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
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.
To learn more about Inertia, Mass, and Newton’s First Law of Motion go to
http://www.glenbrook.k12.il.us/gbssci/phys/Class/newtlaws/u2l1b.html
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
Force created when a mass is acted upon
(amount of matter in object)
by a gravitational field
Constant at any location
Value (magnitude) dependent upon
Numerical measure of inertia (resistance
location
to change)
SI unit is the Newton (1N = 1 kg•m/s2)
SI unit is the kilogram
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
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 TIPS Benchmark P.8.A.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.
Gm1m2
F
Mathematically expressed as:
r2
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).
For more information on this and other gravity misconceptions visit
http://www.astronomy.org/astronomy-survival/miscon11.html
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://amazingspace.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://amazingspace.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
1. Which person has the greatest inertia?
a. 50 kg girl jogging at 5 m/s
b. 70 kg student sitting in class
c. 90 kg man walking at 2 m/s
d. 110 kg football player sitting on the bench
2. Compared to the mass of an object at the surface of the Earth, the mass of the object on
the surface of the Moon is
a. the same
b. twice as great
c. one-half as great
d. one-fourth as great
3. If the mass of an object were doubled, the inertia of the object would be
a. unchanged
b. doubled
c. halved
d. quadrupled
4. Weight can best be described as
a. a measure of the amount of matter in an object
b. a measure of the amount of space an object occupies
c. a measure of the gravitational force on an object
d. a measure of how heavy an object is for its size
5. If the Earth were twice as massive as it is now, then the gravitational force between it and
the sun would be
a. four times as great
b. the same
c. twice as great
d. half as great
6. Astronauts on the orbiting space station appear to be weightless because
a. there is no gravity in space and they do not weigh anything
b. space is a vacuum and there is no gravity in a vacuum
c. the astronauts are far from Earth’s surface at a location where gravitation has a
minimal affect
d. the astronauts are in a state of free fall
7. 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. a weight of 400 N, accelerating downward
b. a weight of 0 N, accelerating downward
c. a weight of 800 N, moving downward at a constant speed
d. a weight of 0 N, moving downward at a constant speed
8. Which graph represents an object falling with terminal velocity?
9. Which graph best represents the relationship between gravitational force and distance
from Earth for an object traveling away from Earth?
10. Which graph best represents the relationship between the mass of an object and its
distance from the center of the Earth?
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
Answers to Sample Test Questions
1. (d)
2. (a)
3. (b)
4. (c)
5. (c)
6. (d)
7. (b)
8. (a)
9. (d)
10. (a)
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.
To investigate the grades 5-8 and grades 9-12 Gravity and Black Holes curriculum go to
http://www.adlerplanetarium.org/education/resources/gravity/index.shtml
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
3. Your Weight on Other Worlds Calculator and Supporting Explanation
Ever wonder what you might weigh on Mars, one of Jupiter’s moons, or a Star? This site is
managed by the Exploratorium: Museum of Science, Art and Human Perception in San
Francisco. Visitors to the site are prompted to input their weight and then select the “calculate”
button to compute your weight on the planets in our solar system, as well as a few different types
of stars.
To access Your Weight on Other Worlds, visit http://www.exploratorium.edu/ronh/weight/.
4. Gizmos! from ExploreLearning
Gizmos! Interactive simulations that make key concepts easier to understand and fun to learn.
Although these simulations are available for purchase, a free trail (30 day) option exists.
Additionally, a five minute free trail can also be used from the links below, select the “Launch
Gizmo!” button. When launched, you have access to the Gizmo! and to the Lesson Materials to
download and use with students. Several Gizmos have been included here, as they directly
support this benchmark. Note that you will need to have the free Adobe Shockwave player
loaded on your computer for these simulations to work.
Weight and Mass
Use a balance to measure mass and a spring scale to measure the weight of objects. Compare the
masses and weights of objects on Earth, Mars, Jupiter, and the Moon.
http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=653
Freefall Laboratory
Investigate the motion of an object as it falls to the ground. A variety of objects can be
compared, and their motion can be observed in a vacuum, in normal air, and in denser air. The
position, velocity, and acceleration are measured through time, and the forces on the object can
be displayed. Using the manual settings, the mass, radius, height, and initial velocity of the
object can be adjusted, as well as the air density and wind.
http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=387
Gravitational Force
Drag two objects around and observe the gravitational force between them as the positions
change. The mass of each object can be adjusted, and the gravitational force is displayed both
vectorally and numerically as the distance between the objects is altered.
http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=411