Calculating the amount of energy that your Rube Goldberg machine wasted" is a bit more complicated. If your system was 100% efficient, then all of the potential energy stored in your
machine would be transferred to the motion of the ping-pong ball pendulum, and as the
ping-pong ball swung upward, its kinetic energy would be converted into gravitational potential
energy.
Based on the law of conservation of energy and the assumption that your system was 100%
efficient (meaning thay no energy was "wasted"), record your prediction for the height of the
ping-pong ball in the space below, and include the calculations that led you to your

You stand staring at a complex contraption of your own design. Hands shaking with excitement, you question if all your hard work calculating, designing, testing, building, and redesigning will pay off. You take a deep breath to calm yourself, and slowly move your hand to set off the first reaction in your highly complicated Rube Goldberg machine. The ping pong ball begins rolling down the intricate ramp setup and curves up the bank of your first right-hand turn. It travels for a bit longer down a slope as it collects speed, destined to meet its stop, dominos. With all of the exhilarating emotions you’re feeling you think, “Will it have enough speed to gently knock down the first domino into the next? Is it going too fast? Will it collide, slamming into all of the dominos at once?”

RUBE GOLDBERG:  

Rube Goldberg was a cartoonist and engineer. He was well known for drawing cartoons with a complex contraption designed to complete a simple task.  

A Rube Goldberg machine uses a set of reactions that work in succession, triggering one event after another until the final event is triggered. Often, each reaction is a simple task that will trigger the next, for example, a row of dominos, a well calculated swinging object, or a ball rolling down a ramp. The most important thing is that each step’s event needs to trigger the following event, and so forth.  

Many things, such as precision, patience, and perseverance will play a role. Imagination, time, and materials are your only constraints. Failure is to be expected and celebrated throughout the engineering process of your machine. With each failure, you will learn something new that you can apply to make your machine even GREATER! Also, it just makes things far more fun. I love to think back about the times I built even the silliest of things with my family. Things would inevitably go wrong and we would laugh and act goofy. However, it was what came next that I have held onto so dearly, even in adulthood, and that is learning from and overcoming those failures. I can remember, even if my parents would sometimes chalk it up to stubbornness, sitting for hours trying different things until I found a solution to the problem.  

All that is left is to try. Try new things and setups that you might not think possible. Look closely as you try each part of your grand machine. With each pass, check to see if there are any improvements or different ways you can trigger the next event. When you get frustrated, ask for help. You’ll be surprised by how others will look at the problem and create a solution you may have never thought about on your own. Embrace the challenge and enjoy the glory as your machine comes together.

THE SCIENCE:  

There are many concepts at play to make a successful Rube Goldberg Machine; potential energy, kinetic energy, mechanical advantage, work, forces, acceleration, momentum, and more – all have an important role. Although the main physics principle driving the action is the conservation of energy. It allows the builder to create a machine with stacks of stored potential energy waiting to be converted into other forms. Often the stored potential energy is in the form of gravitational potential energy, energy an object has due to the position from the ground. Think about when you sit on top of a slide, your gravitational potential energy is relative to your position at the top of the slide and the ground. When you slide down the slide, your potential energy (stored energy) is converted into kinetic energy ( energy of motion), and you pick up speed. This kinetic energy is what you can use to do work on your next event/contraption, that then triggers the next, and so on, until you get to your final event. Potential energy can be stored in elastic materials, springs, and chemical bonds, for example. This potential energy can also be converted into kinetic energy.

Check out some of these videos for ideas and see if you can identify some of the energy transformations.

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west