Ecp5
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This chapter discusses work, energy, and power. It defines work as the product of the force applied and displacement. Kinetic energy is defined as one-half the mass times the velocity squared. The work-energy theorem states that the net work on an object equals its change in kinetic energy. Potential energy includes gravitational potential energy, which depends on mass and height, and elastic potential energy in springs, which depends on the spring constant and displacement. The principle of conservation of mechanical energy applies to closed systems and accounts for changes between kinetic, potential, and nonconservative forces. Power is the rate at which work is done and defined as work divided by time. Example problems demonstrate applying these concepts.
Ecp5
- 1. Chapter 5 Work and Energy
- 2. Chapter 5 Objectives • Understand work and how it is computed • Relate work and kinetic energy • Explain potential and kinetic energy • Apply the principle of conservation of mechanical energy • Explain power and distinguish it from energy.
- 3. Work Demonstrations • Lifting the block • Dropping the block • Pushing the block along the counter • Letting the block slide to a stop • Pushing the block into the counter • Carrying the block across the room
- 4. Definition of Work (95) xW F x Work, J (Joules) Component of the force parallel to the displacement, N Displacement, m
- 5. Net Work (95) • Each force does its own work • Figure 5.1 (95) • Figure 5.2 (95)
- 6. Work Problems (95) • Example 5.1 (95) • Example 5.2 (96) • Conceptual Example 5.3 (98)
- 7. Work Done by Gravity (98) • Substitute into W=Fx • Both weight and are negative, so work is positive as the object drops y gW m g y Work done by gravity, J Acceleration due to gravity, 9.8 m/s2 Mass, kg Vertical displacement, m
- 8. Work Done by Gravity Example (99) • Example 5.4 (99)
- 9. Work Done by a Variable Force (100) • Work done by a constant force • Work done by a variable force • A calculus problem
- 10. Hooke’s Law (100) • Hooke’s Law demonstration
- 11. Hooke’s Law (100) xF k x Force required to stretch the spring by length x, N Force constant of the spring, N/m Displacement of the spring from equilibrium, m
- 12. Work Done on a Spring (101) 21 2W k x Work done in stretching the spring through a displacement x, J Force constant of the spring, N/m Displacement from equilibrium, m
- 13. Springs and Newton’s Third Law (101) • The stretching force and the restoring force are a Newton’s Third Law pair • The stretching or applied force does positive work • The restoring force does negative work
- 14. Deriving the Work-Energy Theorem (102) • Start with the definition of work • Substitute from Newton’s Second Law net netxW F x net xW m a x
- 15. Deriving the Work-Energy Theorem (102) • Recall the kinematics formula • Solve for and substitute into the previous equation 2 2 x 0x xv v 2 a x xa x 2 21 x x 0x2a x v v 2 21 net x 0x2W m v v
- 16. Deriving the Work-Energy Theorem (102) • Distribute to obtain: • We define kinetic energy: 2 21 1 net x 0x2 2W m v m v 21 2KE m v Kinetic Energy, J Mass, kg Velocity, m/s
- 17. The Work-Energy Theorem (103) • Therefore, the Work-Energy Theorem states that the net work done on an object is equally to the change in kinetic energy of the object. • Kinetic energy is the energy of motion. • Every moving object has kinetic energy
- 18. Gravitational Potential Energy (105) • The opposite of work done by gravity • Choose an arbitrary point to measure Δy from • It should be the lowest point in the problem GPE m g y Gravitational Potential Energy, J Mass, kg Acceleration due to gravity, 9.8 m/s2 Change in vertical position, m
- 19. Elastic Potential Energy (107) • The energy stored in a spring • The spring may be either compressed or stretched 21 2EPE k x Elastic potential energy, J Force constant of the spring, N/m Displacement from equilibrium, m
- 20. Conservative Forces (105) • If the work done by a force on an object moving between two points does not depend on the path taken, the force is conservative • Examples: contact forces, tensions, gravity, magnetism
- 21. Nonconservative Forces (105) • If the work done by a force on an object moving between two points depends on the path taken, the force is nonconservative. • Examples: friction, drag, thrust
- 22. Law of Conservation of Mechanical Energy (108) • The total original mechanical energy of a system plus any work done by nonconserva- tive forces is equal to the total final mechanical energy of the system. 1 1 1 2 2 2KE GPE EPE W KE GPE EPE
- 23. Solving Energy Problems (109) • Draw a picture of the problem • Label the energies at position one • Label the energies at position two • Label any work done by nonconservative forces in between positiosn one and two • Substitute into the conservation law and solve
- 24. Energy Problems (109) • Example 5.9 (109) • Example 5.10 (110) • Example 5.11 (111) • Example 5.12 (112)
- 25. Energy-Projectile Motion Lab • Purpose: Use energy to predict the range of a projectile • The set up:
- 26. Power (112) • Power is the rate of doing work • A Watt is a joule/s W P t Power, W Work, J Time, s
- 27. Average Power (113) • An alternate formula x xP F v Average power, W Force parallel to the velocity, N Average velocity, m/s
- 28. Power Problems (114) • Example 5.13 (114) • Example 5.14 (114)
- 29. Chapter 5 Problem Sets • Honors: P. 117, Ex. 28, 30, 34, 40, 46, 58, 66, 68, 72, 74, 84, 88, 98, 102, 118 • UConn: P. 117, Ex. 28, 30, 34, 40, 46, 58, 64, 66, 68, 72, 74, 84, 88, 94, 98, 102, 118, 124