Newton's Second Law

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When Isaac Newton left Cambridge,
he was just looking for a way to avoid the
plague. But during the next 18 months,
Newton made observations that enabled
him to explain the relationship between
light and color and to invent a form of
mathematics called calculus. He also
explained how the universe is held
together in his theory of gravitation and
laws of motion.
Although Newton cornpleted his early
investigations in 7666, his theory of
gravitation and laws of motion were not
published until 1687. Newton's first law
of motion states that all bodies have
inertia. A body at rest tends to remain at
rest, and a moving body will travel at a
constant speed in a constant direction.
Newton's second law of motion picks
up wher e the first law leaves off . This law
A push and a putL are'both
in a change in motioJl. V
states that an object at rest or in mction
will not change its condition unless some-
thing causes the change. What might
make an object move, speed up, slow
down, stop, or change direction?
Force, Mass, and Acceleratian
Newton hypothesized th at the answer
to the question asked abovg'is "a force."
Remember that, ir sclen&,, a fctrce is a
push or a pull. Newton's seccnd law !
of motion states that aI) object begins
to move, speeds up, slows dcwn, comes
to a stop, or changes direction only when
some lorce acts on that object.
For example, a rock on top of a hill
might begin rolling down the hill if some-
one exerted a force on it. Once started
down the hill, the rock would continue to
gain'speed because of the f orce of gravity
forces, and both can result

2. acting on it, The rock would continue
moving along a straight couyse down the
hill until some new force acted on it. This
new force could change its direction,
slow it down, speed it up, or stop it.
Consider a ball rolling across a billiard
table. The ball might speed up, slow
down, or change direction. Why? The
second law says that such a change
The rocks in this picture moved down the hitt
because a force acted on them. V
occurs when a force acts on the ball.
what might provide the necessary force
on a billiard ball to change its motion?
Perhaps the billiard ball is hit by another
ball from behind, from in frotrt, or from
the side. If the contact with the other ball is
from behind, a pushing force changes the
speetJ of the first ball. If the contact is from
the side or front, a pushing force changes
not only the spbed of the ball but also the
direction in which the ball is moving.
Calculating Force
Newton discovered a mathematical
formula that shows how force causes a
change in the speed or direction of an
object. That formula is
Force = mass x acceleration
F = m X a
The units used in this formula are new-
tons (N) for force, kilograms (kd for mass,
and meters per second per second (m/sr)
for acceleration. As you learned in the
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3. A,,Newton's cradle' provides another good example of force changing motion. The force is gen-
erated by the first ball striking the second ball, the second striking the third, and so on. Finally,
when the force is passed on to the last ball, the ball bounces away from the others. When the
ballfalls back and strikes the one before it, the process is repeated in the opposite direction.
previous chapter, the newton is a unit of
weight in the metric system. A newton
is defined as the force needed to accel er-
ate a 1-kg object 1 meter per second
every second.
N= kg x mls2
The formula for forcetells us many
things about the way in which a force
acts on an object. For example, suppose
an object with a mass of 2 kg accelerates
at 5 m/s'. What force was needed to
achieve that acc eleration? To answer that
question, first write the formula for
Nawton's second law.
F=ffiXa
Then substitute the values you know for
this question.
m = 2kg;a = 5m/s2
Look at the engines ,n fhese two
cars. The larger car requires a
larger engine because it has a larger
mass. How can you use Newton's second
law to find out which car requires the
greater force to accelerate it to a spe ed
of 88 kmlh (55 mph) in 10 seconds?

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Mass (ksl
A Figure 1: Force = 10 N
Finally, use the formula to find the
unknown quantity-force
F = m X a
F = ?kg x 5m/sz
F = 10 kg x m/s2
F = 10 N
It would require a {orce of 10 N to make
a 2-kS object accelerate at the rate of
5 m/s every second, or 5 m/s'.
What happens if the same force acts
on a body of greater mass, one of 5 kg,
for example? To find the answer to this
question, use the bar graph in Figure 1.
Notice that the x-axis of the graph shows
seven different masses that are acted on by
a force of 10 N. The y-axis shows the
resulting acceleration.
When you solved this problem, Vou
discovered an important general rule. A
constant force, such as 10 N, causes
greater acceleration in a smaller mass
than it does in a greater mass.
other Appli"ri,ons of the
Second Law
Suppose you wanted to give the same
acceleration to two bodies of different
mass. You can use F : m x a to find out
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Mass (kgl
A Figure 2z Acceteration = 5 m/s'
how to do that, too. Look at the bar
graph in Figure 2. Notice that the f orce
required to produce an acceleration of
5 m/s'increases as mass increases. For
example, a 4-kS mass requires a force of
20 N to accel erate to 5 m/s'. A 2-kS
mass only requires a force of 10 N to
achieve the same acceleration.
Perhaps you'd like to find out what
happens to the acceleration of a 10-kg
object if you chang e the force applied to
it. Look at the bar graph in Figure 3. If
you increase the force on a 10-kg mass,
how is acceleration affect ed?
FEnding the Mass of an Obiect
'How can you find the mass of an
object? Easy, Vou say-just put it on a
balance and read the value. Scientists
know anoth er way to answer this ques-
tion. If they know the rate at which an
object is accel erated by a given force ,
they can calculate the mass of the object.
They find the object's mass by using
Newton'ssecondlaw:F- m x a.
Suppose you apply force of 15 N to
an object of unknown mass, giving that
object an acceleration of 5 m/s'. Look at

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Force (Nl
Mass = 10 kg
the bar graph in Figure 2. Can you use
any of the information in this graph to
solve the probl em? You probably can.
You can also try to rearrange the second
law's formula to solve for mass. If you
determined that the mass of the object is
3 kg, you're right on the mark!
Congratulations!
In fact, the second law gives us a new
way of thinking about mass. Mass is a
measure of a body's inertia. If a large
force'is required to overcome the inertia
lnternet Field Trip
I NVESTTGATION A .WRAF.ITFI
REvlEw 1. What is Newton's second law of motioni
' 2. When a force is applied to an object, what deter-
mines the object's acceleration?
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A How are force, mass, and acceleration
related in a BMX race? u '
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of a body and g; that body moving, the
body has a lot of mass. If only a small
force is needed to move a body, the body
has a small amount of mass. Now you
can find an exact numb er for the mass of
a body, using Newton's second law of ,
motion. I
3. What can you infer about the force needed for a
baseball pitcher to accelerate a ball at a rate of 5 m/s2
compared to the force needed to accelerate the
same ball at a rate of 10 m/sz?
4. Two children ride in a wagon having a maSS of
20 kg. One child has a mass of 30 kg, and the other
child has a mass of 40 kg. What force is needed s)
to accelerate the wagon and its passengers at ffi'
a rate of 5 m/s2? #ff$
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GRTTIGAL
THTNKING
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