FACULTY OF SCIENCE, AUTUMN 2006

PHYS 124 LEC A1 : Particles and Waves (Instructor: Marc de Montigny)

Walker, Physics, Chapter 8: Potential Energy and Conservation of Energy

Oct. 3, 2007 Lecture

• Section 8-1: Conservative and Nonconservative Forces
  • Conservative force F_c: The work W_c it does can be stored in a form of energy that can be released at a later time. Examples include: gravitational force, force by a spring, etc.
  • Nonconservative force F_nc: The work W_nc it does cannot be recovered afterwards as kinetic energy. An example is friction.
  • P. 205, paragraph at bottom: Another definition is that the work done by a conservative force around any closed path is zero. When there exist at least one closed path such that the work done by a force F around it is not zero, then F is nonconservative
    • P. 206, Figure 8-3 shows that gravity is a conservative force
    • P. 206, Figure 8-4 shows that friction is a nonconservative force
• Section 8-2: Potential Energy and the Work Done by Conservative Forces
  • P. 209, Eq. 8-1 (Definition of Potential Energy) : Δ U = U_f - U_i = - W_c (work done by the force when moving from i to f)
  • SI Unit : joule [J]
  • Gravitational Potential Energy (Near Earth's Surface): p. 210, Eq. 8-3 : U = mgy
  • Potential Energy of a Spring: p. 212, Eq. 8-5 : U = ½ k x²
• Section 8-3: Conservation of Mechanical Energy
  • This section deals with conservative forces only, i.e. W_nc = 0
  • P. 216, Eq. 8-7 (Conservation of Mechanical Energy): E_f = E_i
  • P. 216, Eq. 8-8 (Explicit Expression): U_f + K_f = U_i + K_i
  • U denotes all the potential energies corresponding to all conservative forces (gravity, spring, etc.) which appear in the problem.
  • Essentially same physical content as Work-Kinetic Energy Theorem : ΔK = K_f - K_i = W_total = W_c = -Δ U = - (U_f - U_i)
  • Example: P. 236, Prob. 52
  • Example: P. 238, Prob. 81
• Section 8-4: Work Done by Nonconservative Forces
  • This section includes conservative and nonconservative forces, i.e. W_nc ≠ 0
  • Follows from the Work-Kinetic Energy Theorem : ΔK = K_f - K_i = W_c + W_nc = -Δ U + W_nc = - (U_f - U_i) + W_nc
  • P. 223, Eqs. 8-9 and 8-10 : E_f - E_i = W_nc
  • P. 226, Example 8-10
• Section 8-5: OMITTED

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