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3.4Work, Energy, and Power

Conservation of Energy — AP PHYSICS 1 Revision Notes & Topical Questions

5 min read 9 parts Lesson 11 of 14 1 quiz

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Lesson summary

3.4 Conservation of Energy — AP PHYSICS 1 notes: Describe the energies in a system and use conservation of energy, including work by external forces and friction.System choice — the objects included decide which energies and transfers appear.Single object — a system of one object…

  • Interacting objects
  • Mass on a spring
  • Energy conserved
  • Change of energy type
  • General form
  • Closed system

Section 1 of 9Defining the system

Defining the system
System choice
  • System choice the objects included decide which energies and transfers appear.
Single object
  • Single object a system of one object can only have kinetic energy.
    • (a car on a hill has no gravitational potential energy unless Earth is included)
Interacting objects
  • Interacting objects a system with objects that interact through conservative forces,
    • or can change shape reversibly, may have kinetic and potential energy.
Mass on a spring
  • Mass on a spring mass + spring + Earth has kinetic, elastic and gravitational energy.
Counting
  • Counting gravity is external work if Earth is outside the system but a change in Ug if Earth is inside;
    • never count both.

Section 2 of 9Conservation principles

Conservation principles
Energy conserved
  • Energy conserved energy is conserved in all interactions and never created or destroyed.
Change of energy type
  • Change of energy type any change to one type of energy in a system is balanced by changes to other types or a transfer with the surroundings.
General form
  • ΔEsystem = Wext, i.e. ΔK + ΔU + ΔEinternal = Wext.
Closed system
  • Closed system no energy is transferred in or out, so total energy is constant.
Mechanical energy
  • Emech = K + U.
Conserved mechanical energy
  • Conserved mechanical energy if the work on the system is zero and no nonconservative interactions act inside it, Ki + Ui = Kf + Uf.
Nonzero external work
  • Nonzero external work energy is transferred between the system and its environment.

Section 3 of 9Friction and internal energy

Kinetic friction
  • Kinetic friction converts mechanical energy into internal (thermal) energy.
Amount
  • Amount the increase in internal energy equals Ffd, with d the sliding distance.
Energy statement
  • Ki + Ui + Wext = Kf + Uf + ΔEinternal.

Section 4 of 9Energy bar charts

1Purpose
  • Purpose show the relative amounts of K, Ug, Us and Einternal at one instant.
2Features
  • Features flat bars on the zero line mean zero energy;
    • the unit is arbitrary;
    • the total of the bars is the system energy.
3Phases
  • Phases each phase of the motion needs its own chart with a clearly defined instant.
4Block–spring–Earth
  • Block–spring–Earth elastic energy → kinetic energy → gravitational energy as the block climbs a frictionless slope.
5System dependence
  • System dependence block alone shows only K; block + Earth shows K and Ug; spring + Earth shows no K.
    • (block outside the system)

Section 5 of 9Results for frictionless motion

Results for frictionless motion
Drop from rest through h
  • Drop from rest through h v = √(2gh), independent of mass and path.
Pendulum or roller coaster
  • Pendulum or roller coaster the normal force or tension does no work, so energy conservation applies although those forces vary.
Spring launcher
  • ½kx2 = ½mv2.

Section 6 of 9Solving an energy problem

1
Define the system and state whether it is closed or has external work.
2
Choose the initial and final states and a zero for Ug.
3
Sketch energy bar charts for both states, including work or internal energy.
4
Write Ki + Ui + Wext = Kf + Uf + ΔEinternal.
5
Substitute, cancel the mass if possible, and solve.

Section 7 of 9More from the specification

  • Simple pendulum
    • A small bob on a light string of length L

Section 8 of 9Key terms

TermMeaning
Conservation of energyTotal energy of an isolated system is constant.
Mechanical energySum of kinetic and potential energy.
Closed systemSystem with no energy transferred in or out.
Nonconservative forceForce such as friction that converts mechanical energy to thermal energy.
Energy bar chartDiagram of energy types in a system at one instant.

Section 9 of 9Exam technique

1
Counting gravity both as work and as potential energy.
2
Assuming mechanical energy is conserved when friction acts.
3
Including gravitational potential energy when Earth is outside the system.
4
Thinking total energy is lost to friction — it becomes internal energy.

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