AC

Lecture24_Energy_Diagrams

Exam Information

  • Second Exam: Next Monday, February 24, at 6:00 pm

  • Locations: Check my February 17 email

  • Seating: Alternate seating; no sitting in the back row

  • Requirements:

    • Must have UM ID (or another ID)

    • #2 pencil(s)

  • Exam Format:

    • Closed-book, 75 minutes

    • Multiple-choice, 15 questions of equal value

    • No penalty for guessing

  • Allowed Materials:

    • Two 3"×5" notecards (double-sided) for formulas/equations/diagrams

    • Calculator must look like a calculator

  • Prohibited Items:

    • No laptops, cell phones, smartphones, smartwatches, or other communication devices

  • Policy: Individual work only

  • Chapters Covered: 5-7

Office Hours

  • Today: Regular office hours from 1:30 to 3:00 pm in my office (Randall 1480)

  • Health Advisory: If sick, please wear a mask

Summary of Energy Concepts

  • Kinetic Energy (KE): KE = (1/2)mv²

  • Gravitational Potential Energy (GPE): GPE = mgy

  • Elastic Potential Energy (EPE): EPE = (1/2)kx²

  • Work-Energy Theorem: KE_initial + GPE_initial + EPE_initial + W_non-cons = KE_final + GPE_final + EPE_final

  • Conservation of Energy Formula: KE_initial + W_total = KE_final

Problem-Solving Procedure

  1. Draw a picture

  2. Identify independent bodies

  3. Identify forces acting on each body & draw Free Body Diagram (FBD)

  4. Determine conservative and non-conservative forces

  5. Choose initial and final points

  6. Set zero point for potential energy

  7. Write conservation of energy equation

  8. Solve equations analytically

  9. Plug in the numbers

Problem 7.72 Highlights and Concepts

  • Question: Is mechanical energy conserved when the fish is lowered to the equilibrium position?

    • Options: A. Yes, B. No

    • Answer: B. No; hand provides a non-conservative force doing negative work

  • If allowed to fall:

    • Max extension of spring: C. Greater than in equilibrium

    • More kinetic energy results in overshooting equilibrium position

  • Total Force at Max Extension:

    • Options: A. Zero, B. Upward, C. Downward

    • Answer: C. Downward; spring force greater than gravity

Force and Potential Energy

  • Work of a conservative force relates to potential energy as:

    • W_conservative = PE_initial - PE_final

  • Integration and Differentiation:

    • Work and PE relationship is established through integration and differentiation.

Energy Diagrams and Equilibrium

  • Stable vs. Unstable Equilibrium:

    • Stable: Minima in potential energy

    • Unstable: Maxima in potential energy

  • Example questions seek to identify stable equilibrium points and the effects of forces in various scenarios.