Content Benchmark P.12.B.4
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Students know the strength of the gravitational force between two objects increases with mass and decreases rapidly with distance. I/S

Students know the strength of the gravitational force between two objects increases with mass and decreases rapidly with distance. I/S

Most students will be able to say that gravity is the force that pulls things down. Though known prior to his birth, Newton is credited with the discovery that gravity is universal (i.e., any object with mass has a gravitational field). The force that causes objects to “fall” (all objects are PULLED to the CENTER of a mass) on Earth is the (1) same force that causes the Earth to continuously orbit the Sun, and in turn, (2) the Sun to revolve around the center of the Milky Way Galaxy.

Figure 1. Shows the effect of an increasing mass and an increase in distance between the masses (from http://www.physicsclassroom.com/ Class/circles/U6L3c.html)

Gravity, the name referring to the attractive forces between objects, is a theory explaining the cause of these attractions. Through observations of its affect on objects and the use of Newton’s laws of motion, gravitational force is measurable. Gravitational force is a field force that is infinite in distance and therefore extends throughout the universe. However, gravitational force diminishes greatly with separation between the masses (the inverse square law). Newton’s Law of Universal Gravitation states that every object attracts every other object and that the force of attraction is directly proportional to the masses of the objects; and, as stated above, inversely proportional to the square of the distances between the two masses. This law is represented symbolically as:

m₁ = mass of the first object (kg)

m₂ = mass of the second object (kg)

d² = the square of the distances between the centers of the masses (m)

To learn more about Newton’s Law of Universal Gravitation go to http://www.physicsclassroom.com/Class/circles/U6L3c.html.

Thanks to experiments by Henry Cavendish, Newton’s Law of Universal Gravitation can be written as an exact equation when including the Universal Gravitational Constant (G). Cavendish, in the eighteenth century, measured the torsion force in a bar as two large lead spheres were brought close to the masses at the end of the bar. By carefully measuring all the masses, the force of torsion, and the distance the balance was twisted, Cavendish could calculate G. Due to Cavendish’s discovery of the gravitational constant, G = 6.67 x 10-11 N m2/kg2 the universal gravitational law can be written as the exact equation:

F = force (N)
G = gravitational force constant (6.67 x 10-11 N m2/kg2)
m₁ = mass of the first object (kg)
m₂ = mass of the second object (kg)
d² = the square of the distances between the centers of the masses (m)

Gravity is one of the four fundamental forces (the others are the strong nuclear, electromagnetic, and weak nuclear). With G being so small, gravity is the weakest of the four fundamental forces.

To learn more about the four fundamental forces, go to
http://hyperphysics.phy-astr.gsu.edu/hbase/forces/funfor.html#c1

Figure 3. This is a quantitative graph that shows the acceleration on an object, due to the force of gravity, decreasing as the distance between the masses increases. (from http://www.physicsclassroom.com/Class/circles/U6L3e.html)

For more information about the inverse square law and gravity go to http://hyperphysics.phy-astr.gsu.edu/hbase/forces/isq.html#isqg.

Einstein furthered Newton’s work on gravitation with General Relativity, where the cause of the gravitational force is described. In General Relativity, gravitation is a geometric property caused when masses deform space and time. We perceive this geometric property as a force of attraction between masses as defined by Newton’s Law of Universal Gravitation. To learn more about General Relativity, go to http://archive.ncsa.uiuc.edu/Cyberia/NumRel/GenRelativity.html

Other concepts associated with gravity include weight, centripetal force, tides, and escape velocity. To learn more about the connection to gravity, go to
http://hyperphysics.phy-astr.gsu.edu/hbase/grav.html#grvcon.

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Performance Benchmark P.12.B.4

Students know the strength of the gravitational force between two objects increases with mass and decreases rapidly with distance. I/S

Common misconceptions associated with this benchmark:

1. Students incorrectly think that Earth's gravity does not extend beyond the atmosphere and this is why astronauts are “weightless.”

Astronauts appear to be weightless because they are in constant freefall. While the space shuttle, with the astronaut inside, is in orbit around Earth, the shuttle’s velocity is tangential to the orbital path. Because the gravitational force is pulling the shuttle towards the center of Earth and the velocity of the shuttle is tangential, the resulting path of the shuttle is elliptical. This path is what allows freefall to continue, and allows for the apparent weightlessness. This misconception typically stems from the students difficulty in understanding the independence of motion in an x and y coordinate system. In reality, an astronaut orbiting at 400 km above the Earth’s surface will experience g value of approximately 8.7 m/s² (as compared to 9.8 m/s² at Earth’s surface). The astronaut’s resulting weight is only about 10% less at 400 km than at Earth’s surface.

A lengthy description of this misconception is described at http://www.merga.net.au/documents/RP722005.pdf.
Learn more about the physics of orbit at http://www.physicsclassroom.com/Class/circles/U6L4d.html.

2. Students incorrectly think that there is no gravity on the moon.

This misconception may stem from video footage of astronauts on the Moon. The astronauts appear to “float” as they walk across the surface. Because the Moon has mass, it has gravity. Students should understand that the gravitational force between the astronaut and the moon is less because the mass of the moon is so much less than that of the Earth. Because the astronaut’s leg muscles are accustom to carrying a weight six times greater, the astronaut has a much easier time getting around. On the surface of the Moon, the acceleration due to gravity is about 1/6th as much as the Earth’s.

To learn more about this misconception and available resources go to http://hypertextbook.com/facts/2004/MichaelRobbins.shtml.

3. Students often incorrectly believe that gravity increases with height above the Earth's surface.

This is probably due to a misunderstanding of the inverse square law. As distance increases between two masses the force between those masses decreases rapidly.

Read more about Newton’s Law of Universal Gravitational and complete some calculations at http://www.physicsclassroom.com/Class/circles/U6L3c.html.

4. Students incorrectly think that mass and weight are the same, and that they are constant.

Mass is the amount of matter in an object and is directly responsible for the amount of gravitational force. The more massive the object, the larger the gravitational force (the mass of an object can change if pieces of the object are removed). Weight is the affect of a gravitational force on a mass. When a student steps on a scale the student is measuring the amount of gravitational force that is being applied to his mass. If the student was to travel to the moon his mass would be the same, but his weight would decrease by 1/6th. What a diet!

To see actual question that students have asked and the responses given by physicists go to http://amazingspace.stsci.edu/eds/tools/topic/gravity.php.
p=Teaching+tools%40%2Ceds%2Ctools%2C

4. Students incorrectly think that gravity is caused by magnetic fields.

The magnetic fields on Earth provide for a habitable planet because they block solar radiation and are the cause of auroras. Gravity, however, is only caused by mass. The more massive the object, the larger the gravitational force.

To learn more about students understanding of gravity, and for a list of common misconceptions go to
http://www.physics.umaine.edu/ncomins/gravity.htm.

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Performance Benchmark P.12.B.4

Students know the strength of the gravitational force between two objects increases with mass and decreases rapidly with distance. I/S

Sample Test Questions

1. Of the four fundamental forces, which force is the weakest?
a. Strong nuclear force
b. Gravitational force
c. Electromagnetic force
d. Weak nuclear force

2. Which of the following statements about a space shuttle orbiting Earth is true?
a. The astronauts inside the space shuttle are in a gravity free environment.
b. The astronauts inside the space shuttle will experience an absence of mass.
c. The astronauts inside the space shuttle are in constant freefall.
d. The astronauts inside the space shuttle will experience an increase in weight.

3. If Earth suddenly became twice its’ current mass, but its size remained the same, what affect would you notice?
a. Your weight would become twice as great.
b. Your mass would become twice as great.
c. Your weight would become half as much.
d. Your mass would become half as much.

4. A 500 m ladder is placed vertically and you start to climb to the top. Which of the following would be true?
a. As you climbed the ladder your weight would increase.
b. As you climbed the ladder your mass would increase.
c. As you climbed the ladder your weight would decrease.
d. As you climbed the ladder your mass would decrease.

5. What is the cause of the gravitational force between the Earth and the Sun?
a. Earth’s magnetic field causes the gravitational force.
b. The Sun’s rotation about its axis causes the gravitational force.
c. The masses of both the Earth and Sun cause the gravitational force.
d. The tangential velocity of the Earth causes the gravitational force.

6. Which of the diagrams below has the smallest gravitational force between the masses?

Students know the strength of the gravitational force between two objects increases with mass and decreases rapidly with distance. I/S

Answers to Sample Test Questions
1. (b)
2. (c)
3. (a)
4. (c)
5. (c)
6. (d)

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Performance Benchmark P.12.B.4

Students know the strength of the gravitational force between two objects increases with mass and decreases rapidly with distance. I/S

Intervention Strategies and Resources

The following is a list of intervention strategies and resources that will facilitate student understanding of this benchmark.

1. Black Holes and Gravitation
The Adler Planetarium and Astronomy Museum have put together a fairly complete thematic unit about gravity through the lens of Black Hole exploration. The objectives of their unit are:
a. Students will be able to identify gravity as the main mover and shaper of the Universe.
b. Students will identify and describe black holes as extreme examples of gravity.
c. Students will illustrate that our understanding of gravity continues to evolve.

To access the site, go to http://www.adlerplanetarium.org/education/resources/gravity/gravity9-12.pdf

The content resources document can be found at their site: http://www.adlerplanetarium.org/education/resources/gravity/9-12_cb1-1.shtml

2. History of Gravity Debate
The Adler Planetarium and Astronomy Museum have also put together a Socratic debate about the history of gravity. It includes web-based material that students can use to collect information about past ideas. I believe that evaluating past scientists’ work as well as other students interpretation of their work will help weed out misconceptions that students have prior to discussions about the Law of Universal Gravitation.

To view the debate, go to http://www.adlerplanetarium.org/education/resources/
gravity/5-8_gq4-1.pdf

3. The Physics Classroom
Physicsclassroom.com is a website that provides tutorials for students. Students can read about information and concepts that are presented in class, view diagrams and animations, and answer questions. Lesson 3 in “Circular Motion and Planetary Motion” starts off with Newton’s Law of Universal Gravitation.

To visit the tutorials, go to http://www.physicsclassroom.com/Class/circles/U6L3a.html.

4. ASU Physics Modeling Program
Arizona State University runs a modeling physics program. In that program students are given a force concept inventory, the results of the inventory highlight misconceptions about forces.

These misconceptions are found at this site, http://modeling.asu.edu/R&E/forceConceptionTaxon92.doc.

The program at ASU also offers materials that can easily be used in the classroom at http://modeling.asu.edu/Curriculum.html.

A unit overview that deals specifically with this benchmark is found at http://modeling.asu.edu/Modeling-pub/Mechanics_curriculum/
4-FP-inertia/01_U4%20Teachernotes.pdf, or in unit four from the curriculum page.

5. HyperPhysics Web Site
HyperPhysics (http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html) is a Web site from Georgia State University. This is one of the most complete physics content resources available. The site is a lattice of concept maps with hyperlinks to each topic. Most topics have an outline of content with links to further content, applets for practice problems, and further resources.

The section that deals with the gravitation benchmark is http://hyperphysics.phy-astr.gsu.edu/hbase/grav.html#grav. From here students can click on concepts within the map to view more information, and see the interconnections throughout the basic physics concepts.

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