Oct 18, 2020
Child on a swing – classroomclipart.com
Many of us have fond memories of sitting on a swing and learning how to make it go to and fro giving us a feeling of weightlessness for just a few moments. In an article from teachengineering.org we get to understand the science behind this awesome childhood activity.
Today we learn what a pendulum is and how it works in the context of amusement park rides. While exploring the physics of pendulums, we are also introduced to Newton's first law of motion — about continuous motion and inertia.
Pendulums are used in many engineered objects, such as clocks, metronomes, amusement park rides and earthquake seismometers. In addition, engineers know that understanding the physics of how pendulums behave is an important step towards understanding motion, gravity, inertia and centripetal force. Engineers apply their understanding of these motion concepts to determine the force needed to propel an object into outer space, the braking power required to stop a vehicle at high speeds, and the optimal curve of a highway ramp. Teams of engineers work on a wide range of projects and solve problems that are important to society.
Who has been on an amusement park ride called the Sea Dragon? Or, on a similar amusement park ride that looks like a big swinging ship? To get this ride started, a strong motor pushes the ship in an upward direction. Did you know that, after the ride is started, the motor does not need to do any more work, and the ride continues on its own? How do you think the ride stays in motion? Well, after the motor gives it an initial push, the ride uses inertia to keep moving. Inertia is the property of an object to stay moving unless it is stopped by an outside force.
Why doesn't the ride fly all the way around (360 degrees)? Well, gravity pulls the ride down when it gets high above the Earth. Even though the ride is pulled down by gravity, the inertia of the object pushes the ride right back up into the air, creating a swinging motion. Once the ride is in motion, it stays in motion unless an outside force slows it. At an amusement park, a ride like this is stopped by brakes, or else it would just keep swinging and you would be riding it long after closing time! To explain the amusement park ride the way we just did, we used the ideas of a pendulum and Newton's first law of motion.
Who has heard of a pendulum before? A pendulum is made of an object with a mass, called a bob that dangles from the end of a rod or string and swings freely. The amusement park ride we just talked about is actually a huge pendulum. Can anyone think of another example of a pendulum? Anything that swings under its own weight is a pendulum — a playground swing, a curtain cord or a carpenter's plumb. Even your own legs behave like pendulums. In fact, the most efficient way to walk is to let your legs swing at their natural rate. The time it takes for your leg to make its back and forth movement depends on the length of your legs. That's why long-legged people sometimes appear to saunter along; short-legged people, to walk briskly. Some clocks, such as a grandfather clock, have a pendulum that swings to keep track of time. Because pendulums continue to swing without changing their speed unless acted on by an outside force, they can accurately help us measure things like time.
The type of pendulum we described with the Sea Dragon ride is known as a simple pendulum, because it only moves back and forth (like the swings on a playground swing set). Another type of pendulum is a spherical pendulum, in which the bob not only moves back and forth, but in a circular motion. Can anyone think of an example of a spherical pendulum? A tether ball moves as a spherical pendulum. Another example is an amusement park ride that spins you in a big circle. An amusement park ride works like a spherical pendulum.
Why does a pendulum stay in motion? More than 300 years ago, an Englishman named Isaac Newton described the natural behavior of motion and gravity in our world, in what he called the "three universal laws of motion." Newton's first law of motion says that an object in motion stays in motion and an object at rest stays at rest, unless acted upon by an outside force. So, something that is moving keeps moving until something else stops it. Does this remind you of the Sea Dragon ride? Or, have you ever been able to stop ice skating or roller skating without the help of an outside force (perhaps dragging your foot or crashing into someone)? Or, how do you stop when you are swinging on a playground swing?
Sometimes moving objects seem to stop without the help of an outside force. For example, if you slowly roll a ball across the floor, it eventually stops on its own. Does that mean Newton's first law of motion does not always hold true? No! The floor has roughness or friction — a resistance to motion — that slows the ball. In this case, friction is the outside force that stops the ball from rolling. Pendulums work so well because they move through air, which has very little friction.
Engineers often incorporate the ideas of the pendulum and Newton's first law of motion when they design things that we use everyday or that help people in some way. In fact, engineers always must consider the "invisible" natural forces acting on objects in motion, such as inertia, to keep us safe. What are some ways that an engineer might be able to use a pendulum? The continuous swinging of a pendulum keeps time for some clocks.
Engineers use pendulums in designing lots of things, from clocks to amusement park rides. Some engineers who study the Earth and earthquakes, design equipment and sensors such as seismometers, which use the idea of a pendulum to measure earthquakes. Understanding pendulum mathematics helps engineers determine how much swaying back and forth a building can safely withstand during a windstorm or earthquake. If a building might build up too much inertia moving it back and forth, then engineers must figure out ways to safely counteract the movement to protect the people and property. Real-world applications like these make the pendulum and inertia important concepts for engineers — and you — to understand.
Newton's First Law of Motion
Newton's three laws of motion make up the foundation for the known physics of motion. The first law states that an object in motion stays in motion and an object at rest stays at rest, unless acted upon by an outside force. This is the concept of inertia. For example, a book falls until it hits a table, and then the book stops falling because an outside force stopped it from its original path of motion.
Gravity
One of the greatest forces acting on our planet is the force of gravity. This is the force that holds objects down to the Earth, keeping them from flying off into space. In the case of a pendulum, gravity is the force pulling the mass down, while inertia is the property keeping the mass in motion and pulling it back up. When sitting on a swing, the swing does not move until you are pushed or you pump your legs, creating the force that sets you in motion. But, you continue swinging, without extra pumping, until the friction of the air and the swing chain resist the motion. Gravity pulls you down, and inertia keeps you moving (until friction intervenes).
Mathematics of a Pendulum Swing
The motion of a pendulum was first mathematically described by the Italian Galileo Galilei in the late 1500s. Galileo also investigated how things fall, how planets move, and many other natural scientific phenomena. Many of his discoveries grew out of his observations of how a pendulum swings.
As explained by Galileo, we know that the period of a pendulum can be described mathematically by the following equation:
Where:
P = period; which is the time for one pendulum swing [sec]
l = length from the fixed point at the top of the pendulum to the center of mass of the bob [m]
g = gravitational constant (9.8 m per sec2)
π ≈ 3.14 (Pi - dimensionless constant)
Note that this equation does not include terms for the mass of the pendulum or the angle it swings through. The only factor that significantly affects the swing of a pendulum on Earth is the length of its string.
Vocabulary/Definitions
Bob: The weight at the end of the string or rod of a pendulum.
Engineer: A person who applies his/her understanding of science and math to creating things for the benefit of humanity and our world.
Engineering: Creating things for the benefit of humanity and our world.
Friction: A resistance to motion.
Gravity: The Earth's force that pulls everything downward.
Inertia: The property of an object to stay moving unless it is stopped by an outside force.
Newton's first law of motion: An object in motion stays in motion and an object at rest stays at rest, unless acted upon by an outside force
Pendulum: An object attached to a fixed point by a string or rod so that it can swing freely under the influence of gravity and acquired momentum often used to regulate devices, such as clocks.
Simple pendulum: A pendulum that swings back and forth.
Spherical pendulum: A pendulum that swings in a circular motion.
Now that we've learned all about pendulums and Newton's first law of motion, can you explain how the Sea Dragon or big boat swing amusement park ride works? Remember, a pendulum is made of an object with a bob that dangles from the end of a rod or string and swings freely. Newton's first law tells us that an object at rest stays at rest (without outside interference), so a motor must first push the amusement park ride up into the air. Then gravity pulls the ride back down. The ride has inertia, which keeps it in motion. The ride moves up and down with the help of inertia and gravity. The only thing that can stop the ride is friction, which is supplied from the brakes.
Would you want to design an amusement park ride? What ideas do you have? How else do engineers use the ideas they get from pendulums and Newton's first law of motion? Engineers incorporate pendulums in many projects — such as designing clocks, designing amusement park rides, studying the Earth and earthquakes with seismometers, and determining how much swaying movement a structure or tower can safely withstand during storms.
Now that you know how a pendulum works, if you can convince the amusement park ride operator not to use the brakes, you could stay on the amusement park ride for even longer!
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