Work, Power, and Energy

1. Work, Power, and Energy Explaining the Causes of Motion Without Newton

2. Objectives • Define mechanical work • Distinguish the differences between positive and negative work • Define energy • Define kinetic energy

3. Objectives • Define gravitational potential energy • Define strain energy • Explain the relationship between mechanical work and energy • Define power

4. Introduction • The explanations for the causes of motion described in this chapter do not rely on Newton's laws of motion but rather on the relationship between work, energy, and power • Some analyses and explanations are easier if based on work and energy relationships rather than Newtonian mechanics

5. Work • Product of force and the amount of displacement in the direction of that force • Means by which energy is transferred from one object or system to another • U = F(d) • U = work done on an object • F = average force applied to an object • d = displacement of an object along the line of action of the force

6. Work • Units for work are units of force time units of length (ft·lb or Nm) • International units—joule(J) is the unit of measurement for work • 1J = 1Nm

7. Work • To determine the amount of work done on an object we need to know three things: • Average force exerted on the object • Direction of this force • Displacement of the object along the line of action of the force during the time the force acts on the object

8. Work • Discus thrower exerts an average force of 1000N against the discus while the discus moves through a displacement of .6m in the direction of this force • How much work did the discus thrower do to the discus?

10. Work • A weightlifter bench-presses a 1000N barbell—Begins the lift with arms extended and the barbell 75cm above the chest—Lowers the barbell to 5cm above the chest—Lifts the barbell back to the starting position 75cm above the chest—Average force while lowering and lifting 1000N upward • How much work did the lifter do on the barbell from the start until the finish of the lift?

12. Work • How much work during the lowering? • How much work during lifting? • Work can be positive or negative • Positive work is done by a force acting on an object if the object is displaced in the same direction as the force—Examples? • Negative work is done by a force acting on an object when the object is displaced in the direction opposite the force acting on it—Examples?

13. Work • Sample Problem 4.1 (text p. 105) • A therapist is stretching a patient—Therapist pushes on the patient’s foot with an average force of 200N—Patient resists the force and moves the foot 20cm toward the therapist • How much work did the therapist do on the patient’s foot during this stretch?

14. Work • Muscles can also do mechanical work • When a muscle contracts it pulls on points of attachment • Limbs move in the direction of the applied force—Concentric muscle action (positive work) • Limbs move in the direction opposite the applied force—Eccentric muscle action (negative work) • No movement—Isometric muscle action (no mechanical work)

15. Energy • Capacity to do work • Many forms (e.g. heat, light, sound, chemical) • In sports primarily concerned with mechanical energy • Kinetic—energy due to motion • Potential—energy due to position

16. Kinetic Energy • Moving object has the capacity to do work due to its motion • Mass and velocity of an object affects kinetic energy and the capacity to do work • Kinetic energy is proportional to the square of the velocity

17. Kinetic Energy • KE = ½mv² • KE = kinetic energy • m = mass • v = velocity • Units for kinetic energy are units of mass times velocity squared, or kg(m²/s²) or [kg(m/s²)]m or Nm or Joules • Unit of measurement for kinetic energy is the same as the unit of measurement for work

18. Kinetic Energy • How much kinetic energy does a baseball thrown at 80mi/hr (35.8m/s) have? A baseball mass is 145g (.145kg). • Determining the kinetic energy of an object is easier than determining the work done by a force, because we can measure mass and velocity more easily than we can measure force

19. Potential Energy • Energy an object has due to position • Gravitational—Energy due to an object’s position relative to the earth • Strain—Energy due to the deformation of an object

20. Gravitational Potential Energy • Related to the object’s weight and its elevation or height above the ground or some reference point • PE = Wh or PE = mgh • PE = gravitational potential energy • W = weight • m = mass • g = acceleration due to gravity • h = height

21. Gravitational Potential Energy • How much gravitational potential energy does a 700N ski jumper have at the top of a 90m jump? • Bottom of the hill is the reference point

22. Strain Energy • Energy due to the deformation of an object • Related to stiffness, material properties, and its deformation • SE = ½kΔx² • SE = strain energy • k = stiffness or spring constant of material • Δx = change in length or deformation of the object from its undeformed position

24. Strain Energy • How much strain energy is stored in a tendon that is stretched .005m if the stiffness of the tendon is 10,000N/m? • In human movement and sports, energy is possessed by athletes and objects due to their motion (kinetic energy), their position above the ground (potential energy), and their deformation (strain energy)

25. Work—Energy Relationship • Relationship exists between work and energy—Work done on an object can change total mechanical energy • Discus example • What was the velocity of the discus at the end of the period of work?

26. Work—Energy Relationship • Work done = ΔKE + ΔPE +ΔSE • Work done = ΔKE + 0 + 0 • Potential energy is zero because the displacement of the discus was horizontal • m = 2kg • U = 600J • vi = 0m/s • vf = ?

27. Work—Energy Relationship • The work done by the external forces (other than gravity) acting on an object causes a change in energy of the object • U = ΔE • U = ΔKE + ΔPE +ΔSE

28. Doing Work to Increase Energy • In sports and human movement, we are often concerned with changing the velocity of an object • Changing velocity means changing kinetic energy • Large change in kinetic energy (and thus a large change in velocity) requires that a large force be applied over a long displacement • Similar to impulse/momentum relationship

29. Doing Work to Increase Energy • Rules for shot putting indicate that the put must be made from a 7ft diameter circle • Size of the ring thus limits how much work the athlete can do to the shot by constraining the distance over which the putter can exert a force on the shot • Early 20th century, shot-putters began their put from the rear of the ring

31. Doing Work to Increase Energy • Technique has now evolved with shoulders turned toward rear of the circle in the initial stance—Allowed greater displacement of shot before release • Work done on the shot increased—Greater height (potential energy) and velocity (kinetic energy) of the shot at release—Resulted in longer put

33. Doing Work to Increase Energy • Sample Problem 4.2 (text p. 110) • Pitcher exerts an average horizontal force of 100N on a .15kg baseball during delivery of a pitch—Hand and ball move through a horizontal displacement of 1.5m during the period of force application—If the ball’s horizontal velocity was zero at the start of the delivery phase, how fast will the ball be going at the end of the delivery phase when the pitcher releases the ball?

34. Doing Work to Increase Energy • m = .15kg • F = 100N • d = 1.5m • vi = 0 • vf = ? • U = ΔE

35. Doing Work to Decrease Energy • When you catch a ball, its kinetic energy is reduced (or absorbed) by the negative work you do on it • Your muscles do negative work on your limbs and absorb energy when you land from a jump or fall • Average force you must exert to absorb energy in catching a ball or landing from a jump or fall depends on how much energy must be absorbed and the displacement over which the force is absorbed

36. Doing Work to Decrease Energy • Safety and protective equipment used in many sports utilizes the work/energy principle to reduce potentially damaging impact forces • Examples of shock absorbing or energy absorbing materials • Landing pads (gymnastics, high jumping, and pole vaulting) increase displacement of the athlete during the impact period • Sand (long jumper), water (diver), midsole material in shoes (runner)

37. Conservation of Mechanical Energy • Total mechanical energy of an object is constant or conserved when no external forces (other than gravity) act on the object (e.g. projectile motion) • Drop a 1kg ball from a height of 4.91m– Potential energy (PEi) of the ball just before letting go is the same as the kinetic energy (KEf) of the ball just before hitting the ground

38. Conservation of Mechanical Energy • We can determine how fast the ball was going just before it hits the ground • PEi = Kef • mgh = ½mvf² • We could also use the equation from Chapter 2 • vf² = 2gy (p. 66)

39. Conservation of Mechanical Energy • Pole vaulting • Total mechanical energy at the instant of takeoff should equal the total mechanical energy at bar clearance • Vaulters kinetic energy at takeoff is transformed into strain energy as the pole bends, and this strain energy is then transformed into potential energy • Height of a pole vault largely dependent on running speed

40. Power • Rate of doing work • In sports, excelling requires not just the ability to do a large amount of work, but also the ability to do that work in a short amount of time • Power can be thought of as how quickly or slowly work is done

41. Power • SI units for power are watts (W) • 1W = 1J/s • P = U/Δt • P = power • U = work done • Δt = time taken to do the work • P = F(d)/Δt • P = Fv

42. Power • Power can be defined as average force times average velocity along the line of action of that force • Combination of force and velocity determines power output—What is the best tradeoff? • Cycling—Higher gear (higher pedal forces and slower pedal rate) versus Lower gear (lower pedal forces and higher pedal rate)

43. Power • Characteristics of muscles determine the optimal tradeoff between force and velocity • As a muscle’s velocity of contraction increases, its maximum force of contraction decreases • If the muscle’s velocity of contraction is multiplied by its maximum force of contraction for that velocity, the muscle’s power output for each velocity can be determined • Maximum power occurs at a velocity approximately one-half the muscle’s maximum contraction velocity (depending on specific movement and training status)

44. Power • Places a constraint on performance • Duration of activity influences the power output that an individual can sustain • Olympic weightlifter performing a clean and jerk (high force and high velocity) generates a VERY LARGE power output, but only for a brief interval of time • Sprinter, middle distance runner, marathon runner—Power output progressively decreases as the length of the activity increases

46. Summary • Work done by a force is the force times the displacement of the object along the line of action of the force acting on it • Energy is the capacity to do work • Energy can be divided into potential (position) and kinetic (motion) • Potential energy can be divided into gravitational and strain • The work done by a force (other than gravity) causes a change in energy of an object • Power is defined as the rate of doing work