Download Forces Come in Pairs --- Newton`s Third Law Weight and Mass The

Class 22
Galileo change the basic approach of physics, from that of Aristotle
The world view through ideal mathematical laws.
Every object continues in its state of rest or of uniform velocity in a straight line as long as
no net force acts on it.
A system in which Newton's first law does hold is called an Inertial reference frame
Mass and Force →
Fnet =m a
The unit of force is
mass resists force
kg∗m
=1 Newton
s2
Forces Come in Pairs --- Newton's Third Law
When object A exerts a force on object B, then object B exerts a force on object A which is
equal in magnitude and opposite in direction.
Weight and Mass
Weight and mass are not the same.
 =m g 
g
Weight is the force of gravity on an object W
mass is the resistance to acceleration
m=
F
a
The Free-body Diagram
In order to calculate the acceleration of on object we need to calculate the sum of all the forces on an
objects.
Draw vectors representing all the force on the single object.
Equilibrium ---- when the sum of force is zero
The special case when the sum of the forces on a single object is zero is called equilibrium.
The Normal Force
If an object is resting on a surface there will to 2 forces applied by that surface to the object.
One of these force is called the normal force and is perpendicular to the surface.
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Class 22
Friction
Kinetic Friction
F kf =k F N
Not a fundamental law like Newton's Second Law.
Experimental relationship.
Direction of the friction force always is opposite to the direction of the motion.
Static Friction
F kf ≤ s F N
2
Class 22
Circular Motion
ac =
v2
r
The Universal Law of Gravitation
To make this proportionality into an equation we use the universal gravitational constant G
F G =G
m1 m 2
r 122
Based on Keplar's measurements of planetary motion.
Satellites and Weightlessness
A satellite is a ballistic trajectory in which the curvature of the path matches the curvature of the Earth
If one classifies the trajectories according to their initial speeds we have
a long artillery shot → sub orbital flight → circular → elliptical → escape
Geosynchronous Orbit --Period of 24 hours
plane of the orbit is the equator
Weightlessness, Gravity, and the Equivalence Principle
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Class 22
Ch 6. Work and Energy
Work done by a constant force.
W =F d cos 
Kinetic Energy and the Work-Energy Principle
The definition of Energy
Energy is different from all other concepts in physics in that there is no single definition for it.
Instead there are many different kinds of energy.
If we define kinetic energy as
1
2
KE= m v
2
work-energy principle
The work done in changing the state of motion of an object is equal to the change in the kinetic energy.
W net =KE 2 −KE 1 = KE
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Class 22
Potential Energy
While Kinetic energy is associated with motion potential energy is associated with position.
Whereas kinetic energy has an obvious zero, when the velocity is zero, potential energy is only defined
as a change.
Potential energy itself has come in different kinds.
Gravitational Potential Energy
Potential energy is only meaningfully defined as a change when an object moves from one
position to another.
 PE Grav=m g  y 2 − y 1 =m g h
Elastic Potential Energy
1 2
W sp= k x where x is the amount the spring is compressed of stretched.
2
Conservative and Non-Conservative Forces
Springs and gravity store potential energy. Friction does not store potential energy.
Mechanical Energy and its Conservation
If we consider the above equation in the case in which there is no non-conservative work then weget
 KE PE =0
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Class 22
Power – the rate of doing work
Units of Energy
The unit of energy is a Joule
Since work is force times distance, thus
Joule = Newton * meter
Units of Power
power=
Work
time
so the units of power, which are called Watts are
Watt=
Joule
second
By combining the definition of power and work we can obtain a formula to power in terms of force.
P=
W Fd
d
=
=F = F v
t
t
t
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Class 22
Momentum
Force and Momentum
From the definition of momentum it follows that

F=
 p
where
t
p =m v
In the absence of an external force linear momentum is conserved.
Perfectly Inelastic Collisions
In a perfectly inelastic collision the colliding objects stick together.
Collision and Impulse
From Newton's second law we have seen

F=
 p
t
which can be rewritten as

P = Fnet  t
The quantity on the Left hand side of the equation is called the impulse
impulse= Fnet  t
Elastic Collisions in One Dimension
An Elastic collision is one in which the mechanical energy of the colliding particles is conserved.
From conservation of energy and momentum is can be shown that the velocities before and after a
perfectly elastic collision in one dimension are
v A−v B =− v A ' −v B ' 
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Class 22
Draw FBD
a.
1.41∗103 N
b.
1.61∗103 N
a.
1.81∗103 N
8
a.
2.01∗103 N
e. none
Class 22
a
1.2∗10 4 N
a
1.3∗10 4 N
a
1.5∗10 4 N
9
a
1.6∗10 4 N
e. none
Class 22
By Work Energy Thm.
W = KE
1
2
F∗d cos 180mg cos 180 d = m v i
2
1
mg d m v i2
2
F=
d
 
1300kg∗9.8 m / s 2∗2.6m0.5∗1300 kg∗ 3.5
F=
2.6m
10
m
s2
2