3D打印科学项目卷2：物理、数学、工程与地质模型

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"3D Printed Science Projects Volume 2" 是一本由 Joan Horvath 和 Rich Cameron 合著的书籍，专注于3D打印技术在科学项目中的应用，涵盖物理、数学、工程和地质学模型。该书由 Nonscriptum LLC 在加利福尼亚州帕萨迪纳出版，并提供了ISBN号码供电子版和纸质版识别。本书强调了对原创内容的版权保护，禁止未经许可的翻译、重印、复制等行为。正文: 《3D Printed Science Projects Volume 2》是一本深入探讨3D打印科技如何与自然科学领域结合的实用指南。作者Joan Horvath和Rich Cameron是3D打印领域的专家，他们在书中展示了如何利用3D打印技术创建一系列有关物理学、数学、工程学以及地质学的模型。这本书不仅为教育工作者和学生提供了一种创新的教学和学习方式，也为对3D打印技术感兴趣的爱好者们提供了一个实践平台。 1. **3D打印技术介绍**：书中首先介绍了3D打印的基本原理和技术，包括不同的3D打印工艺（如熔融沉积建模、光固化成形等），以及如何选择适合特定项目的3D打印机和材料。 2. **物理学模型**：针对物理学，书中可能包含了一系列3D打印的物理实验模型，例如力与运动的关系模型、电磁学模型、光学模型等，这些模型有助于直观理解复杂的物理现象。 3. **数学模型**：3D打印在数学教育中的应用可能包括几何形状的实体模型，使得学生能够触摸和探索抽象的数学概念，如多面体、曲线表面和复杂数学函数的可视化表示。 4. **工程学模型**：在工程领域，3D打印可以用于制作机械结构、桥梁设计、电路板原型等，使学习者能亲手构建并测试自己的设计，增强工程实践能力。 5. **地质学模型**：地质学部分可能会涵盖地形模型、地壳构造模型、化石复制等，帮助学生理解和研究地球的结构、地质过程以及古生物形态。 6. **电子适应和软件**：书中的3D打印项目可能涉及到电子组件的集成，如3D打印电子外壳、传感器支架等，同时可能介绍如何使用相关计算机软件进行设计和模型优化。 7. **版权和使用权限**：出版商明确指出，书中所有内容受到版权保护，禁止未经授权的复制或传播，提醒读者尊重知识产权。《3D Printed Science Projects Volume 2》是一本综合性的资源，旨在利用3D打印技术推动科学教育的革新，让学习者能够通过亲手制作模型来深化理解科学原理，提高实践操作能力。对于教师、学生、科研人员以及3D打印爱好者来说，这本书无疑是一个宝贵的工具。

J. Horvath and R. Cameron, 3D Printed Science Projects Volume 2,

DOI 10.1007/978-1-4842-2695-7_1

CHAPTER 1

Pendulums

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 motion—a 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 something’s 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 falls—converting 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).

CHAPTER 1 ■ PENDULUMS

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 Hooke’s 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

(1564–1642), Christiaan Huygens (1629–1695), and Isaac Newton (1643–1726). 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 * π * 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/s

CHAPTER 1 ■ PENDULUMS

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 publisher’s page for this book. Go to www.apress.com and search on

this book’s 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1-1.

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