kinetic energy

Kinetic EnergyEnergy due to motion reflects

– the mass – the velocity

of the object

KE = 1/2 mv2

Kinetic EnergyUnits: reflect the units of mass * v2

• Units KE = Units work

NmKE

mssmkgKE

ssmmkgKE

smkgKE

mvKE

2

1

)//(2

1

//2

1

)/)((2

12

1

2

2

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 EnergyCompare 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 momentumof each player

Potential EnergyTwo 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

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?)

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 GPEHow much gravitational potential energy in a

45 kg gymnast when she is 4m above the mat of the trampoline?

Trampoline mat is 1.25 mabove the ground

Calculate GPEGPE 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

More on this

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

…

Strain PEAffected 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 kx2

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• 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

)(2

1 2ifif rrmgvvmFd

PEKEFd

EnergyFd

Click here fora 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

)(2

1 2vivfif rrmgvvmFd

PEKEFd

EnergyFd

) (i vv v m Ft

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

• 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 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

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)