Energy:

The Capacity to Effect Change

Presentation 2003 R. McDermott

Energy is all Around Us:

It causes changes in velocity – kinetic energyIt causes rearrangement – potential energyIt stretches and compresses – elastic energyIt causes heating – dissipated energy

Energy is Energy!

Don’t be confused; all energy is the same, the only difference is the change that energy produces.Energy is like water; pouring it into different containers may make it look different, but it really isn’t.

Kinetic Energy – Energy of Motion

Energy that causes motion is called kinetic energy:

Translational: linear motionRotational: spinning, tumblingVibrational: back and forth

Translational KE = ½ MV2

Example:What is the kinetic energy of a 2000kg car moving at 40m/s?

Answer: 1,600,000 J

Comments:Kinetic energy is directly proportional to mass; doubling the mass doubles the KE

Kinetic energy is directly proportional to the square of the velocity; doubling velocity quadruples the KE

Velocity is a larger factor in determining KE than is mass

Gravitational PE – Energy of Height

Energy stored in gravitational field due to separation of mass and EarthChanges the field geometryWe (erroneously) say that energy is stored in the lifted object, but it is actually in the fieldGravitational PE = MgH

Example:How much potential energy is stored when a 100kg man climbs to the top of a 1000m peak?

Answer: 981,000 J

Comments:Gravitational potential energy is directly proportional to mass and height; doubling either one doubles the PE

Gravitational potential energy is also directly proportional to the gravitational field strength; traveling to a planet with a higher ‘g’ would cause higher PE values for a given height.

Elastic Energy – Energy of a Spring

Stretch or Compression

Energy stored in spring

A type of potential energy

Spring PE = ½ kX2

Example:How much elastic energy is stored in a spring (k= 8 N/m) that is compressed by 0.05 m?

Answer: 0.01 J

Comments:Elastic potential energy for a spring is directly proportional to the spring strength (k); doubling k doubles the PE

Elastic potential energy is also directly proportional to the square of the stretch or compression; doubling quadruples the PE

Stretch/compression is a larger factor in determining PE than is the value of k

Dissipated Energy – “Lost” Energy Non-isolated systemEnergy dispersed into air, ground, etc.Heat, sound, light, etcFriction is a common causeCollisions also lead to dissipated energy

Example:A 2000 kg car moving at 20 m/s brakes to a stop. How much heat is produced in the brakes?

Answer: KElost = Heat Heat = 400,000 J

UnitsWorking from PE = MgH, energy must have units of kg-m2/s2 But using F = Ma, we see that this is must also be equal to a N-mHowever, energy is assigned a derived unit, the Joule, which is equal to the units aboveAll SI energy units are given in JoulesEnergy is a scalar

Energy is Constant – Isolated System

Under normal conditions, energy cannot be created or destroyedAn isolated system/object (no outside interactions) has a fixed amount of energyAlthough the change that energy produces (the “form of energy”) may change, the amount of energy in the system does not

Conservation of EnergyIn an isolated system, the total energy is constant though it may change “form”

A falling object gradually “converts” PE to KEReleasing a spring “converts” PE to KE

In a non-isolated system, total energy can include dissipated energy to maintain a constant total

A braking car converts KE to heat

In these cases, total energy before = total energy after

Conservation

Energy and Position

Solving Conservation Problems:Identify the system/objectEarth is always part of the systemIdentify initial energy “forms”Identify final energy “forms”Set total initial energy equal to total final energySolve

Roller Coaster – Energy Conservation

As a coaster falls, PE is converted into KETotal PE + KE (mechanical energy) is constant

PE lost = KE gainedMgH = ½ MV2

V = (2gH)

Example:A 2000 kg roller coaster car moves to the top of a 100m hill and then falls. Assuming it started at rest, how fast will it be moving when it reaches the bottom of the hill?

Answer: MgH = ½ MV2

V = 44.3 m/s

Follow-up:A 2000 kg roller coaster car moves to the top of a 100m hill and then falls. How fast will the car be moving when it is halfway down?

Answer: 31.3 m/sIt’s the KE that is half, not the velocity!

Spring Example:A 2.0 kg block falls 10 m in compressing a spring (k = 10 N/m). What was the compression of the spring?

Answer: MgH = ½ kX2 X = 6.3 m

AcknowledgementsAnimations courtesy of Tom Henderson, Glenbrook South High School, IllinoisArtwork courtesy of Dr. Phil Dauber