hurling water balloons worth), but I don't know how to find the spring constant! Once I have a formula, the rest will be a breeze, but there are too many options, which always makes my brain explode.

Solved
It turns out that the teacher had a formula that he wasn't giving us. k=Fwx/2BH, I think. Anyway, it has been solved. Thanks for the help, anyway! =D

 

[Delphi51]

It seems to me you could begin with spring energy = kinetic energy given to the balloon. That gives you the initial velocity as an expression with a k in it. From the initial v, you can do a standard 2D projectile motion calc to find the horizontal flight distance x in terms of k and the angle. This expression could be solved for k so you could calculate a value for v and then k from each of your test shots (where you know the angle and x).

 

[nlightner]

As a scientist, it is important to have a clear understanding of the problem and all the available data before attempting to find a solution. In this case, it seems like you have all the necessary information except for the formula for the spring constant. It would be helpful to ask your teacher or do some research to find the correct formula for the spring constant of a water-balloon launcher.

Once you have the formula, you can substitute the known values and solve for the spring constant. It may also be helpful to plot the data points on a graph and use the slope of the line to determine the spring constant. Remember to check your units and make sure they are consistent throughout the calculations.

Additionally, it is important to consider any factors that may affect the accuracy of your results, such as air resistance or variations in the launch angle. You may need to repeat the experiment multiple times and take an average to get a more accurate value for the spring constant.

Overall, finding the spring constant of a water-balloon launcher is a great opportunity to practice using equations and data to solve a real-world problem. Keep in mind the importance of accuracy and precision in your calculations and don't hesitate to ask for help or clarification if needed. Good luck!