Creating a Plinko Launcher for My Board: Ensuring the Puck Makes it Up

[Narzu6425]

I am trying to create a plinko launcher for my plinko board (as you would see in the price is right). I created a pinball type spring launcher and used a bell crank in order to change the horizontal force into a vertical force. I am using a 3.5in spring with a spring constant of 1.09lbs/in. I plan on having about 2 in of compression which results in a spring force of 9.697Newtons.

I want to ensure that the plinko will make it up the board and into its appropriate slots. I am having trouble coming up with right calculation in order to prove that the plinko puck (4oz or .2lb) will make it up the board. I also was wondering if anyone had any input of how to come up with the appropriate angle of the curve in order to ensure the plinko will make a smooth turn. Thank you all so much for your help.

 

[Zula110100100]

I would get the work done by the spring, and then that will give you the KE of the mass.

∫f(x)dx gives you the work done by the spring

I converted to metric and here is what I got

f(x) = 190.88x
so the integral is

∫0 - .0508 95.44x²
gave me ≈.246J

If it is launched vertically you should subtract gravity .89N(gravity on puck) * .0508m = .045J

.246 - .045 = .201J Which should be the KE of the puck when it leaves the spring.
If I did my math right that will only give you .23m(8.9in) of height. So depends on the height of your board, and if it contacts anything on the way up(slides up a slanted surface or anything) You should also subtract the work done by friction.

 

[Narzu6425]

Thank you for the quick response! I am going to give this a shot and see what I can come up with.

I realized that I will need much more height than that so I think I am going to try a spring with a different K value. Unfortunately the launcher has too be place within tight constraints so I can't increase the x value for compression.

 

[Narzu6425]

One more quick question...Once i find my Kinetic energy how do I determine my maximum height?

Do I find the initial velocity first and then use gravity as a negative acceleration?

 

[JHamm]

Just find the potential energy in the spring before it is released,
PE = \frac{1}{2}kx^2
Where k is the spring constant and x is the distance it is compressed. This value is then equal to,
mg(h - \cos (\theta) \mu d)
With m being the mass of the puck, g being the gravitational force, h being the height that it moves up, \theta being the angle of any surface the puck moves against measured from the ground, \mu being the constant of kinetic friction for the surface and the puck and d being the distance it moves along this surface.

 

[Narzu6425]

Awesome, thank you! I was able to figure out my calculations from all of your help :)