Download Module 1 - Kinematics Module 2

Module 1 - Kinematics
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Description of motion
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Defined concepts/terms like
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Equations
Graphical methods
Often described as a “push” or “pull” of one
body on another.
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Concept/definition of Force
Concept/definition of Mass
Concept/definition of Acceleration
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Concept/definition of an Inertial Reference Frame
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Weight
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Force due to gravitational attraction.
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In particular, accelerated motion
A study/application of Newton’s three laws
Requirements
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Vector algebra
A clearly defined Coordinate System (C.S.)
Force
Study of / concerned with the forces that
cause motion
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Requirements
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Position
Velocity
Acceleration
Defined their relationships
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Module 2 - Kinetics
Magnitude:
W = mg
Direction: Towards the center of the earth.
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Bodies can be in contact.
Requires a C.S.
y
^
j
^ x
i
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Bodies can be separated.
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The same regardless if stationary or moving.
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Vector quantity characterized by
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Normal Force
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Mass
A contact force
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Perpendicular (i.e., normal) to the contacting surface.
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Often described as “quantity of matter.”
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A measure of Inertia.
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Mass does not change without physically
altering the object.
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Force acting ON the body by the contacting object.
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Inertial Reference Frame
Newton’s Laws
Newton’s Laws only hold in an Inertial Reference Frame.
That begs the question: What is an Inertial Reference
Frame?
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Inertial Reference Frames do not exist!
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Depending on the application, certain reference frames can
approximate an Inertial reference frame.
Example
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Every body continues in its state of rest or
uniform speed in a straight line unless acted
on by a nonzero net force.
The acceleration of an object is directly
proportional to the net force acting on it and
inversely proportional to its mass. The
direction of the acceleration is in the direction
of the net force acting on the object.
When ever one objects exerts a force on a
second object, the second object exerts an
equal and opposite force on the first.
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Newton’s 2nd Law
⇒
∑F
Newton’s 3rd Law
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= ma
How do we know this?
Whenever one objects exerts a
force on a second object, the
second object exerts an equal
and opposite force on the first.
‰ “To every action there is an
equal and opposite reaction.”
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Units:
mass
acceleration
force
S.I.
kg
m/s2
N
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U.S.
slug
ft/s2
lb
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Free Body Diagram - FBD
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A diagram of the body of interest that has been
isolated from the rest of the world.
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That is, it is Free from its connections to the rest of
the world.
We draw ALL forces that are acting ON the body.
Do NOT draw forces that the body exerts on other
objects.
Force of gravity is always included (if present).
All connections to the rest of the world are replaced
by the corresponding contact force(s).
The “action” force and the
“reaction” force act on different
bodies.
The action BY one body ON
another body.
The force exerted BY a body
DOES NOT influence that body.
The force exerted BY a body
ONLY influences the other body.
That is, it acts ON the other body.
We are only concerned with
forces that act ON a body.
Example
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A man pushes on a crate with a force F which is
directed downward from the horizontal as shown.
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Draw the FBD
y
^
j
^ x
i
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Kinetic Diagram - KD
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Example
A diagram of the body of interest that has been
isolated from the rest of the world.
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That is, it is Free from its connections to the rest of
the world.
We draw the mass*acceleration vector components
ON the KD.
That is, the components of the RHS of Newton’s 2nd
Law.
Requires a coordinate system.
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A man pushes on a crate with a force F which is
directed downward from the horizontal as shown.
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Draw the KD
y
^
j
Example Problem
^ x
i
Example Problem Continued
Given: Matlab Man decides to “borrow” a car from a certain unnamed
professor for a “joy ride.” Seeing a local law enforcement officer about a
kilometer ahead, he slams on the brakes and his car goes from 100. km/hr
to 0 in 50.0 m. Assume that a is constant and that all four wheels
contribute equally to the braking force of the 1500. kg car.
y
^
j
∑F
^ x
i
=
= ma
Required: Find the braking force on each wheel.
v
Set up Kinematic equations
50.0 m
v1 = 100. km/h
v2 = 0
Solve equations
ax = -7.72 m/s2
FB = +2890 N
Check Everything
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