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

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

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

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

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

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

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

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

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

Take a look at the energetics of a roller coaster 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

Calculate GPE Trampoline mat is 1.25 m above the ground 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

Calculate GPE More on this 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

Conversion of KE to GPE and GPE to KE and KE to GPE and …

Strain PE Affected by the object’s amount of deformation stiffness 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

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

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

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

Strain Energy Plyometrics 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

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

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?

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

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

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

GPE Example - Solved 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 - Unsolved 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

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)

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)

KE Example - Solved 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 - Unsolved 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

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

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

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!

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

Energy Conversions in a Roller 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

Conservation of Energy: Example Problem 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

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)