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  1. Practice problem / FREE SAMPLE

    Energy in a charged capacitor →

    Intermediate · Apply a principle. The voltage is squared; capacitance times voltage alone gives charge, not energy.

  2. Practice problem

    Energy in a series spring pair →

    Intermediate · Connect concepts. Find the total stored elastic energy.

  3. Practice problem

    Energy of a circular orbit →

    Intermediate · Connect concepts. Find its total mechanical energy.

  4. Practice problem / FREE SAMPLE

    Energy of a red photon →

    Intermediate · Apply a principle. Use the supplied eV·nm constant with wavelength in nanometres so those length units cancel.

  5. Practice problem

    Energy of a spinning disc →

    Intermediate · Connect concepts. Find its rotational kinetic energy.

  6. Practice problem

    Energy stored during gradual loading →

    Intermediate · Connect concepts. Find the stored elastic energy.

  7. Practice problem

    Energy that changes phase →

    Intermediate · Apply a principle. Find the heat needed to melt it completely at 0°C.

  8. Practice problem

    Equal area is not equal angular speed →

    Advanced · Compare cases. What is ωₚ/ωₐ?

  9. Practice problem

    Equal density, different planet size →

    Intermediate · Compare cases. Find the ratio of surface gravity on the second planet to the first.

  10. Practice problem

    Equal populations, unequal activities →

    Intermediate · Compare cases. Find the ratio of activity A to activity B at this instant.

  11. Practice problem

    Escape from a small world →

    Intermediate · Connect concepts. Find its surface escape speed.

  12. Practice problem

    Estimate an approximation’s error →

    Intermediate · Apply a principle. Estimate (θ − sin θ)/θ to leading order.

  13. Practice problem

    Estimate first, then choose a power of ten →

    Beginner · Compare cases. What is the nearest power of ten to its estimated molecule count, using distance on a logarithmic scale?

  14. Practice problem

    Extract gravity from a straight-line graph →

    Intermediate · Read graphs & measurements. Find the inferred gravitational acceleration.

  15. Practice problem

    Field inside a long coil →

    Intermediate · Apply a principle. Find the interior magnetic-field magnitude.

  16. Practice problem / FREE SAMPLE

    Field near a long wire →

    Intermediate · Apply a principle. For a straight wire the field decreases as inverse distance, not inverse distance squared.

  17. Practice problem

    Field on both sides of a sheet →

    Intermediate · Apply a principle. Find the electric-field magnitude on either side.

  18. Practice problem

    Find friction before the block slips. →

    Intermediate · Compare cases. What is the static friction force on the block?

  19. Practice problem

    Find the boundary between a mixture and all liquid →

    Advanced · Find a missing quantity. What minimum initial water temperature just melts all the ice at equilibrium?

  20. Practice problem

    Find the edge of the static-friction interval →

    Intermediate · Find a missing quantity. What is the minimum upward F that can hold the block at rest?