Terminal Velocity. ΣF = (kv 2 -BW) = 0 V=?

Transcription

1 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=?

2 Linear Kinetics I KIN335 Spring 2005

3 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

4 -mechanics Overview Rigid-body Mechanics Statics system in a constant state of motion Dynamics system undergoes acceleration Positioin, Velocity, Acceleration Kinematics Description of Motion (w/o considering forces) Kinetics Cause & Results due to forces Linear Angular Linear Angular Force Torque

5 Kinetics Causes and Effects due to forces Newton s 2 nd law CAUSES 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

6 Force = m a Force * Torque = r F r Fixed center = Force = m a + I α

7 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.

8 Force? Unit : Newton (N) 1.0 N = (1.0 kg) (1.0 m/s 2 ) 1 lb = N cf) body weight = force = m g Force is Vector Magnitude and direction Classifying forces Internal forces forces

9 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.

10 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,

11 Notations : Normal (reaction) force GRF : Ground reaction force : Static friction force F d : Dynamic friction force W : Body weight or gravitational force F : Applied external force F W W R N R N or GRF F F d F s

12 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 Newton s 1 st law

13 Newton s laws Newton s 1 st 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 2 nd law In case of ΣF = 0, the state of motion (constant velocity or zero velocity) will not change Newton s 3 rd law Action-Reaction Principle Describes how objects interact with one another

14 Acceleration

15 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

16 Free-Body Diagram (FBD) Four Steps to do 1. 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.

17 Example)

18 Whole body + Bat Bat? Body?

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20 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.

21 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 R N Static friction :F s = µ s R N Dynamics (Kinetic) friction : F d = µ d R N µ : friction coefficient ( ) R N :Normal force ( ) F W W

22 Draw the direction of friction?

23 Magnitude of Friction Force F = µ R N Proportional to the normal contact force (R N ) W, W, R N Inversely proportional to the angle of inclination θ, θ, R N Figure 1a θ W θ Wn Wt

24 Magnitude of Friction Force F = µ R N 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

25 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 (F lim ) Dynamic friction : resisting force to prevent movement Static friction coefficient (µ s ) µ s = F lim /R N Dynamic (kinetic) friction coefficient (µ d ) µ d = F /R N Always Force applied

26 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/A Unit : 1.0 Pascal (Pa) = 1.0 N/ 1.0m 2 Cf) 1 psi = Pa

27 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? ( )

28 Addition of forces Vector Addition tip-to-tail method Component (decomposition) method Colinear forces vs Concurrent forces

29 Static Equilibrium In case of ΣF = 0, there is static equilibrium Newton s 1 st law Two case for static equilibrium Stationary (No moving) Constant velocity How to solve problems of static equilibrium 1. Draw FBD 2. Define appropriate coordinate system 3. Establish ΣF = 0 for each axis 4. Solve the unknowns

30 Example)

31 Example) F W F s R N

32 Example ) Static friction coefficient (µ s ) θ

33 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?

34 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 What is the resultant force that acts on the skier?