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Total Mechanical Energy

Total Mechanical Energy. Conservation Laws. state that something is conserved remain constant under certain conditions examples: TME, mass, electric charge, energy. TME is not conserved:. Air resistance

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Total Mechanical Energy

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  1. Total Mechanical Energy

  2. Conservation Laws • state that something is conserved • remain constant under certain conditions • examples: TME, mass, electric charge, energy

  3. TME is not conserved: • Air resistance • A falling object exerts force on the air; the air exerts a force back on the falling object. • This is true of all objects moving through air.

  4. TME is not conserved: • Air resistance • Air resistance increases with increased velocity. • For a falling object, eventually air resistance balances the force of gravity.

  5. TME is not conserved: • Air resistance • When air resistance and gravity, the only two forces on a falling object, are balanced, a = 0; the velocity no longer increases.

  6. TME is not conserved: • Air resistance • This is called terminal velocity. • Kinetic energy remains constant, but potential energy decreases. What happens to it?

  7. TME is not conserved: • Air resistance • The potential energy becomes thermal energy, raising the temperature of the falling object and the air around it.

  8. TME is not conserved: • Air resistance • Thermal energy is not mechanical energy.

  9. TME is not conserved: • Friction • Friction changes mechanical energy to thermal energy, acoustic energy, or other forms. • Brakes are a good example of this.

  10. TME is not conserved: • Friction • Lubrication reduces friction and the change of mechanical energy to thermal and acoustic energy.

  11. TME is not conserved: • Friction • Springs have internal frictional forces. • Ideal springs, by definition, have no significant internal friction.

  12. TME is conserved: • TME is conserved when only conservative forces are at work. • All conservative forces are central forces. • Example: gravity

  13. TME is conserved: • Path-independence: • Work done against gravity is the same regardless of the path taken.

  14. TME is conserved: • p. 221 example: • W = FgΔh • This formula holds regardless of the starting and ending points. • Path-independence is validated.

  15. TME is conserved: • Example 10-1: • Since TME is conserved, both kinetic and potential energy are equal at points B and D.

  16. Escape Speed • the minimum speed that an object of mass m requires to leave a larger object of mass M so that mass m cannot return due to gravitational attraction alone

  17. M vR = 2G r Escape Speed • to calculate: • assumes the speed of the object at an extreme distance is zero

  18. Simple Machines

  19. Machines • A machine is a device that changes the magnitude or direction (or both) of an applied force. • Machines can be simple or complex.

  20. Fout IMA = Fin Mechanical Advantage • definition of ideal mechanical advantage (IMA): ...in the absence of friction

  21. Fout din = Fin dout Mechanical Advantage • other results of IMA: Win = Wout IMA ...in the absence of friction

  22. Fout AMA = Fin Mechanical Advantage • actual mechanical advantage (AMA): ...as actually measured in real life

  23. Inclined Planes • ramps • wedges • screws

  24. Screws • defined: a metal shaft surrounded by a helically coiled wedge • The pitch of a screw is the distance between two successive threads.

  25. Levers • defined: a rigid bar that turns around a pivot (fulcrum) • effort force (Fe) is applied to effort arm (le)

  26. Levers • output force (Fr) is applied to resistance arm (lr) • output force is sometimes called the resistance force or load

  27. Levers • Law of Moments states then when the torques are equal, the lever will be stationary, and: Fele = Frlr

  28. le Fr IMA = AMA = lr Fe Levers • mechanical advantage:

  29. Kinds of Levers • First-class: the fulcrum is between the resistance and effort forces

  30. Kinds of Levers • IMA may be more or less than 1.

  31. Kinds of Levers • Second-class: the resistance is between the fulcrum and effort force • IMA > 1

  32. Kinds of Levers • Third-class: the effort force is between the fulcrum and the resistance • IMA < 1

  33. Wheels and Pulleys • Levers are generally limited in movement. • Wheels are modified levers, with the fulcrum at the center. • Wheels can function as 2nd or 3rd-class levers.

  34. din IMA = dout Wheels and Pulleys • A pulley is a grooved wheel that turns on an axle. • For a single fixed pulley: din = dout = 1

  35. Fr IMA = Fe Wheels and Pulleys • For a movable pulley: = 2 • A movable pulley doubles the effort force.

  36. Wheels and Pulleys • block and tackle system • has both fixed and moveable pulleys • IMA of a block and tackle system is equal to the number of ropes supporting the load.

  37. Mechanical Efficiency • In the real world, the work put out by any machine is always less than the work put into it. • Efficiency is a way to measure how much input work became output work.

  38. AMA η = × 100% IMA Mechanical Efficiency • Efficiency is notated by the Greek letter eta (η). • Stationary pulley systems are nearly 100% efficient.

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