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Conservation of Mechanical Energy

Conservation of Mechanical Energy. 6.5. Mechanical Energy. KE and PE = total mechanical energy E = KE + PE Actually there are other forms of energy to include, but we haven’t met them yet in the book. Work Energy Theorem (again). W nc = (KE f – KE 0 ) + (PE f – PE 0 ) Rearrange

JasminFlorian
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Conservation of Mechanical Energy

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  1. Conservation of Mechanical Energy 6.5

  2. Mechanical Energy • KE and PE = total mechanical energy • E = KE + PE • Actually there are other forms of energy to include, but we haven’t met them yet in the book

  3. Work Energy Theorem (again) • Wnc = (KEf – KE0) + (PEf – PE0) • Rearrange • Wnc = (KEf + PEf) – (KE0 + PE0) • Wnc = Ef – E0 • Nonconservative forces change the total mechanical energy of the system

  4. Wnc = 0 • Wnc = Ef – E0 • If Wnc = 0 like if friction or air resistance is negligible • 0 = Ef – E0 • Ef = E0 • If all forces are conservative, then the total mechanical energy does not change

  5. Conservation of Mechanical Energy • If there is no work done by nonconservative forces • Total mechanical energy is constant KE0 + PE0 = KEf + PEf

  6. Example 1 • A cyclist approaches the bottom of a gradual hill at a speed of 11 m/s. The hill is 5.0 m high, and the cyclist estimates that she is going fast enough to coast up and over it without pedaling. Ignoring air resistance and friction, find the speed at which the cyclist crests the hill. • v = 4.8 m/s

  7. Example 2 • A slingshot fires a pebble from the top of a building at a speed of 14.0 m/s. The building is 31.0 m tall. Ignoring air resistance, find the speed with which the pebble strikes the ground when the pebble is fired (a) horizontally, (b) vertically straight up, and (c) vertically straight down. • v = 28.3 m/s

  8. Conceptual Example • A rope is tied to a tree limb and used by a swimmer to swing into the water below. The person starts from rest with the rope held in the horizontal position, swings down and then lets go of the rope. Three forces act on him; W, T, and air resistance. Can conservation of mechanical energy be used to find the speed when he lets go of the rope?

  9. Conceptual Example • In order to use conservation of mechanical energy, Wnc = 0 • Nonconservative force in example • Tension  perpendicular to the motion so W = 0 • Air Resistance  opposite and parallel to motion • Work does not equal 0 • Cannot use conservation of ME

  10. Reasoning Strategy for Conservation of ME • Identify the external conservative and nonconservative forces that act on the object. For this principle to apply, the total work done by nonconservative forces must be zero. • Choose the location where the PE is taken to be zero. • Set the final total ME equal to the initial total ME.

  11. Practice Work • Don’t conserve energy to solve these problems! • 174 CQ 12 – 14, P 34 – 36, 38, 40, 41 • Total 9 problems

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