Week 2 - Introduction to Forces PDF

BIOMECHANICS WEEK 2 – INTRODUCTION TO FORCES 1 CONCEPTS FROM LAST WEEK MASS THE AMOUNT OF ”STUFF” AN OBJECT CONTAINS MEASURED IN KG WEIGHT AMOUNT OF GRAVITATIONAL FORCE EXERTED ON AN OBJECT MEASURED IN N WEIGHT...

BIOMECHANICS WEEK 2 – INTRODUCTION TO FORCES 1 CONCEPTS FROM LAST WEEK MASS THE AMOUNT OF ”STUFF” AN OBJECT CONTAINS MEASURED IN KG WEIGHT AMOUNT OF GRAVITATIONAL FORCE EXERTED ON AN OBJECT MEASURED IN N WEIGHT IS EQUAL TO MASS MULTIPLIED BY THE ACCELERATION DUE TO GRAVITY (GRAVITATIONAL CONSTANT = 9.8 M/S2) INERTIA RESISTANCE TO ACTION OR TO CHANGE (ACCELERATION) DIRECTLY PROPORTIONAL TO THE MASS OF THE OBJECT (MORE MASS = MORE INERTIA) 2 1  LESSON OUTLINE 1. EXPLAIN WHAT A SYSTEM IS AND HOW IT MOVES 2. DISCUSS FREE BODY DIAGRAMS 3. INTRODUCE NEWTON’S LAWS OF MOTION 4. DEFINE KEY TERMS 5. COMPARE INTERNAL AND EXTERNAL FORCES 6. EXPLORE THE FACTORS AFFECTING FRICTION 7. DESCRIBE CONCURRENT FORCE AND DEPICT GRAPHICALLY 8. REVIEW STATIC EQUILIBRIUM 3 DESCRIBING BIOMECHANICS SYSTEM ANY STRUCTURE OR ORGANIZATION OF RELATED STRUCTURES WHOSE STATE OF MOTION IS OF ANALYTICAL INTEREST COULD BE THE ENTIRE BODY, A SINGLE JOINT, OR AN OBJECT THAT HAS BEEN MOVED BY THE BODY 4 2  DESCRIBING BIOMECHANICS TO BETTER UNDERSTAND OUR SYSTEM, WE NEED TO PULL FROM OUR UNDERSTANDING OF ANATOMICAL TERMINOLOGY, DIRECTIONAL TERMS, AND PLANES/AXIS OF MOTION ANATOMICAL POSITION DIRECTIONAL TERMS (E.G., SUPERIOR/INFERIOR, ANTERIOR/POSTERIOR, MEDIAL/LATERAL, PROXIMAL/DISTAL, SUPERFICIAL/DEEP) PLANES OF MOTION (E.G., SAGITTAL, FRONTAL/CORONAL, TRANSVERSE) AXIS OF MOTION (E.G., SUPEROINFERIOR, ANTEROPOSTERIOR, MEDIOLATERAL) 5 DESCRIBING BIOMECHANICS 6 3  DESCRIBING BIOMECHANICS CENTER OF MASS THE POINT AT THE INTERSECTION OF THE THREE CARDINAL PLANES THAT REPRESENTS THE AVERAGE LOCATION OF A SYSTEM’S MASS CENTER OF GRAVITY AS GRAVITATIONAL PULL IS CONCENTRATED AT THE CENTER OF MASS, IT IS SYNONYMOUS WITH THE TERM CENTER OF GRAVITY 7 DESCRIBING BIOMECHANICS SPATIAL FRAMES OF REFERENCE CARTESIAN COORDINATE SYSTEM A FRAME OF REFERENCE DEFINED BY AN ORIGIN AND TWO OR THREE ORTHOGONAL AXES, EACH PASSING THROUGH THE ORIGIN AND DEFINING ONE SPATIAL DIMENSION 2-D (X AND Y) OR 3-D (X, Y, AND Z) COORDINATE SYSTEMS CAN BE GLOBAL (FIXED) OR LOCAL (SOMATIC) 8 4  NEWTON’S LAWS OF MOTION 1. LAW OF INERTIA ORIGINAL EVERY BODY PERSEVERES IN ITS STATE OF REST, OR OF UNIFORM MOTION IN A RIGHT LINE, UNLESS IT IS COMPELLED TO CHANGE THAT STATE BY FORCES IMPRESSED THEREON SUMMARY OBJECTS AT REST STAY AT REST, OBJECTS IN MOTION STAY IN MOTION EXAMPLES 1. DIVER 2. ASTEROID 9 NEWTON’S LAWS OF MOTION 2. LAW OF ACCELERATION ORIGINAL THE ALTERATION OF MOTION IS EVER PROPORTIONAL TO THE MOTIVE FORCE IMPRESSED AND IS MADE IN THE DIRECTION OF THE RIGHT LINE IN WHICH THAT FORCE IS IMPRESSED SUMMARY FORCE = MASS (M) * ACCELERATION (A) EVERY OBJECT/SYSTEM HAS A MASS. TO MOVE THE SYSTEM, IT HAS TO UNDERGO ACCELERATION, FROM 0 VELOCITY TO SOME VELOCITY (+ OR -) IN ORDER TO DISPLACE ITS POSITION. IF WE WANT TO ACCELERATE THE SYSTEM, WE NEED TO IMPART A FORCE INTO THE SYSTEM EXAMPLES VERTICAL JUMP 10 5  NEWTON’S LAWS OF MOTION 3. LAW OF ACTION AND REACTION ORIGINAL TO EVERY ACTION, THERE IS ALWAYS OPPOSED AND EQUAL REACTION; OR THE MUTUAL ACTIONS OF TWO BODIES ON EACH OTHER AREA ALWAYS EQUAL AND DIRECTED TO CONTRARY SUMMARY TO EVERY ACTION, THERE IS AN EQUAL AND OPPOSITE REACTION EXAMPLES JUMPING 11 NEWTON’S LAWS OF MOTION 4. LAW OF ATTRACTION (LAW OF UNIVERSAL GRAVITATION) ORIGINAL EVERY BODY IN THE UNIVERSE ATTRACTS EVERY OTHER BODY WITH A FORCE DIRECTED ALONG THE LINE OF CENTERS (COM) FOR THE TWO OBJECTS THAT IS DIRECTLY PROPORTIONAL TO THE PRODUCT OF THEIR MASSES AND INVERSELY PROPORTIONAL TO THE SQUARE OF THE SEPARATION BETWEEN THE TWO OBJECTS SUMMARY ATTEMPTS TO EXPLAIN THE INTERACTION OF OBJECTS, EVEN WHEN THEY ARE NOT IN CONTACT (ACTION-AT-A-DISTANCE) 12 6  FREE-BODY DIAGRAMS A SIMPLIFIED REPRESENTATION OF THE SYSTEM FREE OF THE MOVEMENT ENVIRONMENT OFTEN A STICK FIGURE OR GEOMETRIC MODEL OF THE SYSTEM WITH THE CENTER OF MASS AND POINTS OF CONTACT WITH THE ENVIRONMENT DEPICTED FREE BODY DIAGRAMS ARE USED TO ILLUSTRATE ALL THE EXTERNAL FORCES ACTING ON AN OBJECT TO HELP VISUALIZE THE MANY COMPLEX FACETS OF A MOVEMENT SITUATION IN A SIMPLISTIC FORM FOR ANALYSIS LET’S DRAW SOME! 13 FREE-BODY DIAGRAMS - BODY 14 7  FREE-BODY DIAGRAMS – JOINT SEGMENT 15 FREE-BODY DIAGRAMS – HYPOTHETICAL 16 8  FORCE HUMANS INTERACT WITH AND MOVE WITHIN THE ENVIRONMENT THROUGH CONTROLLED APPLICATION OF FORCE FORCE IS A PUSH OR A PULL HOW DOES FORCE AFFECT MOTION? FORCES MAINTAIN OR CAUSE A CHANGE IN MOTION 18 FORCE PROPERTIES DIRECTION – THE WAY IN WHICH THE FORCE IS APPLIED ORIENTATION - THE ALIGNMENT OF THE VECTOR IN RELATION TO THE CARDINAL DIRECTIONS POINT OF APPLICATION – POINT OR LOCATION AT WHICH THE SYSTEM RECEIVES THE APPLIED FORCE MAGNITUDE – AMOUNT OR SIZE OF THE APPLIED FORCE LINE OF ACTION – AN IMAGINARY LINE EXTENDING INFINITELY ALONG THE VECTOR THROUGH BOTH THE TIP AND TAIL 19 9  VECTOR DESCRIBES A FORCE’S MAGNITUDE AND DIRECTION IN GRAPHICAL FORM THE LENGTH OF THE ARROW DESCRIBES HOW STRONG THE FORCE IS, THE DIRECTION OF THE ARROW SHOWS WHICH WAY THE FORCE IS TRAVELLING 20 INTERNAL VERSUS EXTERNAL FORCES INTERNAL EXTERNAL FORCES THAT ACT WITHIN THE OBJECT FORCES THAT ACT ON AN OBJECT DUE OR SYSTEM WHOSE MOTION IS BEING TO ITS INTERACTION WITH THE INVESTIGATED ENVIRONMENT SURROUNDING IT TENSILE APPLIED COMPRESSIVE NORMAL CONTACT FRICTION AIR RESISTANCE WHEN STUDYING MOTION OF AN OBJECT, WE IGNORE INTERNAL FORCES AND CONSIDER ONLY THE EXTERNAL FORCES THAT LEAD TO ITS ACCELERATION. 21 10  INTERNAL VERSUS EXTERNAL FORCES 22 FRICTION FRICTION IS THE FORCE THAT: EXISTS BETWEEN THE SURFACES OF TWO OBJECTS THAT ARE IN CONTACT AND ARE MOVING IN DIFFERENT DIRECTIONS OPPOSES THE MOTION BETWEEN THE SLIDING FORCES 23 11  FRICTION TWO TYPES STATIC FRICTION THIS IS THE FRICTIONAL FORCE THAT MUST BE OVERCOME TO GET AN OBJECT MOVING MAXIMUM LIMITING FRICTION IS THE AMOUNT OF FRICTION THAT DEVELOPS AT THE MOMENT PRIOR TO MOTION KINETIC (DYNAMIC) FRICTION THIS IS THE FRICTIONAL FORCE THAT RESISTS MOTION OF AN OBJECT (SLOWS THE OBJECT DOWN AS IT SLIDES) A RESISTIVE FORCE (OPPOSITE DIRECTION OF THE APPLIED FORCE) 24 FRICTION FRICTION IS F = µN F = FORCE OF FRICTION µ = COEFFICIENT OF FRICTION (PRONOUNCED “MU”) N = NORMAL (CONTACT) FORCE (PROPORTIONAL TO FRICTION (WHEN ONE INCREASES, SO DOES THE OTHER; ACTS PERPENDICULARLY TO FRICTION) FACTORS THAT INFLUENCE FRICTION WEIGHT SURFACE AREA CONTACTING MATERIALS 25 12  FRICTION IN TRAINING AND EXERCISE SLED PUSHING/PULLING WHAT HAPPENS IF YOU ADD MORE WEIGHT TO A SLED YOU ARE PUSHING? WHICH VARIABLE(S) CHANGE? WHAT DO YOU HAVE TO DO AS A RESULT? WHAT ROLE DO THE CONTACT SURFACES PLAY? THINK AND DISCUSS THESE IN BIOMECHANICAL TERMS 26 CALCULATING FRICTION IF THE COEFFICIENT OF FRICTION IS 0.32, THE MASS OF THE OBJECT IS 20 KG, HOW DO WE CALCULATE THE AMOUNT OF FORCE NEEDED TO MOVE THE OBJECT? 27 13  IMPORTANT TERMS RESULTANT FORCE THE RESULT OF THE ADDITION OF TWO OR MORE FORCE VECTORS NET FORCE VECTOR ADDITION OF ALL THE EXTERNAL FORCES ACTING ON AN OBJECT (POSITIVE AND NEGATIVE FORCES) CONCURRENT FORCES FORCES THAT DO NOT ACT ALONG THE SAME LINE OF ACTION, BUT THAT ACT THROUGH THE SAME POINT AT THE SAME TIME COLLINEAR FORCES FORCES THAT HAVE THE SAME LINE OF ACTION, THOUGH SOMETIMES IN DIFFERENT DIRECTIONS (I.E., TUG OF WAR) 29 IMPORTANT TERMS STATIC EQUILIBRIUM ANALYSIS OF OBJECTS AT REST, OR MOVING WITH A CONSTANT VELOCITY (ZERO ACCELERATION) EXTERNAL FORCES ACTING ON A SYSTEM ARE IN EQUILIBRIUM, AND THEREFORE RESULT IN A NET FORCE OF ZERO (∑F = 0) 30 14  CALCULATING RESULTANT FORCE COLINEAR IF FORCES ARE COLINEAR (ACTING IN THE SAME PLANE), THE RESULTANT FORCE IS THE DIFFERENCE BETWEEN THE SUM OF FORCES TUG OF WAR EXAMPLE (MAGNITUDE AND DIRECTION YOU AND YOUR TEAM PULL TO THE LEFT WITH FORCES OF 100 N, 200 N AND 400 N THE OTHER TEAM PULLS TO THE RIGHT WITH FORCES OF 200 N, 200 N, AND 200 N WHICH TEAM WINS? DETERMINE THE MAGNITUDE AND DIRECTION OF THE FORCES BY DRAWING A FREE-BODY DIAGRAM! 31 CALCULATING RESULTANT FORCE CONCURRENT IF FORCES ARE ACTING IN DIFFERENT PLANES OF MOTION, THE RESULTANT FORCE REQUIRES US TO USE TRIGONOMETRY RIGHT-ANGLE EXAMPLE (TWO FORCES) THERE IS A 30 N FORCE UPWARD AND A 10 N FORCE TO THE LEFT SOLVE THIS PROBLEM BY DRAWING A FREE-BODY DIAGRAM! TO SOLVE FOR… MAGNITUDE USE PYTHAGOREAN THEOREM TO FIND HYPOTENUSE (A2 + B2 = C2) = 𝑠𝑖𝑑𝑒 𝑎2 + 𝑠𝑖𝑑𝑒 𝑏2 DIRECTION (VECTOR RESOLUTION) VECTOR PARALLELOGRAM METHOD VECTOR CHAIN METHOD 32 15  CALCULATING RESULTANT FORCE CONCURRENT TRIGONOMETRIC TECHNIQUE PYTHAGOREAN THEOREM - A2 + B2 = C2 C A B 33 CALCULATING RESULTANT FORCE CONCURRENT IF FORCES ARE ACTING IN DIFFERENT PLANES OF MOTION, THE RESULTANT FORCE REQUIRES US TO USE TRIGONOMETRY RIGHT-ANGLE EXAMPLE (TWO FORCES) THERE IS A 30 N FORCE UPWARD AND A 10 N FORCE TO THE LEFT SOLVE THIS PROBLEM BY DRAWING A FREE-BODY DIAGRAM! TO SOLVE FOR… MAGNITUDE USE PYTHAGOREAN THEOREM TO FIND HYPOTENUSE (A2 + B2 = C2) = 𝑠𝑖𝑑𝑒 𝑎2 + 𝑠𝑖𝑑𝑒 𝑏2 DIRECTION (VECTOR RESOLUTION) VECTOR PARALLELOGRAM METHOD VECTOR CHAIN METHOD 34 16  CALCULATING RESULTANT FORCE CONCURRENT A GYMNAST IS ABOUT TO START HIS ROUTINE ON THE HIGH BAR, AFTER HE JUMPS UP TO GRAB THE BAR, HIS COACH APPLIES A FORCE TO THE FRONT AND BACK OF HIS TORSO TO GET HIM TO STOP SWINGING. RELEVANT INFORMATION: HORIZONTAL FORCE OF 20 N EXERTED BY COACH ON THE FRONT OF THE GYMNAST AND 30 N ON THE BACK OF THE GYMNAST UPWARD VERTICAL REACTION FORCE OF 550 N EXERTED BY THE BAR ON THE GYMNAST’S HANDS GYMNAST’S MASS IS 50 KG DRAW A FREE-BODY DIAGRAM TO DEMONSTRATE WHERE THE FORCES ARE ACTING CALCULATE THE RESULTANT FORCE 35 ADDITIONAL PRACTICE QUESTIONS 1. WHAT IS THE WEIGHT OF A 140 KG SUMO WRESTLER? 2. AN AEROBICS INSTRUCTOR WEIGHS 400 N, WHAT IS THEIR MASS? 3. MAIRIN IS A 55 KG ROAD CYCLIST. HERE BIKE WEIGHS 100 N. WHAT IS THE COMBINED WEIGHT? 4. BILLY IS TRYING TO SLIDE AN 80 KG BOX OF EQUIPMENT ACROSS THE FLOOR. THE COEFFICIENT OF STATIC FRICTION BETWEEN THE BOX AND THE FLOOR IS 0.55. IF BILLY ONLY PUSHES SIDEWAYS (HORIZONTALLY) AGAINST THE BOX, HOW MUCH FORCE MUST HE PUSH WITH TO INITIATE MOVEMENT OF THE BOX? 37 17  ADDITIONAL PRACTICE QUESTIONS 5. THE COEFFICIENT OF STATIC FRICTION BETWEEN THE SOLE OF AN ATHLETIC SHOE AND THE BASKETBALL COURT FLOOR IS 0.67. KEN WEARS THESE SHOES WHEN HE PLAYS BASKETBALL. IF KEN EXERTS A NORMAL CONTACT FORCE OF 1400 N WHEN HE PUSHES OFF THE FLOOR TO RUN DOWN THE COURT, HOW LARGE IS THE FRICTION FORCE EXERTED BY KEN’S SHOES ON THE FLOOR? 6. … MORE PRACTICE QUESTIONS ON LUMINATE! 38 QUIZ! AVAILABLE FRIDAY, JANUARY 17 @ 8:00 AM (THAT’S TOMORROW...) – SUNDAY, JANUARY 19 @ 11:59 PM THERE WILL BE NO EXTENSIONS AVAILABLE AFTER THE QUIZ HAS CLOSED AND NO RE-TAKE OPTIONS. DO IT WHILE THE CONTENT IS FRESH! 39 18  COMING UP… NEXT WEEK LECTURE – LINEAR KINEMATICS UPCOMING ASSESSMENTS WEEK 3 – QUIZ #2 (AVAILABLE FRIDAY, JANUARY 24 – SUNDAY, JANUARY 26) WEEK 4 – QUIZ #3 (AVAILABLE FRIDAY, JANUARY 30 – SUNDAY, FEBRUARY 2) WEEK 5 – LITERATURE REVIEW #1 (COMPLETED IN CLASS THURSDAY, FEBRUARY 6) 40 19