Introduction:

This lesson is designed for middle school students with no previous knowledge of centripetal motion or centrifugal force. Also, this lesson does not require that students know anything of Newton's Laws of Motion. This lesson relies quite a bit on students' intuitive understanding of motion and experimentation with motion during the lesson. As such, this lesson could take as long as an hour and as short as thirty minutes depending on how much time you spend demonstrating and experimenting with a merry-go-round (if you have one accessible).

Group Size:

Any

Learning Objectives:

  • Describe centrifugal force and be able to explain why it's not real
  • Describe centripetal motion and why it occurs
  • Explain how centripetal motion and centrifugal force relate to a roller coaster

Guiding Question:

Why was the Scientific Revolution important and how did it contribute to progress?

Materials:

Image, ball on a string or bucket w/ on a string, merry-go-round (if available).

Additional resources:

Books:

  • The Story of Science Newton at the Center by Joy Hakim. Published by Smithsonian Books, 2005. (Chapter 13)
  • The World's Wildest Roller Coasters by Michael Burgan. Published by Capstone Press, 2000.

Procedure:

[Note: This lesson in its entirety can be found as an attached pdf and doc file.]

Lesson Summary:

  • Describe centrifugal force
  • Describe centripetal force
  • Explain the difference between centripetal and centrifugal force
  • Apply each of these forces to a roller coaster ride

Lesson: Centripetal motion

[Start this lesson with the ball and string swinging demonstration. Another demonstration that’s impressive to students: tying a bucket to the end of a light rope, filling it ½ full with water, and swinging it around your head...the water doesn’t come out, students think it’s awesome, and they love to experiment with it themselves.]

Centrifugal and Centripetal Force
Centripetal motion is the motion of an object on a curved path. Think about the ball on the string. If I were to let it go, would it continue in an orbit around my head? [No. You may want to demonstrate what does happen....this requires some space]. But, this is where things start to get tricky. An object traveling in a circle behaves as if it is experiencing an outward force. This force, known as the centrifugal force, depends on the mass of the object, the speed of rotation, and the distance from the center.

In general, the following things are true:

  • The more massive the object, the greater the force
  • The greater the speed of the object, the greater the force
  • The greater the distance from the center, the greater the force
But, here’s the kicker: centrifugal force does not actually exist! It appears quite real to the object being rotated. Think about times you’ve been on a merry-go-round [it’s great if there’s a public park near-by to actually do this on]. Nothing is actually pushing you outward, but as you’re spinning, you feel that if you don’t hold on, you’ll fly off. That’s because the centrifugal force appears so real, it is often very useful to use as if it were real, so we do.

The more massive the object, the greater the force. Think about it...it is much harder for an adult to stay on a merry-go-round than for a child, just as it takes more force to swing a bowling ball around versus a ping-pong ball.

The greater the speed of rotation, the greater the outward force. We know that this is true because a merry-go-round is harder to stay on, the faster it rotates. If you move further out on the merry-go-round, you will have to exert a greater force to stay on. [Try standing in the middle of the merry-go-round versus at the edge as it’s spinning.] In order to stay on a circular path, we must exert a force towards the center.

The force you exert toward the center to stay on the merry-go-round, the “center-seeking” force, is called the centripetal force.

How Does This Relate to a Roller Coaster?
When an object moves in a circle, which is effectively what a roller coaster does when it travels through a loop, the moving object is forced inward toward what's called the center of rotation. It's this push toward the center -- centripetal force -- that keeps an object moving along a curved path.

Centripetal force prevents moving objects from exiting a curve by continuously making them change their direction toward the center of rotation. For a roller coaster, gravity pulls down on the cars and its riders with a constant force, whether they move uphill, downhill, or through a loop. The rigid steel tracks, together with gravity, provide the centripetal force needed to keep the cars on the arching path as they move through the loop.

Gravity always pulls downward with the same strength, and, in the case of a roller coaster, it pulls downward on the cars wherever they are on the track. Near the bottom of a loop, gravity pulls in a direction away from the center of the loop circle. Here, the centripetal force is the difference between the force of the track pushing up and gravity pulling down. Near the top of the loop, however, gravity and the track both act with a downward force and work together to provide the centripetal force; their forces add together. Regardless of where the cars are in the loop, centripetal force is always directed toward the center of rotation. So even if a car you're riding in is at the top of a loop, upside-down, you will feel yourself pressed into your seat. [This is a good place to use a diagram of a roller coaster and arrows of forces]

Often, people confuse centripetal force with centrifugal force. The sensation roller coaster riders experience that makes them feel like they're being pushed into their seats as they go through a loop is commonly referred to as centrifugal force, which, as we talked about before, isn’t really a force at all. Whereas, the centripetal force is an actual force, it’s the one that’s pulling you toward the center of rotation.

To better understand the distinction, put yourself in the rider's place. When the roller coaster car you're riding in changes direction, your body continues to travel in the same direction it was traveling in before the change in direction. If the car and track weren't there, you would continue on this path. As a result, you find yourself pressed against the seat throughout the loop -- perhaps most surprisingly at the top, when you're completely upside-down! If you were to observe your motion relative to the car, however, you'd realize that the seat is actually pushing down on you, inward toward the center of rotation.

Assessment:

Students are asked to answer a series of short answer questions. The assessment can be found as a separate wiki page here, where there is also a pdf and doc version available for download.

Attached Files:

Centripetal Motion Lesson (pdf)
Centripetal Motion Lesson (doc)

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