This document discusses cycloids and their applications in civil engineering. It provides background information on cycloids and explains some of their properties that make them useful in engineering applications. The objectives of the project are to demonstrate some of the properties of cycloids and their uses in engineering through kinematic laws and by developing a physical model to verify the theoretical results.

1. CURVAS ESPECIALES EN LA INGENIERÍA
CIVIL Y SUS APLICACIONES
LA CICLOIDE

2. CONTENIDO: TIPOS DE CURVAS
CURVA

3. MARCO TEÓRICO
Antecedentes y datos históricos
01

4. Antecedentes
SOFTWARE 3
Despite being red, Mars is a
very cold place
Gaudí
Helenas de
las curvas
Jupiter is the biggest planet
in the Solar System
SOFTWARE 4
Saturn is a gas giant and has
several rings

5. APLICACIONES
01 • Dar a conocer algunas
propiedades y sus
aplicaciones en la ingeniería
GENERALIDADES
02
CINEMÁTICA
03 • Usar las leyes de la cinemática
para demostrar que la Cicloide
es una braquistócrona
EXPERIMENTACIÓN
04 • Desarrollar una maqueta nos
permita verificar nuestros
resultados teóricos.
OBJETIVOS DEL PROYECTO

6. CICLOIDE
Se da el nombre
de cicloide a la
curva descrita por
un punto de la
circunferencia,
cuando esta rueda
sobre una recta
sin resbala

7. EXPLICACIÓN DEL PROYECTO
DEMOSTRACIÓN FÍSICO - MATEMÁTICO
Y
X
A
B
A
B
A
B
d1
d2
t1 t2
Hipótesis
Conclusión:
: d1 < d2
t1 > t2

8. En la Recta:
A
B
d1
m = 2 kg
• Encontrar las ecuaciones del movimiento:
• Encontrar las ecuaciones del
movimiento en el eje “x”:
𝜃
W = mg
60°
Wx = mgSen𝜃
Wy = mgCos𝜃
=1 m
m
𝐹𝑥 = 𝑚𝑎
𝑚𝑔𝑆𝑒𝑛𝜃 = 𝑚𝑎
2. 9.81 . 𝑆𝑒𝑛60° = 2. 𝑎
8.49 ≅ 𝑎
• Encontraremos el tiempo “t1” con
ayuda del MRUV
• Calculamos la aceleración:
𝑥𝑓 = 𝑥0 + 𝑣0𝑡 +
1
2
a𝑡2
1 = 0 + 0𝑡 +
1
2
8.49 𝑡2
0.48 ≅ 𝑡
𝑡1 ≅ 0.48 𝑠𝑒𝑔
En la Cicloide:
A
B
• Debemos tener en cuenta lo
siguiente:
d2
d2 = Longitud de la circunferencia
d2 = 2𝜋 𝑟
Fórmula del tiempo
para la cicloide:
𝑡 = 𝜋
𝑎
𝑔
𝑡 = 𝜋
𝑟
𝑔
• En el problema:
d2 = 2𝜋 𝑟
1.09 = 2𝜋 𝑟
0.17 = 𝑟
• Reemplazando en la fórmula:
𝑡 = 𝜋
𝑟
𝑔
= 𝜋
0.17
9.81
≅ 0.41 𝑠𝑒𝑔.
𝑡2 ≅ 0.41 𝑠𝑒𝑔
=1.09 m

9. EXPLICACIÓN DEL PROYECTO
DEMOSTRACIÓN FÍSICO - MATEMÁTICO
A
B
A
B
d1
d2
t1 t2
Hipótesis
Conclusión:
: d1 < d2
t1 > t2

10. EXPERIMENTACIÓN
Materiales Medidas imagen
Regla 20dsre8 ● Foto
Wuncha 20eqr0 ● Foto

11. CONCLUSIONES
1
2
3
Logro Demostra que el tiempo
sdlh
Logro Usamos las formulas de
la cinematica
Logro En as curvas en la vida
re3al

12. INFOGRAPHIC
1 2
4
3
5 6
Venus is the second
planet from the Sun
Jupiter is the biggest
planet of them all
Saturn is composed of
hydrogen and helium
Mercury is the closest
planet to the Sun
Neptune is the farthest
planet from the Sun
Mars is actually a very
cold place

13. ● Spoken level: High
● Written level: High
COMMUNICATION SKILLS
ENGLISH
C1
FRENCH
B2
● Spoken level: Intermediate
● Written level: High

14. Mercury is the closest planet to
the Sun and the smallest one in
the Solar System—it’s only a bit
larger than the Moon
MY VALUES
MERCURY VENUS
Venus has a beautiful name
and is the second planet from
the Sun. It’s hot and has a
poisonous atmosphere

15. Average GPA for this degree
9.12

16. ● Write your educational journey here
● Write your educational journey here
● Write your educational journey here
● Write your educational journey here
● Write your educational journey here
LIST YOUR
STUDIES HERE

17. It’s the closest planet to
the Sun and the smallest
in the Solar System
Venus has a beautiful
name and is the second
planet from the Sun
67%
Despite being red, Mars
is actually a cold place.
It’s full of iron oxide dust
MERCURY VENUS MARS
56% 85%
TECHNICAL SKILLS

18. —SOMEONE FAMOUS
“This is a quote, words full of wisdom that
someone important said and can make the
reader get inspired.”

19. A PICTURE IS WORTH A
THOUSAND WORDS

20. VOLUNTEER WORK
MARS
Despite being red,
Mars is a cold place
VENUS
Venus is the second
planet from the Sun
JUPITER
It’s the biggest planet
in the Solar System

21. AWESOME
WORDS

22. MY FAVORITE TOPICS ON PHYSICS
MERCURY
Mercury is the closest
planet to the Sun
VENUS
Venus is the second
planet from the Sun
JUPITER
Jupiter is the biggest
planet of them all
SATURN
It’s composed of
hydrogen and helium
MARS
Mars is actually a very
cold place
NEPTUNE
It’s the farthest planet
from the Sun

23. SKILLS
MARS
Despite being red, Mars
is a cold place
VENUS
Venus is the second
planet from the Sun
JUPITER
It’s the biggest planet
in the Solar System
SATURN
Saturn is a gas giant
and has several rings
Follow the link in the graph to modify its data and then paste the new one here. For more info, click here
19% 22%
11% 48%

24. MERCURY
It’s the closest planet to
the Sun and the smallest in
the Solar System
VENUS
Venus has a beautiful
name and is the second
planet from the Sun
MY INTERESTS
MARS
Despite being red, Mars is
actually a cold place. It’s
full of iron oxide dust

25. CONTACT ME
● ADDRESS
Your address here
● PHONE
001 664 123 4567
● MOBILE
001 664 123 4567
● EMAIL
Email address here

26. TABLET MOCKUP
You can replace the image on the screen
with your own work. Just right-click on it
and select “Replace image”

27. CREDITS: This presentation template was created by Slidesgo,
including icons by Flaticon and infographics & images by Freepik
THANKS
Do you have any questions?
youremail@freepik.com
+91 620 421 838
yourcompany.com
Please keep this slide for attribution

28. ALTERNATIVE RESOURCES
Here’s an assortment of alternative resources whose style fits that of this template:
● Close up scientist with coats
● Close-up scientist holding flask
● Medium shot woman wearing lab coat
● Female scientist with surgical gloves looking through microscope
● Side view of female scientist looking through microscope
● Side view of female scientist posing in the lab with microscope and surgical gloves
● Crop hand of man chalking graph on blackboard

29. RESOURCES
Did you like the resources on this template? Get them for free at our other websites:
PHOTOS
● Medium shot woman holding glasses
● Medium shot scientist with chemical substance
● Crop hand of man chalking graph on blackboard
● Woman taking notes in laboratory
● Female scientist with surgical gloves writing something on notepad
VECTORS
● Social activity and charity instagram posts

30. In order to use this template, you must credit Slidesgo by keeping the Thanks slide.
You are allowed to:
- Modify this template.
- Use it for both personal and commercial projects.
You are not allowed to:
- Sublicense, sell or rent any of Slidesgo Content (or a modified version of Slidesgo Content).
- Distribute Slidesgo Content unless it has been expressly authorized by Slidesgo.
- Include Slidesgo Content in an online or offline database or file.
- Offer Slidesgo templates (or modified versions of Slidesgo templates) for download.
- Acquire the copyright of Slidesgo Content.
For more information about editing slides, please read our FAQs or visit Slidesgo School:
https://slidesgo.com/faqs and https://slidesgo.com/slidesgo-school
Instructions for use

31. As a Premium user, you can use this template without attributing Slidesgo or keeping the "Thanks" slide.
You are allowed to:
● Modify this template.
● Use it for both personal and commercial purposes.
● Hide or delete the “Thanks” slide and the mention to Slidesgo in the credits.
● Share this template in an editable format with people who are not part of your team.
You are not allowed to:
● Sublicense, sell or rent this Slidesgo Template (or a modified version of this Slidesgo Template).
● Distribute this Slidesgo Template (or a modified version of this Slidesgo Template) or include it in a database or in
any other product or service that offers downloadable images, icons or presentations that may be subject to
distribution or resale.
● Use any of the elements that are part of this Slidesgo Template in an isolated and separated way from this
Template.
● Register any of the elements that are part of this template as a trademark or logo, or register it as a work in an
intellectual property registry or similar.
For more information about editing slides, please read our FAQs or visit Slidesgo School:
https://slidesgo.com/faqs and https://slidesgo.com/slidesgo-school
Instructions for use (premium users)

32. This presentation has been made using the following fonts:
Promt
(https://fonts.google.com/specimen/Prompt)
Atkinson Hyperlegible
(https://fonts.google.com/specimen/Atkinson+Hyperlegible)
Fonts & colors used
#212958 #ffffff #253483
#e8e9eb #e2aa28
#9a7720

33. Create your Story with our illustrated concepts. Choose the style you like the most, edit its colors, pick
the background and layers you want to show and bring them to life with the animator panel! It will boost
your presentation. Check out How it works.
Pana Amico Bro Rafiki Cuate
Storyset

34. You can easily resize these resources without losing quality. To change the color, just ungroup the resource
and click on the object you want to change. Then, click on the paint bucket and select the color you want.
Group the resource again when you’re done. You can also look for more infographics on Slidesgo.
Use our editable graphic resources...

37. JANUARY FEBRUARY MARCH APRIL
PHASE 1
Task 1
Task 2
JANUARY FEBRUARY MARCH APRIL MAY JUNE
PHASE 1
PHASE 2
Task 1
Task 2
Task 1
Task 2

40. You can resize these icons without losing quality.
You can change the stroke and fill color; just select the icon and click on the paint bucket/pen.
In Google Slides, you can also use Flaticon’s extension, allowing you to customize and add even more icons.
...and our sets of editable icons

41. Educational Icons Medical Icons

42. Business Icons Teamwork Icons

43. Help & Support Icons Avatar Icons

44. Creative Process Icons Performing Arts Icons

45. Nature Icons

46. SEO & Marketing Icons

47. Add the title here
Text 1 Text 2 Text 3
Text 4 Text 5 Text 6
2016 2017 2018 2019 2020
“Despite being red,
Mars is actually a
very cold place”
“Mercury is closest
planet to the Sun
and the smallest”
“Neptune is the
farthest-known
planet from the Sun”
“Saturn is a gas
giant and has
several rings”
“Venus is the
second planet from
the Sun and is
terribly hot”
Premium infographics

48. “Mercury is closest
planet to the Sun
and the smallest”
TITLE 1
75% “Mercury is closest
planet to the Sun
and the smallest”
“Mercury is closest
planet to the Sun
and the smallest”
“Mercury is closest
planet to the Sun
and the smallest”
75%
Premium infographics