Chapter 12 Linear Kinetics of Human Movement – Part 3

1. Chapter 12Linear Kinetics of Human Movement – Part 3 Basic Biomechanics, 4th 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 moved W = 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/s2 = 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 andhas 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/s2 = 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 covering1.05 meters in 0.75 seconds. She weighs 598 N (61 kg). How much mechanical power does she generate? • W = Fd61 kg x 9.81 m/s2 x 1.05 m627.9 Nm or J • P = W/t627.9 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 mv2 = ½ kg ∙ (m2/s2) = ½ kg ∙ m/s2 ∙ 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 = magh

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

10. Potential Energy • Which has more potential energy? Boulder has nowhere to go so no potential energy Gas has chemical potential energy. Climber is high up, so she has 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.

11. Sample Potential EnergyProblem • What is the potential energy of a 75 kg barbell lifted and held at a height of 2 m? • PE = magh PE = 75 kg x 9.81 m/s2 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 kx2 k=constant x = distance over which the material is deformed

13. Kinetic Energy • Kinetic energy is the energy of things in motion: • Kinetic energy = 1/2 mass x velocity2 • Which has more kinetic energy? 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)(v2) • KE =.5 x 8 x 42 • KE = 64 kg ∙ m2/s2 • 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 = ½mv2 • OR… (v2)2 = (v1)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 = KE2 – KE1 • KE = ½(mv2) Δ KE = 0 – (.5 x .7 x 452) 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