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Content Benchmark P.8.B.3
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 Physical Science Matter Force and Motion P.8.B.1 P.8.B.2 P.8.B.3 Energy Content Areas Nature of Science (NOS) Life Science Earth Science Physical Science  Students know every object exerts gravitational force on every other object, and the magnitude of this force depends on the mass of the objects and their distance from one another. I/S

In order to understand the subject of gravity and how it behaves, it is important to understand the difference between mass and weight. Many people use these terms interchangeably, however to a scientist these two terms have very different meanings.

Mass is a measure of how much matter is contained in an object. Every atom has a certain mass, and the more atoms there are the more mass an object has. The mass of an object (measured in kilograms) will be the same no matter where in the universe the object is located. Mass is not altered by location, the pull of gravity, or even the existence of other forces. A 5 kg object will have a mass of 5 kg whether it is located on Earth, the Moon, or even Pluto!

Newton's First Law of Motion states that an object at rest tends to stay at rest and an object in motion tends to stay in motion unless acted upon by an unbalanced force. In other words, objects keep on doing what they're doing. Do all objects have the same amount of this "tendency"? NO! Consider an elephant and a mouse both sitting at rest on the ground. When applying the same force to each animal, which one seems more resistant to changing its state of motion? The elephant does, as it has greater mass and therefore a greater "sluggishness" or resistance to change in motion. Inertia is the resistance an object has to a change in its state of motion. The more massive an object, the greater its inertia.

Weight

Weight is the force exerted on an object with mass by a gravitational field, such as that found around a planet. Weight is experienced as a reaction to this force against a solid surface. Weight is calculated as the mass of the object times the acceleration of gravity, w=mg. Since weight is a force, its SI unit is the Newton.

Figure 1 illustrates the astronaut having a mass of 120 kg on both the Earth's and Moon's surface. However, the astronaut's weight on the Moon is 1/6th his weight on Earth. The difference in weight is a result of the gravitational force being weaker on the Moon - the Moon has less mass than Earth and therefore has less gravitational pull, by 1/6th (accepted accelerations due to gravity for Earth and Moon are gEarth = 9.81 m/s2 and gMoon = 1.66 m/s2). Figure 1. Mass is constant while weight is affected by location.
(From http://www.daviddarling.info/encyclopedia/W/weight.html)

Table summarizing the difference between mass and weight

Mass Weight
• Fundamental property of the object (amount of matter in object)
• Constant at any location
• Numerical measure of inertia(resistance to change)
• SI unit is the kilogram
• Force created when a mass is acted upon by a gravitational field
• Value (magnitude) dependent upon location
• SI unit is the Newton (1N = 1kg x m/s2)

Table 1. Mass and Weight Compared

Ever wonder what you might weigh on Mars, one of Jupiter's moons, or a Star? Visit Your Weight On Other Worlds to find out at http://www.exploratorium.edu/ronh/weight/.

Gravity has always existed and is a condition of any object which possesses mass. Newton was the first scientist to accurately explain how the force of gravity acted upon matter within our universe. In one of the greatest examples of scientific observation and critical thinking, Newton concluded that the force that caused an apple to fall to Earth's surface is the same force that keeps the Moon in orbit around the Earth. Newton used a thought experiment to reason how this could be true. An imaginary cannon located on a high mountain fired a ball horizontally; the projectile would eventually fall to Earth, as indicated by the shortest trajectory in the figure, because of the gravitational force directed toward the center of the Earth and the associated acceleration. But as we increase the muzzle velocity for our imaginary cannon, the projectile will travel further and further before returning to Earth. Finally, Newton reasoned that if the cannon projected the cannon ball with exactly the right velocity, the projectile would travel completely around the Earth, always falling in the gravitational field but never reaching the Earth, which is curving away at the same rate that the projectile falls. That is, the cannon ball would have been put into orbit around the Earth. Newton concluded that the orbit of the Moon was of exactly the same nature: the Moon continuously "fell" in its path around the Earth because of the acceleration due to gravity, thus producing its orbit. Figure 2. Newton's Cannon.
(From http://csep10.phys.utk.edu/astr161/lect/history/newtongrav.html)

For further explanation of Newton's Cannon and an interactive animation visit http://www.waowen.screaming.net/revision/force&motion/ncanon.htm.

Gravity and Falling Objects

At the Earth's surface, all objects, regardless of their mass, free fall with the same acceleration. This is known as the acceleration due to Earth's gravity (g) and has a value of approximately 10 m/s2 (accepted value = 9.8 m/s2). Personal experience with falling objects contradicts this idea. Drop a hammer and a feather on Earth, and the resulting motion is not the same for each object. However, in the absence of air resistance ALL objects accelerate at the same rate. A review of Newton's 2nd Law of Motion will help to illustrate how this is true.

Figure 3 shows a boulder (10 kg mass) and a pebble (1 kg mass) in free fall. If Newton's second law were applied to their falling motion, and if free-body diagrams were constructed, you would see that the 10 kg rock experiences a greater gravitational force. This greater force of gravity would have a direct effect upon the rock's acceleration; thus, based on force alone, you might think that the 10 kg rock would accelerate faster. But acceleration depends upon two factors: force and mass. The 10 kg rock clearly has more mass (or inertia) than the 1 kg rock. This increased mass has an inverse effect upon the rock's acceleration. Thus, the direct effect of greater force on the 10 kg rock is offset by the inverse effect of its greater mass; and so each rock accelerates at the same rate - 10 m/s2. The ratio of force to mass (Fnet/m) is the same for each rock in situations involving free fall; this ratio (Fnet/m) is equivalent to the acceleration of the object. Figure 3. Why all objects fall at the same rate.
(From http://www.glenbrook.k12.il.us/gbssci/phys/Class/newtlaws/u2l3e.html)

For greater detail on Newton's Laws of Motion visit MS TIPS Benchmark P.8.B.1

Terminal Velocity

When a solid object moves through a fluid (liquid or gas), a frictional force is created between the object and the fluid. This force is commonly called drag. Sometimes when an object falls through the Earth's atmosphere, this drag force equals the gravitational force on the falling object. With the balanced forces equal to zero, the object falls with a constant velocity and is called "terminal velocity", a terminology made popular by skydivers. Another way of stating terminal velocity would be the velocity when a falling object is no longer accelerating; the force due to gravity is equal to the opposing force of air resistance. When an object continues to fall steadily until air resistance becomes so great that it equals with the pull of gravity and the object can fall no faster.

For greater detail on terminal velocity including an interactive quiz visit http://www.glenbrook.k12.il.us/gbssci/phys/mmedia/newtlaws/sd.html

Weightlessness

Weightlessness is simply a sensation experienced by an individual when there are no external objects touching one's body and exerting a push or pull upon it. Weightless sensations exist when all contact forces are removed. If all support is removed suddenly and a person begins to fall freely, he feels suddenly "weightless" - so weightlessness refers to a state of being in free fall in which there is no perceived support. The state of weightlessness can be achieved in several ways. Figure 4. Examples of weightlessness.
(From http://hyperphysics.phy-astr.gsu.edu/hbase/mass.html#wtls)

Different sensations of apparent weight can occur on an elevator since it is capable of zero or constant speed (zero acceleration) and can accelerate either upward or downward. If the elevator cable breaks then both you and the elevator are in free fall. If you were standing on a bathroom scale while you, the elevator, and scale were falling - the scale would register no weight for you.

An astronaut in space can be weightless, but cannot be without mass. Weightlessness is not the absence of gravity but a special case of constant free-fall. In orbit, one is falling continuously and so one does not "feel" the gravity. The same observable fact occurs with objects dropped on Earth (e.g. skydiving, amusement park free-fall ride).

For detailed explanations and practice calculations on the concept of weightlessness, visit http://hyperphysics.phy-astr.gsu.edu/hbase/mass.html#wtls.

For additional information on contact forces and the meaning and causes of weightlessness, go to http://www.glenbrook.k12.il.us/gbssci/phys/Class/circles/u6l4d.html

Newton's Law of Universal Gravitation

Newton found that he could explain the entire motion of the Solar System from the planets to the moons to the comets with a single law of gravity:

All bodies attract all other bodies, and the strength of the attraction is proportional to the masses of the two bodies and inversely proportional to the square of the distance between the bodies.

Mathematically expressed as: G (universal gravitation constant) = 6.67 x 10-11 N*m2/kg2
m1 = represents the mass of object 1
m2 = represents the mass of object 2
r = represents the distance separating the objects' centers
F = represents the gravitational force pulling the objects together Figure 5. Inverse Square Law for Gravity
(From http://physics.uoregon.edu/~jimbrau/BrauImNew/Chap02/FG02_23.jpg)

Since the gravitational force is directly proportional to the mass of both interacting objects, more massive objects will attract each other with a greater gravitational force. As the mass of either object increases, the force of gravitational attraction between them also increases. If the mass of one of the objects is doubled, then the force of gravity between them is doubled; if the mass of one of the objects is tripled, then the force of gravity between them is tripled; if the mass of both of the objects is doubled, then the force of gravity between them is quadrupled.

Since gravitational force is inversely proportional to the square of the distance between the two interacting objects, more separation distance will result in weaker gravitational forces. If the separation distance between two objects is doubled (increased by a factor of 2), then the force of gravitational attraction is decreased by a factor of 4 (2 raised to the second power). If the separation distance between any two objects is tripled (increased by a factor of 3), then the force of gravitational attraction is decreased by a factor of 9 (3 raised to the second power).

This relationship is known as an inverse square law (Figure 5) and is common in many areas of science; Gravitation, Electrostatics, Electromagnetic Radiation (light intensity), Acoustics (sound intensity).

For additional background on "the Apple, the Moon, and the inverse square law", visit http://www.glenbrook.k12.il.us/gbssci/phys/Class/circles/u6l3b.html

Greater detail on Newton's Law of Universal Gravitation can be accessed at http://www.glenbrook.k12.il.us/gbssci/phys/Class/circles/u6l3c.html

Gravity facts

• Gravity pulls things together - gravity is a "together" force, not a "down" force
• All objects have gravity - mass is an intrinsic property of matter and every object exerts a gravitational attraction on every other object in the universe
• The more massive the object, the stronger the gravitational pull on other objects
• The closer the objects are to each other the stronger the gravitational pull
• Very massive objects (e.g. stars, planets) are spherical because they are so massive and gravity's inward pull is virtually equal in all directions.
• All objects at the Earth's surface fall toward the Earth with the same acceleration

Content Benchmark P.8.B.3

Students know every object exerts gravitational force on every other object, and the magnitude of this force depends on the mass of the objects and their distance from one another. I/S

Common misconceptions associated with this benchmark

1. Students incorrectly think that Isaac Newton invented gravity.

Gravity has always existed and is a condition of any object which possesses mass. Newton was the first scientist to accurately explain how the gravitational force acted upon matter within our universe. He concluded that the force that caused an apple to fall to Earth's surface is the same force that keeps the Moon in orbit around the Earth. Furthermore, the strength (magnitude) of gravity depends directly on the mass of the two objects interacting and inversely squared on the distance separating the two objects. Any object that has mass therefore has gravity; the larger (more massive) the object the greater its gravity (stars, planets, comets, people, apples, gases).

2. Students incorrectly think weight and mass are the same.

Weight and mass are not the same. Mass is a measure of a body's resistance to changes in its state of motion (inertia), which depends on the amount of matter it contains. The International System of Units (SI) expresses the kilogram as the unit of mass. Weight is the force of gravity exerted on a body due to its mass and its location near another, more massive object. Weight is calculated by multiplying an object's mass by gravity (w = mg). The Newton is the unit for weight (1N = 1 kg*m/s2). An astronaut in space can be weightless but cannot be without mass. Weightlessness is not the absence of gravity but a special case of constant free-fall. In orbit, one is falling continuously and so one does not "feel" the gravity. The same observable fact occurs with objects dropped on Earth (e.g. skydiving, amusement park free-fall ride).

For additional information related to "Myths vs. realities: Gravity" including; description, how to use it in the classroom, and related materials visit http://amazing-space.stsci.edu/eds/overviews/myths/gravity.php.p
=Teaching+tools%40%2Ceds%2Ctools%2C%3EMyths
+vs.+realities%40%2Ceds%2Ctools%2Ctype%2Cmyths.php

3. Students incorrectly think that gravity exists only on Earth.

Any object that has mass has gravity. The greater the object's mass the greater its gravity. Gravity also affects objects in space. In fact, objects stay in orbit because of the gravitational force. Without gravity, a satellite launched from the Earth would simply drift off endlessly into space, traveling in a straight line (following Newton's 1st Law of Motion), instead of circling the planet. Gravitational force pulls objects toward the center of the planet, causing them to accelerate and drop toward the planet.

For additional information related to "Myths vs. realities: Gravity" including; description, how to use it in the classroom, and related materials visit
http://amazing-space.stsci.edu/eds/overviews/myths/gravity
.php.p=Teaching+tools%40%2Ceds%2Ctools%2C%3EMyths+vs.+
realities%40%2Ceds%2Ctools%2Ctype%2Cmyths.php

4. Students incorrectly think that gravity affects lighter objects differently than heavy ones.

Aristotle is credited with the origin of this misconception as he stated heavy objects seek their natural place faster than light ones, in other words that heavy objects fall faster. Many centuries later Galileo's famous experiment at the Leaning Tower of Pisa challenged Aristotle's reasoning. In his experiment, Galileo dropped two balls of different mass and found that the heavy ball hit the ground first, but only by a little bit. In the absence of air resistance not only the two balls but all objects would fall at the same rate. More than 400 years later during an Apollo 15 moon walk Commander David Scott conducted the famous hammer and feather demonstration on the surface of the moon. Because they were essentially in a vacuum, there was no air resistance and the feather fell at the same rate as the hammer.

For a flash simulation of Galileo's experiment complete with interactive quiz and explanation, visit http://www.pbs.org/wgbh/nova/pisa/galileo.html.

To view the Apollo 15 Hammer-Feather Drop demonstration, visit http://nssdc.gsfc.nasa.gov/planetary/lunar/apollo_15_feather_drop.html

Content Benchmark P.8.B.3

Students know every object exerts gravitational force on every other object, and the magnitude of this force depends on the mass of the objects and their distance from one another. I/S

Sample Test Questions

1st Item Specification: Understand the relationship between mass and weight.

Depth Of Knowledge Level 1

1. Which person has the greatest inertia?
1. A 50 kg girl jogging at 5 m/s.
2. A 70 kg student sitting in class.
3. A 90 kg man walking at 2 m/s.
4. A 110 kg adult standing in a line.
1. Weight can best be described as a measure of
1. the amount of matter in an object.
2. the amount of space an object occupies.
3. the gravitational force on an object.
4. how heavy an object is for its size.
1. Compared to the mass of an astronaut at the surface of the Earth, the mass of the same astronaut on the surface of the Moon is
1. doubled.
2. the same.
3. ½ as great.
4. ¼ as great.

Depth Of Knowledge Level 2

1. Use graphs #1-4 to answer the question below.    Graph 1 Graph 2 Graph 3 Graph 4

Which graph best represents the relationship between the mass of an object and its distance from the center of the Earth?

1. Graph 1
2. Graph 2
3. Graph 3
4. Graph 4
1. The graph below shows the weight of three objects on the Moon as a function of their mass. The acceleration due to gravity on the Moon is approximately 1.6 m/s2. A fourth object was found to have a weight of 144 Newtons, what would be the mass of this object? The mass would be

1. 144 Kg, because mass and weight are the same on the Moon.
2. 115 Kg, due to the low acceleration of gravity on the Moon.
3. 90 Kg, due to the low acceleration of gravity on the Moon.
4. 0 Kg, because objects are weightless on the Moon.

2nd Item Specification: Explain the relationship between gravity and the motion of falling objects.

Depth Of Knowledge Level 1

1. Astronauts on the orbiting space station 335 Kilometers above Earth appear to be weightless because
1. there is no gravity in space so they do not weigh anything.
2. space is a vacuum and there is no gravity in a vacuum.
3. they are too far from Earth to have weight.
4. the astronauts are in a state of free fall.
1. For a falling skydiver, terminal velocity is reached when the
1. upward force of air resistance is greater than the downward force of gravity.
2. upward force of air resistance is equal to the downward force of gravity.
3. downward force of air resistance is greater than the upward force of gravity.
4. downward force of air resistance is equal to the upward force of gravity.

Depth Of Knowledge Level 2

1. An 800 Newton person is standing on a scale in an elevator. If the elevator cable breaks and the elevator, person, and scale are in free fall, the person would experience a weight of
1. 400 N, accelerating downward.
2. 0 N, accelerating downward.
3. 800 N, moving downward at a constant speed.
4. 0 N, moving downward at a constant speed.
1. Use graphs #1-4 to answer the question below.  Graph 1 Graph 3  Graph 2 Graph 4

Which graph represents an object falling at terminal velocity?

1. Graph 1
2. Graph 2
3. Graph 3
4. Graph 4

3rd Item Specification: Identify and describe qualitatively the relationship between gravitational force, mass, and distance (Universal Law of Gravitation).

Depth Of Knowledge Level 1

1. If the Earth were twice as massive as it is now, then the gravitational force between it and the sun would be
1. four times as great.
2. the same.
3. twice as great.
4. half as great.
1. When a satellite is a distance r from the center of Earth, the force due to gravity on the satellite is F. When the satellite’s distance from the center of Earth is increased, the gravitational force
1. increases.
2. decreases.
3. remains the same.
4. increases then decreases.

Depth Of Knowledge Level 2

1. Use graphs #1-4 to answer the question below.  Graph 1 Graph 3  Graph 2 Graph 4

Which graph best represents the relationship between gravitational force and distance from Earth for an object traveling away from Earth?

1. Graph 1
2. Graph 2
3. Graph 3
4. Graph 4
1. In each diagram below, the mass of two objects is labeled. These masses are separated by a radius. Which diagram would produce the greatest gravitational force between the two objects?
A. Diagram 1
B. Diagram 2
C. Diagram 3
D. Diagram 4

Constructed Response P.8.B.3

1. The data in the table below records the weight of an object at five equal distances from Earth. Location 1 is taken at Earth’s surface.

 Location (#) Distance (Earth Radii) Force (Newton) 1 r 500 N 2 2r 125 N 3 3r 56 N 4 4r 31 N 5 5r 20 N Location #

A. What is happening to the mass of the object as it is taken from Location 1 to Location 5?

B. Plot Force versus Location for the five locations from the data table. Label the x and y-axis with the appropriate labels and units, and provide a graph title.

C. Using your graph, explain and justify what is happening to the weight of the object as the object is taken from Location 1 to Location 5.

Content Benchmark P.8.B.3

Students know every object exerts gravitational force on every other object, and the magnitude of this force depends on the mass of the objects and their distance from one another.  I/S

1. D, DOK level 1
2. C, DOK level 1
3. B, DOK level 1
4. A, DOK level 2
5. C, DOK level 2
6. D, DOK level 1
7. B, DOK level 1
8. B, DOK level 2
9. A, DOK level 2
10. C, DOK level 1
11. B, DOK level 1
12. D, DOK level 2
13. A, DOK level 2

Constructed Response 3-point Answer and Score Rubric: 3 points Response addresses all parts of the question clearly and correctly. Mass is a property of matter that does not depend upon location in a gravitational field. Mass of the object remains constant. Student graph shape matches the key with graph title, and correct labels for both x-axis and y-axis. Weight decreases rapidly with distance as shown in the downward sloping graph. Weight depends on location. As distance increases, weight decreases. The strength of the gravitational field decreases with distance resulting in less weight. 2 points Response addresses all parts of the question and includes only minor errors. 1 point Response does not address all parts of the question. 0 points Response is totally incorrect or no response provided.

Content Benchmark P.8.B.3

Students know every object exerts gravitational force on every other object, and the magnitude of this force depends on the mass of the objects and their distance from one another. 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. Gravity and Black Holes Curriculum Guide and Resources

This curriculum guide, presented by the Adler Planetarium & Astronomy Museum, contains a wealth of resources on exploring the concepts of gravity, black holes, and other related concepts. Learning objectives for this curriculum include; identifying gravity as the main mover and shaper of the Universe, expressing that gravitational force between two objects is always attractive, and illustrating that our understanding of gravity continues to evolve.

For the section that includes questions to guide an inquiry-based approach to exploring the concepts of gravity, black holes, and related concepts go to http://www.adlerplanetarium.org/education/resources/gravity/5-8_guiding.shtml

It's Gravity - a Science NetLinks lesson managed by AAAS uses the Gravity and Black Holes material in a comprehensive online lesson plan http://www.sciencenetlinks.com/lessons.cfm?DocID=390

2. Multimedia Physics Studios - GIF Animations and Explanations

Elephant and Feather - Free Fall Animation and Explanation
The animation does a great job clearing the misconception that heavier objects fall faster than lighter objects. A complete description of how and why all objects fall with the same acceleration is provided. http://www.glenbrook.k12.il.us/gbssci/Phys/mmedia/newtlaws/efff.html

Skydiving Animation and Explanation
The animation examines the motion of a skydiver. As the skydiver gains speed during the fall, air resistance also increases. Ultimately, the air resistance equals the gravitational force and the skydiver no longer accelerates and terminal velocity results.
http://www.glenbrook.k12.il.us/gbssci/Phys/mmedia/newtlaws/sd.html