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Energy

Energy. Overview. What is Work?. Definition The product of the component of the applied force (F) on an object in the direction of displacement, and the magnitude of the displacement (d) Formula

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Energy

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  1. Energy Overview

  2. What is Work? • Definition • The product of the component of the applied force (F) on an object in the direction of displacement, and the magnitude of the displacement (d) • Formula • W = F * d (cosθ), where θ is the angle between the applied force and the direction of displacement = often = 0) • Units • Newton-meters = Joules • Note! No displacement – No work done!

  3. Two models • Push/pull (horizontal) • W = F x d x cosθ (cosθ = 1 for zero angle) • Lifting model (against gravity @ steady speed) • Work = F x d = F x h • But F = weight = mg • W = mg x d (or W = mgh)

  4. Force, Work & Energy • Force: agent of change • Energy: measure of change • Work: way of transferring energy

  5. What is Energy? • Energy = something that objects have – stored up work. • Types? • Mechanical • Chemical • Nuclear • Thermal • Electrical • Solar…

  6. Focus on Mechanical Energy • 2 forms of mechanical energy • Kinetic (KE) • Potential (PE) • Energy is a scalar quantity • Units • Joules (J), same as work

  7. Kinetic Energy (KE) • The KE of an object is the energy that it possesses due to its movement or motion and is equal to the work which the body could do in coming to rest. • Formula • KE = ½ mv2 where • m = mass of the object • v = velocity of the object at that instant

  8. KE Example • What is the kinetic energy of a 1000 kg Honda Civic traveling at 30 m/s? • Given • m = 1000 kg, v = 30 m/s, KE=? • Solve • KE = ½ mv2 • KE = ½ * 1000 * 302 • KE = 450,000 J What about a 100,000 kg locomotive at the same velocity?

  9. Work-Energy Theorem • A body in motion has energy and therefore the capability to do work. • Net work done on a body by an external net force is equal to the change in KE of the body • W = KE = KEf – KE0 = ½ mvf2 – ½ mv02 • Since Work (W) = force (F) * distance (d) * cos, • F * d = ½ mvf2 – ½ mv02 or • F * d = ½ m(vf2 – v02) (assume θ = 0)

  10. Practice – Work Energy Theorem • How much braking force is required to decelerate a 1000 kg (m) Civic from 30 m/s (vo) to 20 m/s (vf) in 250 meters (d)? • Solve for F • F * d = ½ mvf2 – ½ mv02 • F x 250 = 1/2*1000*202 – 1/2*1000*302 • F x 250 = -250,000 • F = -1000 N

  11. Potential Energy (PE) • What is PE? • 2 forms for study • Gravitational PE • Energy due to position • Working against/with gravity in a vertical plane • Elastic PE • Stored energy

  12. Potential Energy (PE) #1 • Gravitational PE of an object is the energy it possesses due to its position, and is equal to the work being done in moving the object to its position from some reference level. • Example - consider a bag of books, mass m, being lifted through height h, for storage on the top shelf in a library - working against gravitational acceleration g. • Formula • PE = mgh

  13. Potential Energy (PE) #2 • Stored/Elastic PE of an object is the energy it possesses due to work being done to compress or expand the structure of the body. • Example 1 – A compressed spring • PE = ½ kx2, where • k = spring constant • x = displacement • Example 2 - A bow and arrow

  14. PE Example • What is the potential energy of a 10 kg box of books that has been lifted to a shelf 3 meters above the floor? • Given • M = 10 kg, g = 9.8 m/s2, d = 3m, PE=? • Solve • PE = mgh • PE = 10 * 9.8 * 3 • PE = 294 J

  15. Summary so far… • Mechanical energy • KE (½ mv2) • Driven by velocity • As v↑ KE↑ (and v-v) • PE (mgh) • Driven by position (height) • As h↑ PE↑ (and v-v)

  16. Energy of Freely-Falling Bodies • When a body falls freely, its velocity increases and so its KE increases. Conversely, its height above the stated reference level decreases and so its PE decreases. • Total Mechanical Energy is constant • PEtop + KEtop = KEbottom + PEbottom (energy conservation) • (mgh + ½ mv2)top= (mgh + ½ mv2)bottom • Mass cancels, showing that the energy transformed is independent of mass. • For a freely-falling body, the total mechanical energy is constant, • KE + PE = constant at any instant

  17. Law of Conservation of Energy (CoE) • Energy can be neither created nor destroyed, but may be converted from one form to another. • The total mechanical energy at any point is constant • The case of a freely-falling body is an example of this law, as PE is being converted to KE.

  18. CoE Example - Roller Coaster

  19. Ski jump/roller coaster model Note: Skier starts from rest – velocity = 0, thus KE = 0

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