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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) kV 2 BW ΣF = (kV 2 -BW) = 0 V=?

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Page 1: Terminal Velocity - Arizona State University | Ranked #1 · PDF file · 2005-04-18Terminal Velocity • The object’s velocity ... Kinematics Kinetics Linear Angular Linear Angular

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) = 0V=?

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Linear Kinetics I

KIN335 Spring 2005

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What you have to know• 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

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-mechanics OverviewRigid-body Mechanics

system in a constant

state of motion

system undergoes

acceleration

Description of Motion (w/o considering

forces)

Cause & Results due to

forces

Statics Dynamics

Kinematics Kinetics

Linear Angular Linear Angular

Positioin,

Velocity,

Acceleration

Force Torque

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Kinetics• Causes and Effects due to forces

Newton’s 2nd law ___________

CAUSES EFFECTS

__________ movement(Mass ×Acceleration)

Net Forces*Linear Kinetics

Rotating movement(Moment of Inertia ×Angular Acceleration)

__________Angular Kinetics

* Resultant force derived from the composition of two or more forces

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=Force m·a

Fixed center

=Force

_____

r

* Torque = r·F

=Force

m·a+

I·α

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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.

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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 Magnitude and direction• Classifying forces

– Internal forces– _________ forces

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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.

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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, …

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Notations

W

RN or GRF

• ____: 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

F F

Fd Fs

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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 motionNewton’s 1st law

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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 lawIn 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

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Acceleration

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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

indicating all acting _______ and _______ due to forces

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Free-Body Diagram (FBD)• Four Steps to do1. Determine the body to be isolated.2. Isolate the body with a diagram that

represents the complete external boundaries.

3. 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….)

4. Indicate the choice of __________ axes directly on the diagram.

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Example)

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Whole body + Bat

Bat? Body?

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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.

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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

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Draw the direction of friction?

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Magnitude of Friction ForceF = µ⋅ RN

• Proportional to the normal contact force (RN) ↑ W, ↑____

↓W, ↓ RN

• Inversely proportional to the angle of inclination ↑ θ, ↓ _____↓ θ, ↑ RN

θ

Figure 1a WtW

Wnθ

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Magnitude of Friction ForceF = µ⋅ RN

• Proportional to the friction coefficient (µ) ↑ µ, ↑ F↓ µ, ↓ F

• µ = f (material, surface condition)depend on characteristics between an object and surface.Metal, rubber, wood,….Sand, oil, water, dry,….

• _______ Friction vs. ________ (Kinetic) Friction Coefficients

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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 /RNAlways

___________Force applied

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Surface area and friction

• The different size of surface area does not create different friction force of an object (_____)

• Why? ________↑Area, ↓Pressure↓Area, ↑Pressure

• Pressure : P = F/AUnit : 1.0 Pascal (Pa) = 1.0 N/ 1.0m2

Cf) 1 psi = 6894.8 Pa

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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? ( )

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Addition of forces

• Vector Addition– “tip-to-tail” method– Component (decomposition) method

• Colinear forces vs Concurrent forces

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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 equilibrium1. Draw FBD2. Define appropriate coordinate system3. Establish ΣF = 0 for each axis4. Solve the unknowns

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Example)

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Example)

W

RN

F

Fs

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Example ) Static friction coefficient (µs)

θ

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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?

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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 is0.08. What is the resultant force that acts on the skier?