

Teachers: This material examines Newton’s Second Law of Motion in a way
that will help you teach the law to your students. The photocopyready
Student Activities pages will give students the opportunity to learn aspects
of the Second Law in a way that they will find interesting and fun. Notes
about each activity appear in the Notes to Teachers section. The activities
can be tailored for the level of your students, and can be completed individually
or in groups. In addition, students will create a logbook, called Newton’s
Lawbook, in which they can take notes and track their findings from the
scientific experiments offered in the Student Activities pages.

Newton’s Second Law of Motion
In the presence of a net force, an object experiences an acceleration.
F=ma

Newton’s Second Law of Motion introduces one of the most important
fundamental concepts in science: mass. Sir Isaac Newton used the word “mass”
as a synonym for “quantity of matter.” Today, we more precisely
define mass as a “measure of the inertia of a body.” The more
mass an object has the more difficult it is to change its state of motion,
whether it is at rest or moving in a straight line at a constant speed.
Think of it this way: An elephant has more inertia than a mouse. It is much
harder to push an elephant across a floor than it is a mouse, and much harder
to stop the elephant once it is moving. Therefore, by definition, an elephant
has more mass than a mouse. 
Newton’s Second Law takes up where the First Law ends.
The First Law describes inertia: A body will not change its existing state
of motion without a net force acting on that body. In other words, without
an outside force a body will remain still if still, or, if moving, keep
moving in the same direction at a constant speed. 

But what happens when a net force interacts with inertia?
The Second Law tells us that a net force will change the velocity of an
object by changing either its speed or its direction. Such a change in velocity
is called an acceleration. So, we can say that a net force gives rise to
acceleration.
The Second Law goes on to mathematically define the exact relationship between
net force and acceleration: The acceleration of an object is directly proportional
to the net force acting on it and is inversely proportional to its mass.
Also, the direction of the acceleration is in the direction of the net force
acting on the object. More simply, and as Newton put it: F=ma, where “F”
(force) and “a” (acceleration) are both vector quantities, and
“m” is the object’s mass. Note that the “F”
in this equation is the net force, that is, the sum of all the forces acting
on the object.
In SI units (metric system), mass is measured in kilograms, acceleration
is in meters per second per second, and the unit of force is the newton
(N). One newton is the force required to impart an acceleration of 1 m/sec2
to a mass of 1 kg (1N = 1 kg m/sec2). By the way, the newton unit of measurement
was named in honor of Sir Isaac himself. 
The Swift Satellite
Swift is a spacebased multiwavelength observatory dedicated
to the study of gammaray bursts. Its purpose is to determine the origin
and nature of these powerful cosmic explosions; determine how the blastwaves
from the bursts evolve and interact with their surroundings; and determine
if these bursts can be used as effective probes of the early Universe.
Scheduled for launch in Fall 2003, Swift is a collaboration between
the United States, the United Kingdom, and Italy.
Newton’s Second Law and the Swift Satellite
Swift has a mass of about 1,400 kilograms, which is about the
same mass as 30 tenyearolds in a bag! In order to get the Swift
satellite into orbit, it will be launched from a Boeing Delta rocket with
a mass of about 231,800 kg. With Swift inside the rocket, the
combined mass of the two will be 233,300 kg!

The Earth’s gravity pulls the rocket (with Swift
inside) down with a force of about 2,285,000 newtons. But the rocket’s
boosters can exert an upward force of about 2,722,000 newtons. This means
that the upward force is stronger than the downward force by about 437,000
newtons. As the rocket lifts off, it will have a net upward force of 437,000
newtons exerted on it. With a total mass of 233,300 kg, the rocket will
accelerate upward at a rate of 1.8 meters per second per second (acceleration
= force / mass). In other words, for every second of travel time the rocket
will increase its velocity by almost 2 meters per second. As Newton’s
Second Law explains it: In the presence of a net force, an object experiences
an acceleration (F=ma). 

Demos and Thought Problems
Teachers: Use the following demonstrations to introduce Newton’s Second
Law to your class.
Place an empty cardboard box and two or three bricks or heavy books on a
table (or the floor). Push the empty box across the table. Note how much
force was required to perform the task. Now put one of the bricks or books
in the box. Again, push it across the table. Was more, less, or the same
amount of force required to accomplish the task? Add another brick or book
to the box and push it across the table again. Was more, less, or the same
amount of force required this time to accomplish the task? Explain the experiment
using the proper physics vocabulary of force, mass, acceleration, velocity,
distance, time, etc. 

Whirl a yoyo at the end of its string in a vertical path.
Ask the students if the yoyo is changing directions. Be prepared to explain
that even though it is traveling in a continuous circle it is indeed changing
directions. Only motion in a straight line is motion that is not changing
its direction. Movement in a circle is actually a continuous changing of
directions. Therefore, it must be undergoing an acceleration.Ask what force
is acting on the yoyo to change its direction. In an open discussion, explain
to students that it is the force of your hand pulling on the string which
changes the yoyo’s direction. Explain that the yoyo is undergoing
two motions at once: It is going up and down as well as left to right. Discuss
other examples of objects which undergo two motions at once. Examples may
include an airplane lifting off from the runway, a skier going down a hill,
or a baseball hit by a batter. To undergo two motions at once requires the
existence of more than one force – one force may get the object moving
while the other changes its direction. For example, the bat may provide
the force to move the ball forward and up into the air, but it is gravity
providing the force which causes it to arc toward the ground again. You
can demonstrate this by throwing or kicking a ball. 
Student Activities
Students: These activities will help you learn all about Newton’s
Second Law of Motion. Use the notebook, which you have designated as your
Newton’s Lawbook, to take notes, track your progress, and evaluate
findings from the experiments you will conduct. Start by writing down
Newton’s Second Law of Motion.

Newton’s Second Law of Motion
In the presence of a net force, an object experiences an acceleration.
F=ma

Activity #1: Collision
on the Tracks
In this experiment you will examine Newton’s Second Law of Motion
by investigating the relationships between force, mass, and acceleration.
Materials
You will need the following items for this experiment:
• two identical ball bearings
• two marbles with different masses (similar sizes), each with less
mass than the ball bearings
• two tracks, 1 meter each
• a ruler
• a stopwatch
• a balance or scale
Procedure
1. Determine the mass of each ball bearing and marble. Record the masses
in the Table below.


Mass (gm) 
Marble 1


Marble 2 

Ball Bearing 1 

Ball Bearing 2 


2. Set up a ramp, 1 meter in length. Use books or a board to incline
the ramp at an angle
of 5 to 10 degrees.
3.Starting from the top of the ramp, put marks along the track at 30 and
60 centimeters.
4. Place the other track at the end of the incline. Make sure there’s
a smooth transition where the
tracks are joined. Put a book at the end of the last track.
5. Put one of the ball bearings at the bottom of the inclined track, where
it becomes level.
Part 1


1. Put the marble with the smallest mass at the top of the inclined track.
Use a ruler to hold
the ball steady.
2. Before you release the marble, predict what will happen when the marble
hits the ball bearing.
3. Remove the ruler and let the marble roll down the track. Observe what
happens when the
marble hits the ball bearing. Was it what you expected? Why or why not?
Record your
notes in your Newton’s Lawbook.
4. Repeat the experiment, using a stopwatch to measure how long it takes
the marble to roll
down the track and hit the target ball bearing. Use this information,
along with your
calculations of the marble’s mass, to calculate the acceleration
of the marble. Enter your data
and calculations in the Table below.
5. Repeat the experiment twice more. First, start the marble at the 30
cm mark. Second, start
it at the 60 cm mark. Record your data and calculate the acceleration
of the marble in
the Table below.

Average Time
(sec) 
Distance Covered
(cm) 
Average Speed
(cm/sec) 
Final Speed
(cm/sec) 
Acceleration
(cm/sec/sec)


100 




70 




40 




6. Replace the small marble with the larger one. Place it at the top
of the ramp. Predict
what will happen when this marble hits the ball bearing. Let the marble
roll and observe
what happens. Were your predictions right? Why or why not? Enter your
observations in
your Newton’s Lawbook.
7. Finally, roll the second ball bearing down the ramp. What will happen
this time when it
strikes the other ball bearing? Write your predictions and results in
your Newton’s Lawbook.
Part 2
1. In this experiment you will investigate what happens to the target
ball bearing after it is
struck by a rolling marble. Roll the lightest marble from the top of the
incline, letting it
hit the target. Use a stopwatch to record the time it takes the target
ball to travel the 1 meter
to the book. Perform the experiment three times and determine the average
time. Record
your results in the Table below.
2. Repeat the above procedure with the more massive marble and then with
the other ball
bearing. Enter your data and results in the Table below.


Time 1 (sec) 
Time 2 (sec) 
Time 3 (sec) 
Average Time (sec) 
Marble 1 




Marble 2 




Ball Bearing 





3. What was the reaction of the target ball bearing after the impacts
from each of the three
balls? Relate your observations to Newton’s Second Law of Motion.
Write your thoughts
in your Newton’s Lawbook.
4. Now calculate the results for the target ball in the Table below.
Think About It


Average
Target Ball
Roll Time
(sec) 
Distance
Target Ball
Moved
(cm) 
Average
Speed of
Target Ball
(cm/sec) 
Final Speed
of Target Ball
(cm/sec) 
Acceleration
of Target Ball
(cm/sec/sec) 
Marble 1 

100 



Marble 2 

100 



Ball Bearing 

100 




Now let’s put it all together. Look at the force applied by the
rolling ball (Fi = miai) and the acceleration of the target ball (at =
Fi/mt). Note that “i” represents impact, and “t”
equals target.
Write your answers to the following questions in your Newton’s
Lawbook.
1. What happened to the motion (acceleration) of the target ball as the
force from the rolling
balls increased (due to the larger masses)?
2. Using mathematical language, explain the relationship between force
and acceleration.
Activity #2: Projectile Motion – Motion
in Two Dimensions
As you know, when you throw a ball it inevitably falls back to the ground.
Newton’s First Law of Motion tells us the ball would travel in a
straight line forever unless a force acts on the ball. So a force must
be acting on the ball. But what force? The answer, of course, is gravity.
The pull of gravity between the Earth and the ball causes the ball to
drop. All pulls or pushes are called forces. The pull (force) of gravity
causes rising objects to decelerate (a negative acceleration); the pull
of gravity causes falling objects to accelerate.
Whether you throw a ball, hit one with a bat, or launch one from a cannon,
the ball follows a curved path called a trajectory. The shape of the path
is a parabola. All tossed balls, regardless of their initial speed or
the height at which they were released, follow a parabolic trajectory.
In this experiment you will investigate some of the properties of this
motion. You will investigate what factors affect the shape of the trajectory,
how they affect it, and why they affect it in that way.
Materials
You will need the following items for this experiment:
• a dart gun with rubber suctiontipped darts (available at most
toy stores)
• a measuring tape
• a protractor
• a black marker
• a large piece of cardboard or posterboard
You can make your own “big” protractor for this experiment.
Here’s how: Find or cut out a
12” x 12” piece of posterboard or cardboard. Using a protractor,
start at a given point and make lines with a black marker at angles of
0, 15, 30, 45, 60, 75, and 90 degrees. Tape or glue of some sort of handle
to the back of the board to make it easy to hold in a vertical position.
Procedure
1. For each trial, keep the dart gun at the same height above the ground.
This can be done by
appointing the same student to fire the gun each time. Have him or her
pick a position from
which to fire the gun for each trial, i.e., from the top of a chair or
table top.
2. Use a protractor (storebought or homemade) to tilt up the gun at a
given angle. Shoot the
gun and measure the horizontal distance traveled. Mark where the dart
first hits the ground,
not where it finally comes to rest after bouncing. Repeat the procedure
three or four
times for each angle to average the results, and use four or five different
angles.
3. In your Newton’s Lawbook, summarize the results by drawing a
graph that shows the
horizontal distance traveled on a Yaxis and the angle at which you launched
the dart as
the Xaxis.
4. From the results of the experiment, determine the angle that the dart
should be launched in
order for it to travel the farthest horizontal distance. Be ready to defend
your answer. Also, be
prepared to discuss any uncertainties you came across in the experiment.
5. In your Newton’s Lawbook, explain all your observations and results
of the experiment in
terms of forces, masses, and accelerations.
Notes to Teachers
Activity #1: Collision on the Tracks
Part 1
Students can calculate the acceleration of the rolling ball by figuring
out the ball’s mass and the amount of time it took to roll down
the ramp. The average speed can then be calculated by figuring out the
distance rolled and the time it took to hit the target. The average speed
must be determined in order to calculate the ball’s speed at the
bottom of the ramp. Since the ball is undergoing uniform acceleration,
its velocity will change linearly – from its initial velocity to
its final velocity. Thus, the average velocity is simply:

Equation Here 

To calculate the acceleration of the ball at the time of
impact, subtract the ball’s initial speed (which is zero) from its
final speed and divide by the time it took to hit the target. In this
exercise acceleration is independent of mass, but it does depend on diameter
(since the balls are rolling, not sliding or freefalling) so choose the
balls to be as close to the same size as possible, and don’t use
any hollow balls. The acceleration for the balls of different masses should
then be the same.
Part 2
Students will find that the balls with a larger mass will cause the target
ball to travel the 100 cm distance in less time. Point out that although
the mass of the impactor ball changes, the mass of the target ball remains
constant.
Use this experiment to explain the following concepts to your students:
a) In accordance with Newton’s First Law of Motion, the target ball
remained at rest until it
was acted on by the force of the impact of the ball that was rolled down
the incline. This
force varied depending on the mass of the impact ball.
b) The force imparted to the target ball is found by multiplying the mass
times the acceleration
of the impact ball.The impact balls all had (about) the same acceleration,
but different masses.
c) The larger the force imparted to the target ball, the larger its acceleration.
Students should
understand that the rate of acceleration of the target ball depends on
the mass (and therefore,
force) of the rolling ball. This is Newton’s Second Law. Mathematically,
this represents a
direct relationship. As one variable goes up, the other variable goes
up proportionally. In
other words, if the mass is constant, the force and acceleration are directly
proportional.
Activity #2: Projectile Motion – Motion in Two Dimensions
To begin this lab, perform the following demonstration: Fire the gun horizontally
and note where the dart lands. Ask your students to think about what happens
when the dart is fired horizontally. Once the dart first leaves the gun,
it will continue to travel horizontally at its initial speed, since no
force is being applied in the horizontal direction. We know this from
Newton’s First Law of Motion. However, once the dart is shot from
the gun, the force of gravity acts on the dart, pulling it directly downward
toward the ground (perpendicular to the motion of the horizontallyfired
dart). Newton’s Second Law tells us that this force will introduce
an acceleration to the dart in the downward direction.
Ask students what could be done to make the dart travel farther. If the
students suggest tilting the gun up, try it. If not, tilt it up at about
20 degrees and shoot the dart again. Ask students what they notice about
where the dart lands. From this, lead them into the investigation of what
angle they need to shoot the dart in order to make it travel the farthest
distance.
What factors determine how far a projectile will travel in the horizontal
direction? The distance is determined by the initial speed of the projectile,
the mass of the projectile, the amount of friction (including air resistance)
the projectile encounters, the height from which the object is projected,
and the angle at which it is projected. In the experiment done here, several
of these factors are made virtually constant: the initial speed of the
dart as it leaves the gun; the dart’s mass; the air friction (assuming
the experiment is not done outside on a windy day); and the height at
which the dart was shot. As a result, we can investigate the relationship
between the distance traveled and the angle of initial velocity.
We will, for now, ignore air friction and think only about the initial
velocity of the dart and the acceleration due to gravitational force.
Students will figure out that firing the dart at a slight upward angle
will cause it to travel a greater horizontal distance. However, horizontal
speed is lost and the distance traveled is shortened when the firing angle
becomes too steep. At a large launch angle, most of the force exerted
on the dart moves it upward, rather than forward.
What angle will achieve the maximum horizontal distance? In the real world,
the actual angle will vary from experiment to experiment because of differing
air resistance effects. However, the results should cluster around the
theoretical expectation, 45 degrees.
Extension Activities – As extensions to the lab, consider the following:
• Have students investigate how the height of the dart gun above
the ground affects the results of the
experiment. Using a given angle, have them shoot the gun at different
heights and measure the distance
traveled for each trial.
Air friction was ignored in the main part of the experiment. However,
in reality, air friction serves
to constantly decrease the horizontal velocity of the dart. In this extension
activity, students
will find that, at some point, increasing the height of the launch doesn’t
make the dart travel a greater
horizontal distance. This is because of air friction. As the dart moves
through the air, the air gradually
slows down the dart. Eventually, all of the dart’s forward motion
is lost and it falls straight down.
Students will find that the dart will no longer go farther if they try
to increase the time the dart is in
the air by increasing the height of the firing position.
• Have students investigate how the mass of the dart effects the
results for a given launch height and a
given angle. Use gum, wax, or tape to stick a dime or penny to the suction
tip of the dart.
Resources
Copies of these materials, along with additional information on Newton’s
Laws of Motion and Law of Gravitation, are available on the Swift Mission
Education and Public Outreach Web site:
http://swift.sonoma.edu/education/
• NASA Web sites:
NASA’s official Web site  http://www.nasa.gov
Swift Satellite  http://swift.gsfc.nasa.gov
• NASA Education Resources:
Swift’s Education and Public Outreach Program  http://swift.sonoma.edu
SpaceLink, Education Resources  http://spacelink.nasa.gov
Imagine the Universe!  http://imagine.gsfc.nasa.gov
StarChild  http://starchild.gsfc.nasa.gov
• NASA’s Central Operation of Resources for Educators (CORE):
http://core.nasa.gov/index.html
Check out these videos:
“Liftoff to Learning: Newton in Space” (1992), $15.00
“Flight Testing Newton’s Laws” (1999), $24.00
• Newton’s Laws of Motion:
http://www.grc.nasa.gov/WWW/K12/airplane/newton.html
• Newton’s Law of Gravitation:
http://csep10.phys.utk.edu/astr161/lect/history/newtongrav.html
• Conic Sections:
http://www.keypress.com/sketchpad/java_gsp/conics.html
http://cs.jsu.edu/mcis/faculty/leathrum/Mathlets/conics.html
• Newton in the Classroom:
http://www.physicsclassroom.com/Class/newtlaws/newtltoc.html
http://www.glenbrook.k12.il.us/gbssci/phys/Class/newtlaws/u2l1a.html
Acknowledgments
Creators:
Kara Granger, Maria Carrillo High School, California
Laura Whitlock, NASA’s Swift Mission, California
Science and Education Reviewers:
Thomas C. Arnold, State College Area High School, Pennsylvania
Margaret Chester, The Pennsylvania State University, Pennsylvania
Alan Gould, Lawrence Hall of Science, California
Bruce H. Hemp, Ft. Defiance High School, Virginia
Derek Hullinger, University of Maryland, Maryland
James Lochner, NASA Goddard Space Flight Center, Maryland
Jane D. Mahon, Hoover High School, Alabama
Ann Parsons, NASA Goddard Space Flight Center, Maryland
Original Artwork and Design: Aurore Simonnet, Sonoma State University,
California
Painting of Sir Isaac Newton by Enoch Seeman, 1726
Editor: Stacy Horn, San Francisco, California


