Skeletal Muscle - Tension

1. Skeletal Muscle - Tension (2) active tension (muscle activation) Excitation-contraction coupling Ca2+, ATP Muscle size (cross-sectional area) Muscle length (stretch) Rate coding (frequency modulation) & motor unit recruitment Shortening velocity Temperature Fiber-type Reflexes

2. Force-velocity relationships: types of muscle contractions Isometric - muscle length remains constant Static mechanics SFx,y = 0; ST = 0 Isotonic Concentric (shortening) Eccentric (lengthening)

3. Force-velocity relationships: types of muscle contractions Concentric Contraction - shortening contraction The torque produced by the muscles at the joint overcomes resistance to movement Inertia and weight of body segments/limb Outside contact forces (impact, free weight, etc.)

4. Force-velocity relationships: types of muscle contractions Eccentric Contraction The torque produced by muscles at the joint is less than the resistance to movement 1. Muscle must produce some tension 2. Usefulness Braking against a powerful/rapid movement in order to protect joints/muscles (co-contraction) Ex. Lifting a heavy weight Braking against gravity (also protection) Ex. Letting down a heavy weight Precise movement towards a target Ex. Catching a softball

5. Force-Velocity Relationship

6. Torque-angle relationships

7. Anatomical Analysis of Movement

8. Anatomical Analysis of Movement

9. Mechanical Work A force applied an object multiplied by the displacement of that object in the direction of the applied force SYMBOL: W FORMULA: W = F•d UNITS: Metric - Joules (J) 1J = 1 N•m English – foot•lbs Exs. Lifting a free weight, riding a cycle ergometer, pushing a sled (if frictional force measured - dynamometer)

10. Mechanical Work Problem: Calculate the work involved in lifting a 300 N weight a height of .6 m W = F•d W = (300N)(.6 m) W = 180 N•m = 180 J

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12. Energy DEFINITION: the ability to produce work. It is manifested in various forms: Motion (kinetic) Position (potential) Strain (spring) Heat, light, sound UNITS: Joules (J), calories

13. Energy Types: Formula: Motion (kinetic) Ek = 1/2 m•v2 Position (potential) Ep = m•ag•h Strain (spring) Es = 1/2k•x2 Heat, light, sound UNITS: Joules (J), calories

14. Mechanical Gross Efficiency Efficiency = mechanical work/energy Most exercises (weightlifting, climbing stairs, cycling) ~ 20% efficient!

15. Mechanical Efficiency Walking and running >>20% efficient! Why? “Natural springs” (arch of foot, Achilles’ tendon, muscles)

16. Strain Energy – ApplicationNatural Springs • For a man with a mass of 70 kg running at a velocity of 4.5 m/s, the arch of the foot will store about 17 J of energy when the foot is at maximum compression. • Each Achilles’ tendon + plantar flexors stores about 35 J of energy. • Other muscles (ex. quads) store >20 J of energy • This equals a return of over 50% of the energy expended while running (~110 J). • Energy Savings when recoil force used during pushoff

17. Mechanical Efficiency Walking and running >>20% efficient! Why? “Natural springs” (arch of foot, Achilles’ tendon, muscles) Legs act as a pendulum in locomotion f = 1/(2?)??(ag/l) Where: ag = acceleration due to gravity l = distance from axis of rotation to center of mass (gravity) most efficient running speed will match the dynamic pendulum frequency of the limbs this is a dynamic frequency which changes as joint angles change in a multi-segmented limb Aging, stroke, injury, crutches, neuromuscular disease decrease efficiency dramatically

18. Power The amount of work performed in given time period (rate of work performed. SYMBOL: P FORMULA: P = W/Dt = F•d/Dt = F•v strength x speed UNITS: Metric – watts (W) 1W = 1J/sec English – horsepower

19. Power and Work Calculation GIVEN: A person weighing 580 N runs up a flight of 30 stairs, each with a height of 25 cm. The time for this effort is 15 seconds. FIND: The work and power done

20. Power and Work Calculation

21. Force-Velocity Relationship

22. Concentric Force - Velocity Curve

23. Power – Velocity Curve

24. Power and Force – Velocity Curves

25. Muscle Dynamics Strength Dead lift Bench press Lifting a suitcase Power 100 m dash High jump Shot put Speed Badminton swing Frisbee throw Short shop stab for a line drive

26. Energy DEFINITION: The capacity to do work UNITS: The same as the units for work (joules) Two Forms of motion Kinetic Energy Potential Energy

27. Kinetic Energy DEFINITION: The energy of motion. SYMBOL: KE FORMULA: KE = 1/2(mv2) (Kinetic energy equals one-half of an object’s mass times the square of its velocity.) For a motionless body, v = 0, therefore KE = 0

28. Kinetic Energy Calculation GIVEN: A ball with a weight of 70 N is rolling with a velocity of 3 m/s. FIND: The kinetic energy of the ball m = weight / g = 70 N / 9.81 m/s2 = 7.14 kg KE = 1/2(mv2) = 1.2(7.14 kg)(3 m/s)2 = 32.11 J

29. Potential Energy DEFINITION: The energy of position. SYMBOL: PE FORMULA: PE = m•ag•h (Potential energy equals the weight of an object times its height above a surface to which it could fall.) Increasing an object’s height increases its potential energy.

30. Potential Energy Calculation GIVEN: A ball with a weight of 70 N is resting on a shelf that is 2 m above the floor FIND: The potential energy of the ball PE = m•ag • h = 70 N • 2 m = 140 J