Conservation of Energy (College Board AP® Physics 1: Algebra-Based): Study Guide

Energy in a system

• Defining a system is an important concept in Physics, especially in energy questions

• The objects included in a system determine the energy transfers taking place

Energy bar charts

• Energy bar charts are used to show the relative amounts of different types of energy in a system at a point in time

Anatomy of an energy bar chart

• Features of an energy bar chart:

  • Flat bars on the zero line represent zero energy of that type

  • The 'units' of energy used are arbitrary and only make sense relative to each other

  • The amount of each energy type is given for a specific instant in time

  • The sum of the values of each energy type is equal to the total energy of the system

Defining a system

• A system that is composed of only a single object can only have kinetic energy

• For example, consider a car driving along a road:

  • The system is defined as only the car

  • The car has kinetic energy because it is in motion

  • Even if the car drives up a hill, the car on its own as a system cannot have gravitational potential energy because the Earth is not included in the system

• A system that contains objects that interact via conservative forces or that can change their shape reversibly may have both kinetic and potential energies

• For example, consider a mass oscillating vertically on a spring:

  • The system is defined as the mass, the spring, and the Earth

  • The spring has elastic potential energy when it is compressed or stretched

  • The mass has kinetic energy when it is in motion

  • The mass has gravitational potential energy as it moves through a height

  • As long as all the objects involved in the energy transfers are included in the system, both the kinetic and potential energies can be included

Analyzing a system

• Consider a system consisting of a block, a spring, and the Earth

• The block is used to compress the spring; the block is then released and it travels up a frictionless inclined slope

• The spring has elastic potential energy when it is compressed

• The elastic potential energy is transferred to the block as kinetic energy as the block is set in motion

• The kinetic energy is transformed into gravitational potential energy as the block travels up the slope

• The energy ends up as gravitational potential energy when the block stops moving

• Each phase of the block's motion needs its own energy bar chart

• The phase of motion or the instant in time represented in the energy bar chart should be clearly defined

Conservation of energy

• The conservation of energy principle states that:

Energy cannot be created or destroyed; it can only be transformed from one form to another

• This means that any energy transferred into, out of, or within a system has to be accounted for

• Any change to a type of energy within a system must be balanced by an equivalent change of other types of energies within the system or by a transfer of energy between the system and its surroundings

• Energy is always conserved in all interactions, but the way the system is defined determines which energy transfers are relevant

• In this way, a system may be selected so that the total energy of that system is constant

• For example, consider a simple pendulum:

  • Energy is transformed from gravitational potential to kinetic and back again

  • If the system is defined as the pendulum and the Earth, then the total mechanical energy of the system is constant, but the amounts of kinetic and potential energy change

• Mechanical energy is the sum of a system’s kinetic and potential energies

Energy bar charts for a simple pendulum

• If the work done on a selected system is zero and there are no nonconservative interactions within the system, the total mechanical energy of the system is constant

  • Nonconservative forces, like friction, transfer energy away from the system

  • If no nonconservative forces act, like on the frictionless slope, then the total mechanical energy of the system is constant

  • The energy is transferred between potential and kinetic energies of objects within the system, but the energy is conserved within the system

• If the work done on a selected system is nonzero, energy is transferred between the system and the environment

  • If nonconservative forces are present, then the work done by these nonconservative forces, , means that energy is transferred from the system and dissipated to the surroundings

  • The total amount of energy is conserved, but it is not constant within the system