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Transcript
Newton’s Second and
Third Law of Motion
Newton’s Second Law of Motion
•
A commonsense law.
•
The force on an object is equal to its mass multiplied by its
acceleration.
•
Mass is the amount of matter an object has.
F  ma
is the time rate of change of velocity. (Velocity is speed
Acceleration
in a given direction.)
•
Newton’s Second Law of Motion
•
The more massive an object, the more inertia.
•
The more inertia an object has, the harder it is
to get it moving.
•
Double the force - double the acceleration.
Double the mass - halve the acceleration.
•
Mass
•
…is the measure of the inertia of an object.
•
Inertia is the tendency of an object to continue in its
original motion
•
…is measured in kilograms.
•
… is how much matter is in an object..
Weight
•
The weight of an object FW is the
response of MASS to the
GRAVITATIONAL FORCE.
•
FW = m g
•
g = 9.81 m/s2
Units
•
•
•
•
The units of mass is the kilogram (in MKS
system) and the slug (in Imperial system).
Mass is a SCALAR quantity.
The unit of force in the MKS system is the
Newtons, where a force of 1 N will give a
mass of 1 kg an acceleration of 1 m/s2 . In the
Imperial system, the unit of force is the
pound.
Force is a VECTOR quantity.
Units of Force
•
SI unit of force is a Newton (N)
kg m
1N  1 2
s
•
US Customary unit of force is a pound (lb)
•
1 N = 0.225 lb
Gravitational Force
•
•
•
Mutual force of attraction between any two
objects
Expressed by Newton’s Law of Universal
Gravitation:
m1 m2
Fg  G 2
r
G = universal gravitational constant =
6.67x10-11 N-m2/kg2
Example
If two objects (m1 = 100 kg) and (m2 = 1000 kg) are
separated by 0.5m, what is the gravitational force
between them?
Example: Answer
m1 m2
Fg  G 2
r
2 

100kg 1000kg
11 N  m
Fg  6.67x10
2
2 
kg  0.5m

5
Fg  2.668x10 Newtons
Example: Answer
• Notice the very, very small answer.
Gravity is the WEAKESS force by far.
• So - why are WE so aware of it?
• Because we are next to an incredibly
large & massive object - the Earth.
Newton’s Second Law of Motion
•
Examples:
1) Throwing a baseball
2) Slingshot (David & Goliath)
3) Hail
4) Moving cars (1)
5) Moving cars (2)
Example
If a mass of 1 kg is accelerated 1 m/s2 by a
force of 1 N, what would be the acceleration of
2 kg acted on by a force of 2 N?
(a) 0 m/s2
(b) 1 m/s2
(c) 2 m/s2
(d) 3 m/s2
(e) unable to determine
Answer (b)
•
If a mass of 1 kg is accelerated 1 m/s2 by a
force of 1 N, what would be the acceleration
of 2 kg acted on by a force of 2 N?
F  ma
aFm
a  2N
m

1
2kg s2
Newton’s Third Law of Motion
•
“To every action (force) there is always opposed an
equal reaction (force): or, the mutual actions of two
bodies upon each other are always equal, and
directed to contrary parts. ”
•
The least intuitive law.
•
Every object that exerts a force on another object is
always acted upon by a reaction force.
Newton’s Third Law of Motion
Examples:
1.
2.
3.
4.
5.
6.
Recoil of a gun.
Thrust of a rocket.
Rebound of a hammer from a struck nail.
Book sitting on a table.
Walking.
Lumberjack running on a log in a lake.
Example
If a Mack truck
and a
Volkswagen
have a headon collision,
which vehicle
will experience
the greater
impact force?
a) the Mack truck
b) the Volkswagen
c) both the same
d) ... it depends on other factors
Example: Answer (c)
If a Mack truck
and a
Volkswagen
have a headon collision,
which vehicle
will experience
the greater
impact force?
Answer: Newton’s Third Law ~
action and reaction
Example
Consider the apple at rest
on the table. If we call the
gravitational force exerted
on the apple action, what
is the reaction force
according to Newton's 3rd
Law?
Example: Answer
Consider the apple at rest
on the table. If we call the
gravitational force (by the
earth) exerted on the
apple action, what is the
reaction force according
to Newton's 3rd Law?
Answer: The gravitational force exerted
by the apple on the earth
Example
If a mass of 10 kilograms is accelerated at
5 meters per second per second, what is
the force acting on it?
Example: Answer
m
kg m
F  10 kg x 5
 50 2 = 50 newtons
s
s
s
Example
What acceleration will result when a
12-N net force applied to a 3-kg
object?
(a) 0 m/s2
(b) 4 m/s2
(c) 36 m/s2
(d) Unable to determine
Example: Answer (b)
What acceleration will result when a
12-N net force applied to a 3-kg
object?
F  ma
aFm
a  12N
m

4
3kg
s2
Example
A 1-kg rock is thrown at 20 m/s
straight upward. Neglecting air
resistance, what is the net force that
acts on it when it is half way to the top
of its path?
(a) 0 N
(b) 4.9 N
(c) 9.8 N
(d) 20 N
(e) Unable to determine
Answer (c)
Answer: The only force
acting on the rock is
gravity.
F=ma
F = (1) (9.8)=9.8N
Classical Mechanics…
The End
(for now…)