Solving the Spring Launcher Puzzle: Making it Work at Different Heights

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I have designed a spring launcher for my class and it works really well using the range equation...x=sqrt(Rmg/KSin2(Theta)). So I have made a contraption that displaces the spring by x metres. I even have re-arranged and have it working using angles of launch and determining the range (R). Both work great.

Here is my dilemma, I am having issues figuring out the proper angle (or displacement) to use when the spring does not land on the same level as the launch...i.e. either higher or lower in a target basket. I am having a hard time figuring out how to manipulate the equations to include the height. I have tried manipulating the equation from http://www.mwit.ac.th/~Physicslab/hbase/traj.html#tra8" but to no avail.

• x = how far you pull the spring back in meters
• R = range: how far you want the spring to go in meters
• m = mass of the spring in Kg
• g = acceleration of gravity 9.8 m/s/s
• K = spring constant in Newtons / meter
• Theta = angle of launcher from horizontal

If anyone can help me with this, it would be greatly appreciated.

 

[eljose79]

Thank you for sharing your spring launcher design with us. It sounds like you have put a lot of effort into creating a successful contraption.

In regards to your dilemma, I understand that you are having trouble determining the proper angle or displacement to use when launching the spring at a target that is not on the same level as the launch. This is a common issue when trying to apply equations to real-world situations.

To incorporate the height into your range equation, you can use the following formula:

R = x + (tan θ)x - (1/2)(g)(x^2/v^2)(1 + (tan θ)^2)

Where:
• x is the horizontal displacement
• θ is the angle of launch
• v is the initial velocity of the spring
• g is the acceleration due to gravity

This formula takes into account the vertical displacement of the target and adjusts the range accordingly. You can also rearrange this equation to solve for the angle of launch if you know the other variables.

I hope this helps you with your calculations. Keep in mind that there may be some factors that can affect the accuracy of your results, such as air resistance and the weight of the target. It may be helpful to conduct some experiments to fine-tune your calculations and ensure the best accuracy.

Best of luck with your spring launcher and future experiments.