work-energy-principle

Work-energy principle

What is the work-energy principle?

• The work-energy principle has many forms, but is in essence an energy balance

  • the final amount is the initial amount plus any energy put in (or minus any taken out)

  • it’s a bit like money in a bank account!

• The principle can be written as:

  • total final energy = total initial energy ± work done by non-gravitational forces

    • or, using subscripts for final and initial,

  • “total energy” here means the sum of gravitational potential energy and kinetic energy

    • e.g. 

  • Non-gravitational forces are any external forces that are not related to gravity

    • e.g. frictions, tensions, driving forces, etc

    • but wouldn’t include weight, , because work done against gravity has already been considered in the GPE part

  • Use + for work done by forces that “help” the object to move forwards

    • e.g. tension in a string pulling forwards, a driving force, etc

  • Use – for work done by forces that “hinder” (resist) the object from moving forwards

    • e.g. friction, tension in a string pulling backwards, a resistance force, air resistance, etc

• Some situations may have more than one form of work done

  • add or subtract each one, depending whether they help or hinder

How else can the work-energy principle be written?

• You can write the work-energy principle in terms of gains or losses in KE and GPE

  • but this method can cause a lot of sign errors!

• Write out each term in the original version, “total final energy = total initial energy ± work done by non-gravitational forces”

  •  use subscripts for final and initial

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