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Joan Horvath - 3D Printed Science Projects Volume 2: Physics, Math, Engineering and Geology Models

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3D Printed Science Projects Volume 2: Physics, Math, Engineering and Geology Models
Author:
Joan Horvath / Rich Cameron
Publisher:
Apress
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Year:
2017
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Learn physics, engineering, and geology concepts usually seen in high school and college in an easy, accessible style. This second volume addresses these topics for advanced science fair participants or those who just like reading about and understanding science. 3D Printed Science Project Volume 2 describes eight open-source 3D printable models, as well as creative activities using the resulting 3D printed pieces. The files are designed to print as easily as possible, and the authors give tips for printing them on open source printers. As 3D printers become more and more common and affordable, hobbyists, teachers, parents, and students stall out once theyve printed some toys and a few household items. To get beyond this, most people benefit from a starter set of objects as a beginning point in their explorations, partially just to see what is possible. This book tells you the solid science stories that these models offer, and provides them in open-source repositories. What you will learn:Create (and present the science behind) 3D printed modelsReview innovative ideas for tactile ways to learn concepts in engineering, geology and physicsLearn what makes a models easy or hard to 3D printWho This Book is For:The technology- squeamish teacher and parents who want their kids to learn something from their 3D printer but dont know how, as well as high schoolers and undergraduates.

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Joan Horvath and Rich Cameron 2017

Joan Horvath and Rich Cameron 3D Printed Science Projects Volume 2 10.1007/978-1-4842-2695-7_1

1. Pendulums

Joan Horvath 1 and Rich Cameron 1

(1)

Nonscriptum LLC, Pasadena, California, USA

This chapter looks at the deceptively simple world of pendulums. First we cover why pendulums swing back and forth as they do, and tie this into the general idea of simple harmonic motiona type of oscillatory motion in which a system stores energy (in a spring or by working against gravity) and then uses that stored energy to move back to its original position.

Some of the experiments in this chapter are classic high school or undergraduate physics demonstrations, and in some cases would benefit from non-3D-printed parts. However, if you do not have access to typical school lab items, you can still do some respectable explorations with the parts we give you in this chapter, plus a pair of chairs and some string. We point out possible upgrades as we go.

This chapter (like all the others in this book) first lays out a bit of science background and then develops 3D-printable models that explore these concepts. We talk about what we learned just by the process of creating the model, and finally give some tips about how you might use these models to teach the topics they demonstrate. The models are available for download from the link on the copyright page of this book.

Simple Harmonic Motion

What makes a pendulum swing back and forth, or a ball on a spring boing back and forth? Simple harmonic motion is a phenomenon that occurs when something moves in a way that converts energy from potential energy to kinetic energy and back again. In an ideal world, the sum of somethings kinetic energy plus its potential energy is always a constant. If you raise something up high, it has potential energy. It is not moving, but you had to expend energy to get it where it is. When you let go, it fallsconverting this potential energy into kinetic energy, the energy of motion. When it hits the ground, it dissipates that energy into making a big hole or cloud of dust.

But simple harmonic motion is about conversion of potential into kinetic energy in a back and forth way. Suppose you have a table built into the wall. Imagine that you have a big spring attached to the wall, with a heavy ball attached in turn to the spring and resting on the table. If you stretch the spring by pulling the ball away from the wall, and then let go, it will bounce back and forth for a while across the table. It is oscillating because you stretched the spring to start things off (storing potential energy in the spring). When you let go, the spring converted that potential energy into kinetic energy (motion). It will likely then compress the spring and stop when the spring is compressed by the same amount that you stretched it initially, and then shoot back out. This process will continue until friction and air resistance bring it to a stop.

Note

The principle that the force needed to compress or extend a spring is proportional to the distance the spring is extended or compressed is called Hookes Law . British physicist Robert Hooke proposed it over three and a half centuries ago, in 1660.

It is pretty easy to think about a mass on a spring oscillating back and forth on a table as an example of trading off potential and kinetic energy. But what about a pendulum swinging back and forth without any external forces on it (other than being pulled to one side to start the motion)? The more you pull the pendulum bob to one side, the more potential energy you are giving it because you are also raising it. When you let go, the mass will fall (converting some of its potential energy into kinetic energy), constrained by its string. It will have enough kinetic energy to carry the mass up to the other side, and stop, having converted all the kinetic energy back into potential energy. Air resistance and friction at the pivot point will eat away at the total energy over time, but if these can be minimized a pendulum can oscillate for a long time.

Note

The basic work on pendulums has its heritage in the work of Galileo Galilei (15641642), Christiaan Huygens (16291695), and Isaac Newton (16431726). Early practical applications focused on pendulum clocks. Huygens is credited with developing the first working pendulum clock.

As it turns out, the period of a simple pendulum (a weight swinging on a light string or wire) is given by the equation

Period = 2 * * sqrt(l / g)

where l is the length of the string and g is the acceleration due to gravity (9.8 meters per second squared on earth). This formula only applies for swings under about 15 degrees either side of the centerline. It is an approximation that starts to become inaccurate for bigger swings. There are other terms proportional to the square (and higher powers) of the sine of this angle to the vertical. These terms are small when the sine of this angle is small, but become significant as the angle gets larger.

Note

We use the programming convention of using * to mean multiply , and sqrt() for square root of , plus the standard abbreviations for meters (m), centimeters (cm), and other metric quantities. Thus meters per second squared becomes m/s2.

The important property, though, is that the period depends only on the length of the string supporting the mass and not on the mass (unlike the spring example) or any other property of the pendulum. This is why pendulums were of interest first in clocks, and later on in other investigations that we talk about a little later in this chapter.

Friction (including air resistance) will eventually stop these oscillatory motions in the real world. The existence of friction acts as a damping force which takes energy out of the system, eventually bringing it to rest. As you will read in the Learning Like a Maker section in this chapter, we spent a lot of time battling friction in our designs.

The Models

In this chapter we start out with a simple pendulum (a mass on a string) and then move on to physical (sometimes called compound ) pendulums, which are stiff parts that swings back and forth as a whole. Finally, we combine some of these to show the counterintuitive behavior of two or more simple pendulums connected together, or of a double pendulum , which connects two physical pendulums. The double pendulum displays chaotic behavior seemingly-random oscilations.

Tip

If you are new to 3D printing, you might want to look at Appendix A first, which talks about both 3D printing in general and using OpenSCAD in particular. All the models in this book are written in OpenSCAD. Electronic copies of all the models in this can be downloaded from the publishers page for this book. Go to www.apress.com and search on this books title to get to the correct page.

Simple Pendulum

The first model is a simple pendulum bob designed to be hung from a string. It has room for a few coins to be packed inside to weigh it down a little. It is set up to take up to four United States pennies, but there is a parameter, coins_diameter , which is the diameter of the desired coin, in mm. For U.S. pennies, it should be 19.5 mm; for quarters, 25 mm. If you live in other countries, you can find out the relevant coin dimension by doing an online search for the word diameter followed by the name of your coin. Add about half a millimeter to the actual diameter to allow for imprecision and some tolerance to allow the coins to be inserted and removed easily. The simple pendulum model (sized for pennies) is shown in Figure .

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