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Chapter 4
Newton’s Second Law
of Motion
How does an object move when a force acts on it?
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Physics 1 (Garcia) SJSU
Force & Acceleration
Newton’s First Law of Motion,
Zero Force
implies
Constant Velocity
(same as uniform motion)
Definition of Acceleration,
(Change in Velocity)
(Acceleration) =
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(Time interval)
Physics 1 (Garcia) SJSU
Force Implies Acceleration
From those two results we have that,
Net Force
not Zero
implies
Velocity
not
Constant
implies
Object
Accelerates
So if there’s a net force on an object, that implies that the object accelerates.
Also have that if an object accelerates, that implies that there’s a net force.
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Physics 1 (Garcia) SJSU
Force Causes Acceleration
• Net Force-The combination of all forces
that act on an object
• The acceleration of an object is directly
related to the net force on an object (force
and acceleration change in the same
direction)
More Force, More Acceleration
The greater the net force on an object, the
greater the acceleration of that object.
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Physics 1 (Garcia) SJSU
Acceleration Goes As Force
Larger the net force, greater the acceleration
Double the Force
Triple the Force
Half the Force
implies
implies
implies
Acceleration “goes as” Force
Force “goes as” Acceleration.
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Double the Acceleration
Triple the Acceleration
Half the Acceleration
Mathematically, we write
Force ~ Acceleration.
Physics 1 (Garcia) SJSU
Check Yourself
You push on a crate with 100
Newtons of force. If the
friction force is 100 Newtons,
does the crate accelerate?
Does that mean that the crate
is not moving?
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Check Yourself (cont.)
Now push with 150 N; friction is still 100 N.
Does the crate accelerate?
A friend helps push with an additional 150 N.
By how much does acceleration increase?
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More Mass, Less Acceleration
The greater the mass of an object, the less it
accelerates when acted on by a force.
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Mass Resists Acceleration
• Acceleration is inversely proportional to
mass
– Inversely-the 2 values change in opposite
directions
• As mass increases, acceleration decreases for a
given force
• As mass decreases, acceleration increases for a
given force
Mass & Acceleration
For a given force, greater mass, smaller the acceleration
Double the Mass
Triple the Mass
Half the Mass
Acceleration goes as
the inverse of mass.
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implies
implies
implies
Half the Acceleration
Third of the Acceleration
Double the Acceleration
Mathematically, we write,
Acceleration ~ 1/(Mass).
Physics 1 (Garcia) SJSU
Check Yourself
NO
FRICTION
?????
?????
?????
?????
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Physics 1 (Garcia) SJSU
Newton’s Second Law
• Also called the Law of Acceleration
• The acceleration produced by a net force on an object
is directly proportional to the magnitude of the net
force, is in the same direction of the net force, and is
inversely proportional to the mass of the body.
or
A=F/M
Newton’s Second Law of Motion
Acceleration goes as net Force.
Acceleration goes as inverse of Mass.
Acceleration only depends on Force and Mass.
(Net Force)
(Acceleration) =
(Mass)
Acceleration is in the direction of the net Force.
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Physics 1 (Garcia) SJSU
Weight on Earth
From the Chapter 2, acceleration of gravity on Earth is
10 meters per second per second. (Notation: g = 10 m/s2 )
From Newton’s Second Law,
(Force) = (Mass) X (Acceleration)
For example, weight (force of gravity) for 1 kg is
1 kg
( 10 Newtons ) = ( 1 kg ) X ( 10 m/s2 )
10 N
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Physics 1 (Garcia) SJSU
Demo: Elevator Cable
Tension in elevator cable depends on acceleration
Zero
acceleration
5 m/s2 upward
( ½ g upward)
5 m/s2 downward
( ½ g downward)
10 m/s2 downward
(Free fall)
0N
15 N
10 N
5N
1 kg
1 kg
1 kg
1 kg
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Physics 1 (Garcia) SJSU
Free Fall Acceleration
Newton’s Second Law explains why all
objects fall with same acceleration.
Ratio of
weight/mass
always the same
since weight
depends on mass.
Analogy with ratio of
circumference /
diameter always
equals pi (3.1415…).
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Physics 1 (Garcia) SJSU
Demo: Drop the Sheet
A flat sheet of paper falls slowly because of
air resistance.
What happens if we place it on top of a
book, blocking the air from reaching it?
Air
Resistance
Weight
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Friction and Air Resistance
Friction and air resistance are forces opposing motion.
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Friction
Origin of friction is molecular interaction between
solid surfaces.
Friction is complicated.
Friction depends on
support force and on
properties of the surface.
Basic properties of
friction first established
by Leonardo da Vinci.
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Air Resistance (Drag)
Origin of drag is molecules of gas (or liquid) striking
a moving object.
Drag force depends on:
•Size (area) of the object
•Speed of the object
Larger the size or speed,
larger the drag.
Also depends on shape of object,
density of gas or liquid, etc.
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Physics 1 (Garcia) SJSU
Air Resistance on a Falling Object
Gravity force on an object
(i.e., weight) is constant but
air resistance depends on an
object’s speed.
As a falling object gains
speed, the resistance force
gets larger so the net force
decreases.
Net force is sum of:
Weight (downward)
Resistance (upward)
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Physics 1 (Garcia) SJSU
Check Yourself
Golf ball has more mass than a ping-pong
ball. Force of gravity is greater on:
golf ball, ping-pong ball, or the same?
The two balls are the same size; when
speeds are equal, drag force is greater
on which ball?
Which ball falls faster (which has greater
acceleration)?
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Physics 1 (Garcia) SJSU
Ping
pong
Ball
Golf
Ball
Drag
Weight
Terminal Speed
Speed of falling objects increases until drag force
balances weight.
When forces balance, zero acceleration
so constant velocity.
Speed for which air resistance balances
weight called terminal speed.
High terminal speed
(better open the chute!)
Low terminal speed
(large area of chute)
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Demo: Drop the Cat
Cats seem to have an uncanny ability to
survive falls from high places. For example,
cats have been known to survive falls of up
to 32 stories. By contrast, dogs rarely
survive falls of more than six stories.
Humans usually die when they fall from
such heights.
In a study of cats that had fallen from up to 32 stories, an
interesting finding emerged: while the rate of injury in cats
seemed to increase linearly depending on the length of the fall,
after seven stories, the rate of injury seemed to level off! In
other words, the survival rate and severity of injuries were no
more severe in a cat that fell seven stories than in one that fell
32 and in some cases, injuries were even less!
From: www.animalhealthcare.ca
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Physics 1 (Garcia) SJSU
Demo: Drop the Cat (cont.)
After further study, the reasons for this discrepancy
became clear. When a person falls from a
building, maximum speed or "terminal velocity"
(120 mph) is reached after 32 stories. Cats, on the
other hand, achieve terminal velocity at 60 mph
after falling only five stories!
Until a cat reaches terminal velocity, it will experience
acceleration and tend to reflexively extend its
limbs, making it more susceptible to injuries.
However, when a cat reaches terminal velocity, its
vestibular system (i.e. the organs of balance)
become less stimulated, causing the cat to relax.
It will then orient its limbs more horizontally (splaylegged), thereby increasing air drag in much the
same way a parachute does. In this posture, the
force of impact also appears to become more
evenly distributed.
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Physics 1 (Garcia) SJSU
Mass & Weight
Mass: Quantity of matter in an object
Weight: Force of gravity on an object
Weight
Mass is a universal property.
Weight depends on gravity
(different on Moon).
Earth
Moon
Mass is the measure of inertia.
Metric unit for mass is the kilogram.
Metric unit for weight is Newton (since it’s a force)
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Physics 1 (Garcia) SJSU