Lesson: How Do Things Fall?Contributed by: Integrated Teaching and Learning Program, College of Engineering, University of Colorado Boulder
Educational Standards :
Learning Objectives (Return to Contents)
After this lesson, students should be able to:
Introduction/Motivation (Return to Contents)
(Challenge students to jump in the air and try to stay there without holding on to anything or standing on anything.) Why can't you stay up in the air? (Answer: It cannot be done, due to gravity.) The effects of the force of gravity are far-reaching and dramatic. All matter in the universe is pulled towards all other matter by gravitational attraction. Objects that have more mass pull more than objects with less mass. That's why we say we are pulled towards the surface of the Earth, rather than saying the Earth is pulled to us, when, in fact, both statements are true!
Gravity is the dominant force in the universe. Gravity keeps planets in their orbits around the sun, and the moon in orbit around the Earth. Gravity is why the planets are round, and gravity pulled enough mass together to make the Sun hot. On a smaller scale, gravity is why baseballs don't always fly out of the ball park when they're hit.
It is useful to know about the force of gravitational attraction to make predictions about how things fall or stay up. If scientists and engineers didn't know how the force of gravity behaves, they couldn't build spaceships, airplanes or buildings! Luckily, since gravity is everywhere, there are some good ways to learn more about how it works. People can measure how strong gravity is, and what direction in which it pulls. We can learn how things fall with some experiments that we can do anywhere in the world, or even at out-of-the-world places like the moon!
Understanding gravity is so important that scientists have launched two satellites for the purpose of measuring the force of gravity all over the Earth. The gravity field of the Earth is fairly uniform and differences are not easily perceptible. However, if you have a very sensitive gravity meter, you can measure small variations in the Earth's gravity field. Aerospace engineers in the US and Germany designed and built two satellites, nicknamed Tom and Jerry, and launched them into space in March 2002. Tom follows Jerry in the same orbit, with Tom always about 200 kilometers behind Jerry. Small changes in gravity under the satellites cause small changes in the distance between them. Other forces like drag from the atmosphere also change the distance between Tom and Jerry. Scientists and engineers developed instruments that let them measure only the movements in Tom and Jerry that are caused by gravity. This allows the satellites to monitor movement of mass in the ocean, atmosphere, land surface and polar ice until about 2015. See http://www.csr.utexas.edu/grace/ to learn more about the Gravity Recovery and Climate Experiment (GRACE).
Hand out the Planetary Mass and Gravity Worksheets and give students 10 minutes to complete them.
Just like the aerospace engineers who launched Tom and Jerry to measure gravity all over the Earth, we will use scientific instruments to learn more about the effects of gravity.
Lesson Background & Concepts for Teachers (Return to Contents)
On the Shoulders of Giants: The Law of Universal Gravitation
Gravity is responsible for much of the structure of the universe. Indeed, it is the dominant force in the universe. The planets continuously travel around the sun in elliptical orbits. Many moons orbit the various planets. Saturn's rings are composed of orbiting bodies ranging from huge ice boulders to tiny ice particles. The asteroid belt consists of countless chunks of material, all orbiting the sun. Satellites are held in their orbit by Earth's gravitational pull. Even Earth's nearly spherical shape is caused by gravity. And, any object you drop on Earth will fall toward the center of the Earth.
Many important scientific developments preceded Sir Isaac Newton and enabled him to understand the force of gravity. Galileo developed the ideas of acceleration and inertia through careful observation and experimentation with inclined planes and falling objects. Tycho Brahe built the first astronomical observatory capable of precise measurement and compiled 20 years of data showing the planets' motions and positions throughout the year. Johannes Kepler used Brahe's data to determine the laws of planetary motion (Kepler's laws of planetary motion). He was the first to show that the planets move in elliptical orbits with the sun at one focus of the ellipse (Kepler's first law). Kepler also determined that the speed of a planet changes as it moves through its orbit, with the planet moving faster when it is nearer the sun (Kepler's second law). Finally, Kepler determined that the square of the time for a planet to complete one orbit is proportional to the cube of its average distance from the sun (Kepler's third law). Newton was the first person to understand how the work of Galileo and Kepler fit together.
First, Newton recognized that an object moves in a straight line unless a force acts upon it (Newton's first law of motion). Using Kepler's second law, Newton was able to show that the force acting on the planets was toward the sun, because the orbits curved toward the sun. Based on Kepler's third law, Newton was able to determine that the force from the sun is inversely proportional to the square of the distance between the sun and a planet. Newton had also observed that there is a force between a falling object and the Earth that makes the object fall. He conceived that the force between the Earth and a falling object was the same as the force between the sun and a planet.
So, although Newton didn't discover gravity, he realized that gravity was a universal force and determined its magnitude. He was the first to understand that every object in the universe is gravitationally attracted to every other object in the universe. Newton said that he was able to comprehend gravity because he "stood on the shoulders of giants," crediting the important work of such thinkers, astronomers and scientists as Galileo, Brahe and Kepler.
What is the Law of Universal Gravitation? How Does It Describe Gravity?
The Law of Universal Gravitation, one of Newton's great achievements, states that the gravitational force between two objects is proportional to the masses of the objects and inversely proportional the square of the distance between them:
Where: g = gravitational constant (9.8 m/sec2)
m1 = mass of the first object [kg]
m2 = mass of the second object [kg]
d = distance between the two objects [m]
F = gravitational force [N]
The gravitational force between any two objects is always attractive. That is, any two objects will accelerate toward each other due to their gravitational attraction. When an apple falls from a tree, the Earth pulls on the apple, but the apple also pulls on the Earth.
How Does Gravity Compare with the Other Forces?
There are four fundamental forces in nature: the gravitational force, the electromagnetic forces, the strong nuclear force and the weak nuclear force. Gravity is the weakest of the four fundamental forces. Gravity is always attractive, while the electromagnetic force can be either attractive or repulsive. The strong and weak nuclear forces dominate at distances smaller than the size of the nucleus of an atom. The electromagnetic force dominates at the atomic level. But gravity dominates in the universe, even though it is the weakest force, because there is so much matter in the universe and much of it is aggregated into sizeable lumps. So, beyond the atomic level, gravity is the dominant force.
What Is Weight? How Can an Object Be Weightless?
A force produces acceleration of the body on which the force is applied. Any two objects will accelerate toward each other due to their gravitational attraction. If they are already touching, they still exert a gravitational force on each other. Weight is the force an object exerts against some supporting structure such as a floor or a scale. An object's weight is equal to the product of its mass and the gravitational acceleration constant:
W = mg
Where: m = mass of the object (kg)
g = gravitational constant (9.8 m/sec2)
So, an object's weight varies depending on the gravitational acceleration it is experiencing, whereas its mass is always the same. You would weigh much more on Jupiter and much less on the moon than you do on Earth. You even weigh slightly more on the top of a mountain compared to your weight in the deepest ocean trench because there is more mass between you and the center of the Earth, and therefore a greater gravitational acceleration, when you are on top of a mountain.
An object is weightless when it is in free fall — its acceleration is equal to the gravitational acceleration. Even though there is still gravitational force acting on an astronaut in free fall the astronaut feels weightless because there is no supporting structure against which to feel weight. Even if a scale were held at the astronaut's feet, it wouldn't read a weight for the astronaut because it would be falling with the same acceleration as the astronaut. Of course, the astronaut still has weight, but cannot sense it due to the lack of a supporting force. This type of weightlessness isn't "true weightlessness." True weightlessness can only occur when all the gravitational forces on a body are exactly canceled such that the body experiences no gravitational force at all and, therefore, travels in a straight line.
Vocabulary/Definitions (Return to Contents)
Associated Activities (Return to Contents)
Lesson Closure (Return to Contents)
Lead a class discussion on the force of gravity. Use the following questions to stimulate discussion. What objects are affected by gravity? (Answer: All objects.) Does the force of gravity pull things together, or push them apart? (Answer: Pull things together.) What happens if you drop two similarly shaped objects — one heavy and one light — at the same time? (Answer: They reach the ground at the same time because gravity accelerates them both the same amount. Since they are shaped the same, they are slowed down the same amount by air resistance and hit the ground at the same time.) What if you drop two objects having the same mass, but one object is small and the other is large and flat? (Answer: The small object hits the ground first because the large, flat object is slowed down by air resistance.)
Attachments (Return to Contents)
Assessment (Return to Contents)
Brainstorming: In small groups, have the student engage in open discussion. Remind students that no idea or suggestion is "silly." All ideas should be respectfully heard. Ask the students:
Prediction: If you drop two items that are shaped the same, have the students predict which will hit the ground first, the heavier object, or the lighter object? (Answer: They will hit the ground at the same time.)
Voting: Ask a true/false question and have students vote by holding thumbs up for true and thumbs down for false. Count the votes, and write the totals on the board. Give the right answer.
Lesson Summary Assessment
If students successfully completed their Planetary Mass and Gravity Worksheet without help from peers, they have demonstrated an evidence-based understanding of the relationship between mass and gravity.
Send-a-Problem: Have students write their own questions about gravity. Each student on a team creates a flashcard with a question on one side and the answer on the other. If the team cannot agree on an answer they should consult the teacher. Pass the flashcards to the next team. Each member of the team reads a flashcard and everyone attempts to answer it. If they are right, they pass the card on to another team. If they feel they have another correct answer, they can write it answer on the back of the flashcard as an alternative answer. Once all teams have tested themselves on all the flashcards, clarify any questions.
Lesson Extension Activities (Return to Contents)
Assign students to conduct an Internet or library search to learn about artificial satellites: Have students look up information about man-made satellites and answer the following questions: How are they used? Who uses them? What are the typical orbits they use? Who designs and builds artificial satellites? What are natural satellites? Why do satellites not fall back to the ground? Lead a brief discussion of student findings during the next class period.
References (Return to Contents)
Gravity Recovery and Climate Experiment (GRACE) project:http://www.csr.utexas.edu/grace/.
Hewitt, Paul G. Conceptual Physics. Boston, MA: Little, Brown and Company, 2002.
Kagen, S. Cooperative Learning. San Juan Capistrano, CA: Kagan Cooperative Learning, 1994. (Source for Send-a-Problem assessment.)
Leaning Tower of Pisa: http://www.endex.com/gf/buildings/ltpisa/ltpnews/physnews1.htm.
ContributorsXochitl Zamora-Thompson, Ben Heavner, Malinda Schaefer Zarske, Denise W. Carlson
Copyright© 2004 by Regents of the University of Colorado.
Supporting Program (Return to Contents)Integrated Teaching and Learning Program, College of Engineering, University of Colorado Boulder
Acknowledgements (Return to Contents)
The contents of this digital library curriculum were developed under a grant from the Fund for the Improvement of Postsecondary Education (FIPSE), U.S. Department of Education and National Science Foundation GK-12 grant no. 0338326. However, these contents do not necessarily represent the policies of the Department of Education or National Science Foundation, and you should not assume endorsement by the federal government.