Energy: The Capacity to Effect Change Presentation 2003 R. McDermott

Energy is all Around Us: It causes changes in velocity – kinetic energy It causes rearrangement – potential energy It stretches and compresses – elastic energy It 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 motion Rotational:spinning, tumbling Vibrational:back and forth Translational KE = ½ MV 2

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 Earth Changes the field geometry We (erroneously) say that energy is stored in the lifted object, but it is actually in the field Gravitational PE = Mg  H

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 k  X 2

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 system Energy dispersed into air, ground, etc. Heat, sound, light, etc Friction is a common cause Collisions 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:KE lost = Heat Heat = 400,000 J

Units Working from PE = Mg  H, energy must have units of kg-m 2 /s 2 But using F = Ma, we see that this is must also be equal to a N-m However, energy is assigned a derived unit, the Joule, which is equal to the units above All SI energy units are given in Joules Energy is a scalar

Energy is Constant – Isolated System Under normal conditions, energy cannot be created or destroyed An isolated system/object (no outside interactions) has a fixed amount of energy Although the change that energy produces (the “form of energy”) may change, the amount of energy in the system does not

Conservation of Energy In an isolated system, the total energy is constant though it may change “form” A falling object gradually “converts” PE to KE Releasing 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/object Earth is always part of the system Identify initial energy “forms” Identify final energy “forms” Set total initial energy equal to total final energy Solve

Roller Coaster – Energy Conservation As a coaster falls, PE is converted into KE Total PE + KE (mechanical energy) is constant PE lost = KE gained Mg  H = ½ MV 2 V =  (2g  H)

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:Mg  H = ½ MV 2 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/s It’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: Mg  H = ½ k  X 2  X = 6.3 m

Acknowledgements Animations courtesy of Tom Henderson, Glenbrook South High School, Illinois Artwork courtesy of Dr. Phil Dauber