Download Terminal Velocity

Terminal Velocity
• The object’s velocity
when the acceleration of
falling become ______.
• Air resistance
(Aerodynamic drag)
f(drag coefficient, surface
area, square of velocity,
air density)
kV2
BW
ΣF = (kV2-BW) = 0
V=?
Linear Kinetics I
KIN335 Spring 2005
What you have to know
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•
•
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•
•
•
•
Kinetics?
Force? External or Internal forces
Mass, Inertia, Acceleration
Revisit Newton’s laws of motion
Free-body diagram? (Graphic, Very Crucial!!)
Friction forces (static and dynamic friction)
Pressure
Static equilibrium problems
Dynamics equilibrium problems
Impulse-Momentum Relationship
-mechanics Overview
Rigid-body Mechanics
Statics
Dynamics
system in a
constant
state of motion
system
undergoes
acceleration
Positioin,
Kinematics
Kinetics
Velocity,
Description of Motion
(w/o considering
forces)
Cause &
Results due to
forces
Acceleration
Linear
Angular
Linear
Angular
Force
Torque
Kinetics
• Causes and Effects due to forces
Î Newton’s 2nd law ___________
CAUSES
Î
EFFECTS
Linear Kinetics
Net Forces*
__________ movement
(Mass ×Acceleration)
Angular Kinetics
__________
Rotating movement
(Moment of Inertia ×
Angular Acceleration)
* Resultant force derived from the composition of two or more forces
Force
=
m·a
Fixed center
Force
r
=
* Torque = r·F
Force
_____
=
m·a
+
I·α
Force?
• Enable an object to start moving, stop moving, and
change directions.
• Combination of two or more forces enables us to
maintain our balance in stationary positions.
• Force is a push or a pull (simple definition).
• Mechanical definition: Something accelerates
when it starts, stops, speeds up, slow down, or
changes direction.
• YK’s definition: Something causes an object’s
movement.
Force?
• Unit : Newton (N)
1.0 N = (1.0 kg)·(1.0 m/s2)
1 lb = __________ N
cf) body weight = force = m·g
• Force is Vector Î Magnitude and direction
• Classifying forces
– Internal forces
– _________ forces
Internal forces
• Forces that act within the object or
system whose motion is being
investigated.
• Example:
– ___________________ within
the whole system
– Muscle contraction
• Important in the study of sport
biomechanics related with the
nature and causes of ________.
• Incapable of producing changing
in the motion of the body’s center
of mass.
External forces
• Forces that act on an object as a result of its
interaction with the environment surrounding it.
• Classifying external forces
– ____________ force(s) : gravitational force, electrical
and magnetic force
– _______ forces : air resistance, water resistance,
ground reaction force(GRF), normal (contact) force,
friction, …
Notations
• ____: Normal (reaction)
force
• GRF : Ground reaction
force
• ___ : Static friction force
• Fd : Dynamic friction
force
• W : Body weight or
gravitational force
• F : Applied external
force
W
RN or GRF
W
RN
F
F
Fd
Fs
Mass
• Quantity of matter composing a body
• Direct measure of a body’s _________ to
change in ______ motion (i.e., an object’s
inertia w.r.t linear motion)
• The measure of ________
• Inertia? Tendency of a body to resist a
change in its state of motion
Î Newton’s 1st law
Newton’s laws
• Newton’s 1st law
– Every body continues in its state of rest, or of uniform motion in
a straight line, unless it is compelled to change that state by
forces impressed upon it.
– Special case of Newton’s 2nd law
In case of ΣF = 0, the state of motion (constant velocity or zero velocity)
will not change
• Newton’s 3rd law
– Action-Reaction Principle
– Describes how objects interact with one another
Acceleration
Free-Body Diagram (FBD)
• Sketch that shows a defined system in _________ with all
of the force vectors acting on the system
• a pictoral representation of Newton's second law Î
indicating all acting _______ and _______ due to forces
Free-Body Diagram (FBD)
•
Four Steps to do
1.
2.
Determine the body to be isolated.
Isolate the body with a diagram that
represents the complete external
boundaries.
Represent all ________ forces that act
on the isolated body in their proper
positions within the diagram.
(Gravitational force, GRF, Normal
force, Friction force, Push or Pull, Air
resistance….)
Indicate the choice of __________ axes
directly on the diagram.
3.
4.
Example)
Whole body + Bat
Bat?
Body?
Friction Review Objectives
• Understand friction force and the factors
that contribute to friction force.
– Coefficient of friction
– Normal reaction force
– Surface area (?)
• Know how to calculate friction forces and
coefficients of static and dynamic (or
kinetic) friction.
Friction Force
• Surface _________ due to normal
force acting on the surface.
• Vector (magnitude and direction)
• Direction : _______ to the surface
& __________ to movement or
opposite to tendency of movement
• Magnitude : F = µ⋅ RN
– Static friction :Fs = µs⋅ RN
– Dynamics (Kinetic) friction :
Fd = µd⋅ RN
µ : friction coefficient
(_________________)
RN :Normal force
(___________________)
F
W
W
Draw the direction of friction?
Magnitude of Friction Force
F = µ⋅ RN
• Proportional to the
normal contact force
(RN) Î ↑ W, ↑____
↓W, ↓ RN
• Inversely proportional
to the angle of
inclination
Î↑ θ, ↓ _____
↓ θ, ↑ RN
θ Wn
θ
Figure 1a
W
Wt
Magnitude of Friction Force
F = µ⋅ RN
• Proportional to the friction coefficient (µ)
Î ↑ µ, ↑ F
↓ µ, ↓ F
• µ = f (material, surface condition)
Îdepend on characteristics between an object and surface.
ÎMetal, rubber, wood,….
ÎSand, oil, water, dry,….
• _______ Friction vs. ________ (Kinetic) Friction
Coefficients
Static vs. Dynamics Friction
•
•
•
Static friction (before moving) :
Proportion to ___________ but
opposite direction.
Max static friction (about to
move) : Max resisting force to
prevent movement (Flim)
Dynamic friction : ________
resisting force to prevent
movement
Static friction coefficient (µs)
µs = Flim /RN
• Dynamic (kinetic) friction
coefficient (µd)
µd = F /RN
Always
___________
•
Force applied
Surface area and friction
• The different size of surface
area does not create different
friction force of an object
(_____)
• Why? Î ________
↑Area, ↓Pressure
↓Area, ↑Pressure
• Pressure : P = F/A
Unit : 1.0 Pascal (Pa) = 1.0 N/ 1.0m2
Cf) 1 psi = 6894.8 Pa
Friction in sport and human
movement
• Friction is good or bad in sport and human movement?
• Following action will increase friction or decrease friction
coefficients?
– The grips of racket or bat are made of materials such as
leather or rubber ( )
– The soles of the balling shoes are designed to ( )
friction coefficient
– Waxing the bottom of snow skis ( )
– Touching rosin bag prior to pitching ( )
– Spike of the sole of running shoe ( )
– What about chalks of gymnast’s hand? ( )
Addition of forces
• Vector Addition
– “tip-to-tail” method
– Component (decomposition) method
• Colinear forces vs Concurrent forces
Static Equilibrium
•
•
In case of ΣF = 0, there is static equilibrium
Newton’s 1st law
•
Two case for static equilibrium
–
–
•
Stationary (No moving)
Constant velocity
How to solve problems of static equilibrium
1.
2.
3.
4.
Draw FBD
Define appropriate coordinate system
Establish ΣF = 0 for each axis
Solve the unknowns
Example)
Example)
F
W
Fs
RN
Example ) Static friction coefficient (µs)
θ
Q4 (chap 4) Dave is trying to pull Dana on a sled across a flat
field. Dave pulls on the rope attached to the sled with an
upward and forward force of 300 N. This force and the rope
are directed at an angle of 30° above horizontal. Dana’s mass
is 50 kg, and the sled’s mass is 8 kg. If the coefficient of static
friction between the sled runners and the snow is 0.10, will
Dave move the sled?
A 60-kg skier is in a tuck and moving straight down a 30° slop. Air
resistance pushes backward on the skier with a force of 10 N (this
force acts in a direction upward and parallel to the 30° slope). The
coefficient of dynamic friction between the skis and the snow is
0.08. What is the resultant force that acts on the skier?