1. Chapter 12 Linear Kinetics of Human Movement – Part 3 Basic Biomechanics, 4 th edition Susan J. Hall Presentation Created by TK Koesterer, Ph.D., ATC Humboldt State University

2. WORK Work done on a body by a force is equal to the product of its magnitude and the distance the body moves in the direction of the force. Work = Force magnitude x Distance movedW = Fd Positive work: motion in same direction as applied force (concentric) Negative work: motion in opposite direction as applied force (eccentric) Common units: joule (J) J = Nm =.7376 ft∙lb Mechanical work  caloric expenditure This is a jewel

3. Sample Work Problem A weight lifter performs a two-hand snatch, a lift in which a barbell is raised overhead in one continuous motion. If he lifts 60 kg upward, 2 meters, what amount of work did he perform? 60 kg x 9.81 m/s 2 = 589 N (F = ma) 589 N x 2 m = 1178 Nm or Joules The weight lifter holds the 60 kg barbell overhead. How much work does he perform? 589 N x 0 m = 0 Nm or Joules

4. Sample Work Problem Adrian has a body mass of 76 kg and has an arm length of 61 cm (distance from chin to bar). If he performs 10 pull-ups, what amount of work did he perform? 76 kg x 9.81 m/s 2 = 745.5 N 745.5 N x 0.61 m = 454.8 Nm or J How much work does Adrian perform on his descent? Eccentric contraction is negative work.

5. POWER Power: rate at which mechanical work is performed Power = Work=W change in time  t Power = force x distance =Fd change in time  t Since v = d /  t, Power = Fv Units: watts (W)1 W = 1 J/s English Units: horsepower 1 hp = 550 ft·lb/s (746W)

6. Sample Power Problem Brianna bounded up the six steps covering 1.05 meters in 0.75 seconds. She weighs 598 N (61 kg). How much mechanical power does she generate? W = Fd 61 kg x 9.81 m/s 2 x 1.05 m 627.9 Nm or J P = W/t 627.9 J / 0.75 s = 837.2 J/s or Watts

7. ENERGY Energy: the capacity to do work Forms: mechanical, chemical, nuclear, heat, etc. Mechanical energy is capacity to do mechanical work. Units are the same as work: joules

8. ENERGY Kinetic energy (KE): energy of motion KE = ½ mv 2 = ½ kg ∙ (m 2 /s 2 ) = ½ kg ∙ m/s 2 ∙ m = ½ mass ∙a∙ distance KE = ½ Force ∙ distance (N ∙ m or J) Potential energy (PE): energy by virtue of a body’s position or configuration PE = (wt)(h) = N ∙ m (J) or lb ∙ ft PE = ma g h

9. Potential Energy Energy due to position or composition. Stored Energy.

10. Potential Energy Which has more potential energy? A gallon of gas can move a car 30 miles, but a rock climber landing on a car won’t really move it much at all. Boulder has nowhere to go so no potential energy Climber is high up, so she has potential energy Gas has chemical potential energy.

11. Sample Potential Energy Problem What is the potential energy of a 75 kg barbell lifted and held at a height of 2 m? PE = ma g h PE = 75 kg x 9.81 m/s 2 x 2 m =1471 Nm

12. Strain Energy Strain energy (SE): capacity to do work by virtue of a deformed body’s return to its original shape A form of potential energy SE = 1/2 kx 2 k=constant x = distance over which the material is deformed

13. Kinetic Energy Which has more kinetic energy? Kinetic energy is the energy of things in motion: 2Kinetic energy = 1/2 mass x velocity 2 Not moving no kinetic energy Velocity is 1800 km/hour mass is 10 grams 140 km/hour 145 grams 10 times more energy than the baseball

14. Sample Kinetic Energy Problem What is the kinetic energy of an 8 kg bowling ball rolling with a velocity of 4 m/s? KE = ½(m)(v 2 ) KE =.5 x 8 x 4 2 KE = 64 kg ∙ m 2 /s 2 KE = 64 Nm or J

15. Conservation of Mechanical Energy Consider a ball tossed vertically into the air Law of conservation of mechanical energy: When gravity is the only acting external force, a body’s mechanical energy remain constant (PE + KE) = C –C is a constant indicating the total amount of energy in a system when gravity is the only external force acting on the system –As PE increases, KE decreases and vice-versa

16. Sample Problem A 10 kg pumpkin is dropped off a building’s roof from a height of 18 m. What is the velocity immediately before impact with the sidewalk? PE + KE = C PE = (wt)(ht) and KE = ½mv 2 OR… (v 2 ) 2 = (v 1 ) 2 + 2ad

17. Principle of Work & Energy The work of a force is equal to the change in energy that it produces on the object acted on W =  KE +  PE +  TE Mechanical work  caloric expenditure ~25% of energy consumed by muscle is converted into work, thus ~75% is thermal energy or used in chemical processes. TE = Thermal Energy

18. Sample Problem How much mechanical work is required to catch a 0.7 kg hockey puck shot traveling at a velocity of 45 m/s? W = Δ KE = KE 2 – KE 1 KE = ½(mv 2 ) Δ KE = 0 – (.5 x.7 x 45 2 ) Δ KE = 708.75 Nm

19. Summary Mechanical work is the product of force and the distance through which the force acts Mechanical power is the mechanical work done over a time interval Mechanical energy has two forms: kinetic and potential When gravity is the only acting external force, the sum of the kinetic and potential energies possessed by a given body remains constant Changes in a body’s energy are equal to the mechanical work done by an external force