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7 Conservation of Energy

7 Conservation of Energy. Potential Energy The Conservation of Mechanical Energy The Conservation of Energy Mass and Energy Hk: 23, 27, 39, 47, 55, 65, 69, 71. Potential Energy. Potential Energy is stored energy Potential Energy is position dependent (KE is speed dependent)

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7 Conservation of Energy

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  1. 7 Conservation of Energy • Potential Energy • The Conservation of Mechanical Energy • The Conservation of Energy • Mass and Energy • Hk: 23, 27, 39, 47, 55, 65, 69, 71

  2. Potential Energy • Potential Energy is stored energy • Potential Energy is position dependent (KE is speed dependent) • Ex. object at higher height has more PE • Types of PE: gravitational, elastic, electric, magnetic, chemical, nuclear. • /

  3. Conservative Forces • When the work done by a force moving from position 1 to 2 is independent of the path, the force is Conservative. • The work done by a Conservative Force is zero for any closed path. • Conservative Forces have associated Potential Energies • /

  4. Non Conservative Forces • Produce thermal energy, e.g. friction • Work done by Non Conservative Forces is path dependent, e.g. longer path, more work required • /

  5. Potential Energy Functions

  6. Elastic Potential Energy

  7. Ex. Elastic Potential Energy • 100N/m spring is compressed 0.2m. • F = -kx = -(100N/m)(0.2m) = -20N • U = ½kx2 = ½(100N/m)(0.2m)2 = 2J • /

  8. Gravitational Potential Energy

  9. Ex. Gravitational Potential Energy • Ex: A 2kg object experiences weight (2kg)(9.8N/kg) = 19.6N. • At 3m above the floor it has a stored energy of mgy: • (2kg)(9.8N/kg)(3m) = 48.8Nm = 48.8J. • /

  10. Conservation of Energy • Individual energy levels change. • Sum of all individual energies is constant. • /

  11. Conservation of Mechanical Energy

  12. KE E Ug

  13. Ex. Conservation of Mechanical Energy: Object dropped from height h above floor.

  14. 1 2 3

  15. y y Energies and speeds are same at height y Accelerations at y are not same

  16. Work Energy with Friction

  17. s Example: The smaller the frictional force fk, the larger the distance, s, it will travel before stopping.

  18. 1 5 2 4 3 A 2.00kg ball is dropped from rest from a height of 1.0m above the floor. The ball rebounds to a height of 0.500m. A movie-frame type diagram of the motion is shown below.

  19. By energy conservation, the sum of all energies in each column is the same, = E1 = mg(1) = 19.6J Calculate v2: (use 1st and 2nd columns) mg(1) = ½ m(v2)2. g = ½ (v2)2. v2 = 4.43m/s Calculate PE-thermal: (use 1st and 5th columns) mg(1) = mg(1/2) + PE-thermal mg(1/2) = PE-thermal PE-thermal = 9.8J

  20. Calculate PE-elastic: (use 1st and 3rd columns) PE-elastic + PE-thermal = mg(1) PE-elastic + 9.8 = 19.6 PE-elastic = 9.8J Calculate v4: (use 1st and 4th columns) ½ m(v4)2 + PE-thermal = mg(1) ½ m(v4)2 + 9.8 = 19.6 ½ m(v4)2 = 9.8 (v4)2 = 2(9.8)/2 v4 = 3.13m/s

  21. Potential Energy & Force

  22. Equilibrium • Stable: small displacement in any direction results in a restoring force toward Equilibrium Point • Unstable: small displacement in any direction results in a force away from Equilibrium Point • Neutral: small displacement in any direction results in zero force

  23. Mass and Energy

  24. Efficiency & Thermodynamics

  25. Summary • Potential Energy function & force • The Conservation of Mechanical Energy • The Conservation of Energy • Mass and Energy • /

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