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Conservation of Energy

Conservation of Energy. Path Dependence. What happens to work as a rollercoaster goes down hill then up again? What if the roller coaster took a less steep path?. Reversible Process. If an object is acted on by a force has its path reversed the work done is the opposite sign.

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Conservation of Energy

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  1. Conservation of Energy

  2. Path Dependence • What happens to work as a rollercoaster goes down hill then up again? • What if the roller coaster took a less steep path?

  3. Reversible Process • If an object is acted on by a force has its path reversed the work done is the opposite sign. • This represents a reversible process. y2 F = -mg h y1

  4. Closed Path • If the work done by a force doesn’t depend on the path it is a conservative force. • Conservative forces do no work on a closed path. From 1 to 2, the path A or B doesn’t matter From 1 to 2 and back to 1, the path A then the reverse path B gives no work

  5. Nonconservative Force • Not all forces are conservative. • In particular, friction and drag are not conservative. d Negative work is done by friction to get here F = -mFN -d Negative work is also done returning the box F = mFN

  6. Net Work • The work-energy principle is DK = Wnet. • The work can be divided into parts due to conservative and non-conservative forces. • Kinetic energy DK = Wcon + Wnon d Ff Fg

  7. Kinetic and Potential Energy • Potential energy is the negative of the work done by conservative forces. • Potential energy DU = -Wcon • The kinetic energy is related to the potential energy. • Kinetic energy DK = -DU+ Wnon • The energy of velocity and position make up the mechanical energy. • Mechanical energy Emech = K + U

  8. Conservation of Energy • Certain problems assume only conservative forces. • No friction, no air resistance • The change in energy, DE = DK + DU = 0 • If the change is zero then the total is constant. • Total energy, E = K + U = constant • Energy is not created or destroyed – it is conserved.

  9. No Absolute • Potential energy reflects the work that may be done. • The point U = 0 is arbitrary • At the top of a table of height h: • U = mg(y+h) • The same experiment is shifted by a constant potential mgh: • U = mgy + mgh = mgy + C y2 y y1 h

  10. Solving Problems • There are some general techniques to solve energy conservation problems. • Identify all the potential and kinetic energy at the beginning • Identify all the potential and kinetic energy at the end • Set the initial and final energy equal to one another • Nonconservative forces reduce the final energy

  11. The hill is 2.5 km long with a drop of 800 m. The skier is 75 kg. The speed at the finish is 120 km/h. How much energy was dissipated by friction? Using Friction and Energy q

  12. Find the total change in kinetic energy. Find the total change in potential energy. The difference is due to friction (air and sliding). DK = ½ mv2 - 0 = ½(75 kg)(130 m/s)2 = 5.4 x 105 J DU = mgh = (75 kg)(9.8 m/s2)(-800 m) = -5.9 x 105 J Wnon = DK + DU = -0.5 x 105 J Friction and Height

  13. Universal Gravitational Work • Gravity on the surface of the Earth is a local consequence of universal gravitation. • How much work can an object falling from very far from the Earth do when it hits the surface? r RE

  14. Universal Gravitational Potential • The work doesn’t depend on the path. • Universal gravity is a conservative force • The potential is set with U = 0 at an infinite distance. • Gravity acts at all ranges • Gravity is weakest far from the source

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