1FORCESChapter 1What is a FORCE? Push or a Pull Newton’s 2ndLaw: A force is something that has the ability to accelerate an object MECHANICALLY the object will Start Stop Speed up or down Change directionsUnits of Measure NEWTON (N) 1.0 N = 1 kg· m / s2 1.0 N = 0.225 lb 1 lb = 4.448 N FORCE = VECTOR Vector – mathematical representation of anything that is defined by size and magnitudeClassifying ForcesInternalAction – ReactionCannot change motion of object(See Mechanical Loads on body)MusclesStudy of injuryExternalResponsible for producing changes in motionMechanical Loads on the Human Body¾ Compression ¾ Tension¾ Shear¾ Stress¾ Torsion¾ Bending¾ Combined loadingWAYS MUSCLE FORCE ACT ON BONESÔ COMPRESSION: squeezing force (long axis)Ô TENSION: pulling apart, when muscles pull or contract (long axis)Ô SHEAR: slides, displaces, or shear with respect to each otherÔ TORSION: bone twists around long axis; a fixed bone at one endÔ BENDING: eccentric (off-center force) bone bends with compression and tension2BENDING & TORSION Loaded objects in bending subject to C/T stress Torsion = twisting; long axis Combined loadingEXTERNAL FORCES• Result of interaction with the environment• 2 Types of external forces•Contact• Solid or fluid objects• Can be resolved into parts/componets (┴ & //)• Perpendicular = NORMAL contact force• Parallel = FRICTION force• Non-contact (Gravity ~ weight)Figure 4.3FRICTIONforce acting parallel to the interface of two surfaces that are in contact during the motion or impending motion of one surface as it moves over the other.Mechanical Behavior of Bodies in Contact Friction:Maximum static friction (Fm)Kinetic friction (Fk)  F = µRCoefficient of friction: Coefficient of static friction (µs) Coefficient of kinetic friction (µk)FRICTIONFf= R= FfRR = normal force= coefficient of frictionµµµMay also see “N” for normal Coefficient of Friction: index of the interactionbetween 2 surfaces in contact Normal Reaction Force ®: force acting ⊥to 2 surfaces in contact Maximum Static Friction (Fm):max amount of friction generated between 2 static surfaces Kinetic friction (Fk):friction force during motion3MAXIMUM STATIC FRICTION FORCEFm=s RKinetic frictionFk= µkRµStatic Frictionµkis always smaller than µsAltering Amount of Friction Vertical component of force Increasing m Gloves Wax on a surfboard Wax on skis RosinFree Body DiagramFigures:1.161.171.191.20Defining QuantitiesVECTORKinematic = velocity, acceleration, displacementKinetic= force, weight, torqueSCALARHave magnitude not directionMass, volume, lengthFOUR PROPERTIES OF FORCE (VECTOR)1)Magnitude(size)2)Direction(orientation)3)Point of application4)Line of actionVector Algebra•Vector• Kinetic vector quantities • force weight, pressure, specific weight & torque• Kinematic vector quantities• Displacement, velocity & acceleration• Scalar quantities• Mass, volume, length & speed4Graphic Solution of Vector Problems Graphic vector manipulation may yield approximate result30 N = 3 cm35 N = 4.5 cm1 cm = 10 NVECTORSComposition- adding, subtracting and multiplying 2 or more vectors (RESULTANT)ScalarsGraphicallyRemember…magnitude & directionVector Composition Resultant vector “Tip-to-tail” vector compositionVector #1Vector #2Resultant vectorTip to Tail MethodResultantVECTORS Resolution- to break down into component parts For RIGHT triangles use: SIN COS TAN If unsure, use: LAW of COSINESHmmm…not sure about this. I better make it to a tutoring session because we’ll deal with it all semester!RESOLUTION Perpendicular components relative to a plane or structure 2 perpendicular components are different but representative of original Graphic solution must be to scale Trig solution uses Law of CosinesC2 = A2+ B2– 2(A)(B) cos Θ5Vector ResolutionVerticalHorizontalExample: A ball is thrown into the airTrigonometric Solution of Vector Problems A more accurate procedure for quantitatively dealing with vector problemsTrig VECTOR ResolutioncompcompSoh Cah ToaStatic Equilibrium¾Net Forces¾Newton’s 1stand 2ndLaws¾If ∑F = 0, ∆ v = 0 and vice versa¾If object is at rest or v is constant, NET F = 0¾In both cases, Feare in equilibrium¾Object is in STATIC equilibriumStatic Equilibrium Statics ~ branch of mechanics ANALYZE: Unmoving object (iron cross) External forces / Athlete’s strength Free Body Diagrams Mechanical representation of forcesStatic Analysis Newton’s 2ndLaw ∑F = ma In static situations, a = 0 so ∑F = 0 ∑F = net external force or vector sum of F Must consider magnitude and direction (sense of forces) Upward = positive (+) Downward = negative (-) External forces equal but in opposite directions6Vertical & Horizontal Forces ∑FxHorizontal forces ∑FyVertical forces R = reaction force To determine REACTION forces: Free body diagram (show all forces) Gravitational forces (weight) Collinear forces = 1 equation Concurrent forces = V & H equationsComponents of