Diary of a Student Engineer Part 9: Rube Goldberg Machine Part 2

And so, the final installment! In this blog I’m going to run through the design of the second half of my Rube Goldberg Machine and then finally present the video showing it in action. So back to where I left off…

Step 7

Using the last value we calculated as 0.36 N for the force generated by the cardboard weight on the wheel, it was clear that this force was far too small to trigger any sort of subsequent reaction, hence I bumped up the amount of cardboard on the weight by another 200 grams to get 0.3 kg, resulting in an increased force of about 1.1 N. This was still very small of course, however it was just about enough required for this next step. Here, I used a simple horizontal lever design to transfer the force to a delicately positioned shovel standing upright. In practice this shovel was standing against a chair and only required a small amount of displacement to dislodge it from place and fall over. This was incredibly frustrating at times but nonetheless, it worked.

Step 8

Next, it was time to include a pulley system of some sort. The mechanism here was very simple; when the shovel fell over it would loosen the tension in the string attached to a bottle of water (weight) on the pulley hoist. This tension generated by the water bottle also helped make the shovel more likely to fall over. But one design consideration I should have paid more attention to is the unintended external force caused by the wind, resulting in the shovel and water falling at the wrong time!

Step 9

Now with a force in the shape of a half-filled bottle of water lying just above a set of ‘dominos’ — just a few books, bottles and weights. I could use the bottle to trigger this domino effect. As the vertical displacement between the water weight and the first domino is quite short, I will discount the dynamic force that is generated when it falls down. This simplifies the problem to a simple statics equation where the downward force is: mg = 0.25*9.81 = 2.45 N. However, I needed a horizontal force to trigger the dominos. So, for the first domino — a small plank of wood, I improvised by placing a small basket at a 45 degree angle on top. This slope separates the downward force into two components: vertical and horizontal. Taking this slope to be 45 degrees, the subsequent force applied to knock down the plank of wood is half: 1.23 N. Given that, the base of the wooden plank had a small base area the moment from this force was more than enough to cause the domino to fall.

Step 10

At the end of the domino sequence, I placed an unopened 1.5 kg bag of porridge oats to generate a more significant force when it fell over so it would open a clothes peg. The maths here is very similar to that done in the previous blog post for the rake falling on the bike wheel, however instead of generating circular motion in a bike wheel, the aim is to compress the spring in the clothes peg enough so that the peg opens. This of course relies on the stiffness of the spring, and I won’t pretend I carried out extensive testing to find out this value, all that matters is a 1.5 kg bag of porridge oats was enough to do the job.

Step 11

Nearly there now, the penultimate mechanism of this machine utilises the pendulum/ simple harmonic motion principle to transfer a force to a ball. I used a swing set in my garden to achieve this, where a weight was suspended using a string attached to the peg mentioned in the previous step.

I can actually again use the same energy equation I’ve used ubiquitously in these blog posts to calculate the energy in the system and velocity of the weight when it strikes the ball. The weight is about 2.5 kg and only suspended about 30 degrees from the vertical on a 1m piece of rope. Hence it’s potential energy is (2.5)*g*(1–1Cos30) = 3.29 J. I can then calculate the velocity as it strikes the ball using the equation: 3.29 = 1/2*(2.5)*v². The resulting velocity is 1.62 m/s and momentum = 4.05 kg m/s.

Step 12

The final step is a trivial one, I simply placed some guide rails for the ball to slide down into a box labeled GOAL. As you will see, the consequences of adding this step at the end were ironic.