ANGULAR KINETICS (Part 1 Statics) Readings: McGinnis (2005), Chapter 5.

Transcription

1 NGUL KINTICS (Part 1 Statics) eadings: McGinnis (2005), Chapter 5. 1 Moment of Force or Torque: What causes a change in the state of linear motion of an object? Net force ( F = ma) What causes a change in the state of angular motion of an object? Net moment of force or torque i.e., ngular analog of force is moment of force or torque. Centric vs. eccentric force: Centric force: Force whose line of action passes through an object's center of gravity (if there is no fixed axis) or through a fixed axis of rotation for an object. ffect produced? no fixed axis - linear acceleration only fixed axis - no motion

2 ccentric force: Force whose line of action passes off-center (i.e., eccentric) to an object's center gravity or its fixed axis of rotation. ffect produced? no fixed axis - linear and angular acceleration fixed axis - angular acceleration 2 upper arm e.g., muscle force e.g., eccentric force applied to tennis ball (e.g., biceps brachii muscle force forearm topspin forehand) n eccentric force produces a turning effect on an object... a Moment of force or Torque

3 Factors influencing the magnitude of a torque or moment: 1. Magnitude of the eccentric force 2. Distance from the axis of rotation that the force is applied... i.e., the moment arm of the force 3 M = F d Torque or ccentric Moment moment of force arm force Moment arm (d ) - the perpendicular distance from the line of action of the force to the axis of rotation (i.e., shortest possible distance between axis and line of action). e.g., moment produced by a muscle elb. ext. elbow jt. center elbow flexor elbow flexor forearm

4 e.g., Torques about the elbow during a biceps curl? 4 ccentric forces? weight in hand forearm weight muscle moments joint friction Perspective 1: esistance (barbell) 4 barbell weight = 200 N elbow-to-barbell distance = 35 cm 3 Moment (Nm) forearm angle (deg)

5 5 Perspective 2. lbow flexors (muscle torque) muscle force mid ~90deg late ~30deg early ~150deg jt. angle 150deg

6 e.g., torques during pedaling W Cycling - peak pedal force 14 tooth cog = 2.5 cm radius rear wheel = 35.5 cm radius 400 N crank arm = 175 mm 52 tooth chainring = 9.5 cm radius F ground Pedal F = 400 N Force delivered to road for propulsion? 1. Torque created by F pedal about crank axle: M C = (400 N) (17.5 cm) = N cm 2. Tension in chain (F chain ): M C = 7000 N cm = F chain (9.5 cm) F chain = N 3. Torque created by F chain about wheel axle: M W = (737 N) (2.5 cm) = N cm 4. Force delivered to ground: M W = 1843 N cm = F ground (35.5 cm) F ground = N ( lb)

7 Is the pedaling position shown one of the more or less effective positions for generating propulsive torque? 7 More effective... both the force applied to the pedal and its moment arm tend to be high at this time stimate of average propulsive force at ground? N stimate of resistive forces at 400 W? air resistance: 25 N rolling resistance: 5 N Bicycle gearing effects: ffect of shifting from a large sprocket to small sprocket at the pedals... decrease moment arm created by front sprocket (step 2) increase tension in chain (step 2)

8 increase F ground (step 4) i.e., given force applied to the pedal delivers a larger force at the ground; pedaling is "easier" but it requires more crank rotations to travel a given distance ffect of shifting from a large sprocket to small sprocket at the rear wheel... decrease moment arm created by rear sprocket (step 3) decrease torque developed about rear wheel axle (step 3) decrease Fground (step 4) i.e., given force applied to the pedal delivers a smaller force at the ground; pedaling is "harder" but it requires fewer crank rotations to travel a given distance 8

9 LVS 9 Multi-torque system serving as a simple machine - a rigid body with two or more moments acting on it e.g., human forearm during biceps curl e.g., pry bar For any lever, we can always identify: 1. an axis of rotation () 2. at least a pair of eccentric forces - usually described as force () and resistance ()

10 Lever as a simple machine a lever can serve to: 1. multiply the effect produced by a force e.g., a pry bar 2. increase the speed with which a body point can be moved e.g., lower leg during kicking Small speed of shortening of muscle... produces high speed of movement at distal end

11 Lever cannot serve to multiply both force and speed; it produces one effect at the expense of the other - a tradeoff. 11 Lever Classifications First class: - - dvantage - can be either force or speed... depends on relative sizes of and moment arms e.g., scissors (two 1st class levers connected together) e.g., forearm - concentric action of triceps (elbow extension) against resistance

12 12 Second class: - - dvantage - always force at the expense of speed... because moment arm > moment arm There are no notable anatomical examples of 2nd class levers. e.g., wheelbarrow

13 Third class: - - dvantage - always speed at the expense of force... because moment arm > F moment arm Many anatomical examples - most body segments function as 3rd class levers. 13 e.g., concentric action of biceps (elbow flexion) against resistance e.g., concentric action of quadriceps (knee extension) against resistance

14 Important implication of third class lever for human movement: muscles usually insert close to joint; resistances often carried on distal aspects of extremities... esult: muscles must generate high forces relative to resistances that must be moved BUT... a small amount and speed of shortening can produce large, fast movements at distal end of segment. e.g., What is the magnitude of the muscle force () needed to maintain the horizontal position of the forearm as shown in the diagram below? deg 5 cm a 18 cm 12 N 40 cm b 200 N

15 M CW = [( a d Wa ) + ( b d Wb )] = (12 N 18 cm) (200 N 40 cm) = 216 N cm 8000 N cm = 15 M CCW = (5 cm sin 60 ) = (4.33 cm) For static equilibrium, Thus N cm = (4.33 cm) = 8216 N cm / (4.33 cm) = (i.e., ~ lb) i.e., In this simple static equilibrium example, the muscular force needed to maintain the forearm in its horizontal position is substantially higher than the weight held in the hand (~ higher) because of the relatively short moment arm of the muscle relative to that of the weight. Demonstrates a typical situation in the human lever system... high muscle forces relative to resistances being moved.