Kinetic Energy

1. Kinetic Energy Energy due to motion reflects • the mass • the velocity of the object KE = 1/2 mv2

2. Kinetic Energy Units: reflect the units of mass * v2 • Units KE = Units work

3. Calculate Kinetic Energy How much KE in a 5 ounce baseball (145 g) thrown at 80 miles/hr (35.8 m/s)?

4. Calculate Kinetic Energy Table of Variables Mass = 145 g  0.145 kg Velocity = 35.8 m/s

5. Calculate Kinetic Energy Table of Variables Select the equation and solve:

6. Calculate Kinetic Energy How much KE possessed by a 150 pound female volleyball player moving downward at 3.2 m/s after a block?

7. Calculate Kinetic Energy Compare KE possessed by: • a 220 pound (100 kg) running back moving forward at 4.0 m/s • a 385 pound (175 kg) lineman moving forward at 3.75 m/s Bonus: calculate the momentum of each player

8. Potential Energy Two forms of PE: • Gravitational PE: • energy due to an object’s position relative to the earth • Strain PE: • due to the deformation of an object

9. Gravitational PE • Affected by the object’s • weight • mg • elevation (height) above reference point • ground or some other surface • h GPE = mgh Units = Nm or J (why?)

10. Calculate GPE How much gravitational potential energy in a 45 kg gymnast when she is 4m above the mat of the trampoline? Take a look at the energetics of a roller coaster

11. Calculate GPE How much gravitational potential energy in a 45 kg gymnast when she is 4m above the mat of the trampoline? Trampoline mat is 1.25 m above the ground

12. GPE relative to mat Table of Variables m = 45 kg g = -9.81 m/s/s h = 4 m GPE relative to ground Table of Variables Calculate GPE More on this

13. Conversion of KE to GPE and GPE to KE and KE to GPE and …

14. Strain PE Affected by the object’s • amount of deformation • greater deformation = greater SE • x2 = change in length or deformation of the object from its undeformed position • stiffness • resistance to being deformed • k = stiffness or spring constant of material SE = 1/2 kx2

15. Strain Energy • When a fiberglass vaulting pole bends, strain energy is stored in the bent pole .

16. Strain Energy • When a fiberglass vaulting pole bends, strain energy is stored in the bent pole • Bungee jumping .

17. Strain Energy • When a fiberglass vaulting pole bends, strain energy is stored in the bent pole • Bungee jumping • Hockey sticks .

18. Strain Energy • When a fiberglass vaulting pole bends, strain energy is stored in the bent pole • Bungee jumping • When a tendon/ligament/muscle is stretched, strain energy is stored in the elongated elastin fibers (Fukunaga et al, 2001, ref#5332) • k = 10000 n /m x = 0.007 m (7 mm), Achilles tendon in walking • When a floor/shoe sole is deformed, energy is stored in the material . Plyometrics

19. Work - Energy Relationship • The work done by an external force acting on an object causes a change in the mechanical energy of the object Click here for a website

20. Work - Energy Relationship • The work done by an external force acting on an object causes a change in the mechanical energy of the object • Bench press ascent phase • initial position = 0.75 m; velocity = 0 • final position = 1.50 m; velocity = 0 • m = 100 kg • g = -10 m/s/s • What work was performed on the bar by lifter? • What is GPE at the start & end of the press?

21. Work - Energy Relationship • Of critical importance • Sport and exercise =  velocity • increasing and decreasing kinetic energy of a body • similar to the impulse-momentum relationship

22. Work - Energy Relationship • If more work is done, greater energy • greater average force • greater displacement • Ex. Shot put technique (121-122). • If displacement is restricted, average force is __________ ? (increased/decreased) • “giving” with the ball • landing hard vs soft

23. Gravitational Potential Energy • Gravitational potential energy: • PE that an object has by virtue of its HEIGHT above the ground • GPE = mass x freefall acceleration x height • GPE = mgh = (Fd) • mg = weight of the object in Newtons (F) • h = distance above ground (d) • GPE stored = Work done to lift object

24. A 65 kg rock climber ascends a cliff. What is the climber’s gravitational potential energy at a point 35 m above the base of the cliff? Given: m = 65 kg h = 35 m Unknown: GPE = ? J Equation: PE = mgh Plug & Chug: PE = (65 kg)(9.8 m/s2)(35 m) Answer: GPE = 22000 J GPE Example - Solved

25. What is the gravitational potential energy of a 2.5 kg monkey hanging from a branch 7 m above the jungle floor? Given: m = 2.5 kg h = 7 m Unknown: GPE = ? J Equation: GPE = mgh Plug & Chug: GPE = (2.5 kg)(9.8 m/s2)(7m) Answer: GPE = 171.5 J GPE Example - Unsolved

26. Kinetic Energy • Def: the energy of a moving object due to its motion • Moving objects will exert a force upon impact (collision) with another object. • KE = ½ (mass) (velocity)2 • KE = ½ (mv2)

27. The Impact of Velocity • Which variable has a greater impact on kinetic energy: mass or velocity? • Velocity! It’s SQUARED! • Velocity as a factor: • Something as small as an apple: • At a speed of 2 m/s = 0.2 J • At a speed of 8 m/s = 3.2 J(4 x velocity = 16x energy)

28. What is the kinetic energy of a 44 kg cheetah running at 31 m/s? Given: m = 44 kg v = 31 m/s Unknown: KE = ? J Equation: KE = ½ mv2 Plug & Chug: KE = ½ (44 kg)(31 m/s)2 Answer: KE = 21000 J KE Example - Solved

29. What is the kinetic energy of a 900 kg car moving at 25 km/h (7 m/s)? Given: m = 900 kg v = 7 m/s Unknown: KE = ? J Equation: KE = ½ mv2 Plug & Chug: KE = ½ (900 kg)(7 m/s)2 Answer: KE = 22050 J KE Example - Unsolved

30. Work-Energy Theorem • Imagine a rigid body that does work or has work done on it to overcome only inertia (i.e. to accelerate it) • Doesn’t experience friction, nor does it rise or fall in a gravitational field • Under these conditions the net work done equals the body’s change in kinetic energy. • W = ΔKE = KEf - KEi

31. Conservation of Energy • Objectives • Identify and describe transformations of energy • Explain the law of conservation of energy • Where does energy go when it “disappears”? • Analyze the efficiency of machines

32. Conservation of Energy • The Law of Conservation of Energy • Energy cannot be created nor destroyed, but can be converted from one form to another or transferred from one object to another • Total Energy of a SYSTEM must be CONSTANT!

33. Conservation of Energy • Total Mechanical Energy = Kinetic + Potential • TME = KE + PE • TME must stay the same! • If a system loses KE, it must be converted to PE • In reality… some is converted to heat • We will USUALLY consider frictionless systems  only PE & KE

34. Energy Conversions in aRoller Coaster • Energy changes form many times. • Energy from the initial “conveyor” • Work stored: Grav. Potential Energy • Some PE is converted to KE as it goes down • Some KE is converted to PE as it goes up • Where does the coaster have max. PE? • Where does the coaster have min. PE? • Where does the coaster have max. KE? • Where does the coaster have min. KE? • Where could energy be “lost”? • Friction, vibrations, air resistance

35. You have a mass of 20 kg and are sitting on your sled at the top of a 40 m high frictionless hill. What is your velocity at the bottom of the hill? Given: m = 20 kg h = 40 m Unknown: v = ? (at bottom) Equations: TME = PE + KE PE = mgh KE = ½ mv2 Plug & Chug: At Top: ME = mgh TME = (20 kg)(10 m/s2)(40 m) TME = 8000 J At Bottom: TME = ½ mv2 8000 J = ½ (20kg)(v2) v2 = 800 m2/s2 v = 28.3 m/s Conservation of Energy:Example Problem

36. Other Forms of Energy • Mechanical Energy – the total energy associated with motion • Total Mechanical Energy = Potential Energy + Kinetic Energy • Examples: roller coasters, waterfalls • Heat Energy – average kinetic energy of atoms & molecules • The faster they move, the hotter they get! • Ex. Boiling water, • Chemical Energy – potential energy stored in atomic bonds • When the bonds are broken, energy is released • Ex. Combustion (burning), digestion, exercise • Electromagnetic Energy – kinetic energy of moving charges • Energy is used to power electrical appliances. • Ex. Electric motors, light, x-rays, radio waves, lightning • Nuclear Energy – potential energy in the nucleus of an atom • Stored by forces holding subatomic particles together • Ex. Nuclear fusion (sun), Nuclear fission (reactors, bombs)