Conservative Forces and the Potential Energy Function · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Forces that bank energy

Science · Energy · ages 18-19
Name ______________________   Date ____________

  1. A conservative force does zero total work around any closed loop.

    Circle one:   True   False

  2. What makes a force conservative?

    • Its work is the same along any path between two points
    • It never does any work at all
    • It always points in the same direction

  3. Which pair of forces is non-conservative?

    • Gravity and the spring force
    • Friction and air drag
    • Gravity and air drag

  4. What is the potential banked in a spring stretched by x?

    • k times x
    • Half k times x squared
    • k divided by x

  5. What is the gravitational potential banked by lifting a mass?

    • Half mass times speed squared
    • Mass times g divided by height
    • Mass times g times height

  6. How is potential difference related to the work of a conservative force?

    • It equals the work done
    • It equals minus the work done
    • It is unrelated to the work done

  7. A potential curve slopes steeply downhill at some point. Which way does the force point there?

    • Uphill, against the slope
    • Downhill, with the slope
    • Nowhere, since slope means zero force

  8. A student pushes a merry-go-round through three turns back to the start and expects the same energy as one turn. What is wrong?

    • Three turns must always cost less than one
    • The loop test guarantees zero work for pushes
    • Push pull work is path dependent, so extra turns cost extra energy
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Forces that bank energy W1-mt__053R9wrQy-s1

  1. True · The return trip gives back exactly what the outward trip took.
  2. Its work is the same along any path between two points · Path independence is the defining mark of a conservative force.
  3. Friction and air drag · Friction and drag drain energy along the way, and longer paths cost more.
  4. Half k times x squared · The growing spring pull integrates to half k times stretch squared, either direction.
  5. Mass times g times height · The work of lifting against steady weight is stored as mass times g times height.
  6. It equals minus the work done · Rising potential means the force did negative work, so the difference is minus the work.
  7. Uphill, against the slope · Force is minus the slope, so a downhill slope pushes back uphill.
  8. Push pull work is path dependent, so extra turns cost extra energy · Pushing is generally non-conservative: every revolution adds more work.
Worksheet · LightMySky