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  1. Practice problem

    How much does a gas warm when it cannot expand? →

    Intermediate · Connect concepts. Find the temperature increase.

  2. Practice problem

    How much does a triangular force pulse change velocity? →

    Intermediate · Read graphs & measurements. What is the cart’s velocity immediately after the pulse?

  3. Practice problem / FREE SAMPLE

    How much faster are the hot molecules? →

    Intermediate · Compare cases. Thermal kinetic energy scales with temperature, while speed is obtained from its square root.

  4. Practice problem

    How much force crosses the contact? →

    Intermediate · Connect concepts. Find the contact force on the 4 kg block.

  5. Practice problem

    How much heat must an ideal engine absorb? →

    Intermediate · Connect concepts. How much heat does it absorb from the hot reservoir per cycle?

  6. Practice problem / FREE SAMPLE

    How much inward force is required? →

    Intermediate · Apply a principle. Square the speed before dividing by the radius; this gives the radial acceleration.

  7. Practice problem

    How much of the block is submerged? →

    Intermediate · Apply a principle. Find the fraction of its volume submerged.

  8. Practice problem / FREE SAMPLE

    How quickly does the spring cycle? →

    Intermediate · Apply a principle. The ratio of stiffness to inertia determines angular frequency squared.

  9. Practice problem

    How uncertain is the rectangle? →

    Intermediate · Read graphs & measurements. What is its approximate worst-case fractional area uncertainty?

  10. Practice problem

    Infer a gas model from its energy split →

    Intermediate · Connect concepts. What is its ratio γ = Cp/Cv?

  11. Practice problem

    Infer a source from a reversed branch current →

    Intermediate · Find a missing quantity. What is the source emf?

  12. Practice problem / FREE SAMPLE

    Infer damping from peak energies →

    Advanced · Read graphs & measurements. An energy ratio and an amplitude ratio have different decay exponents.

  13. Practice problem

    Infer tension from wave speed →

    Intermediate · Find a missing quantity. Find its tension.

  14. Practice problem

    Infer the braking acceleration →

    Intermediate · Find a missing quantity. Find its acceleration, with initial motion positive.

  15. Practice problem

    Infer the mass distribution from a descent →

    Intermediate · Find a missing quantity. What value of β follows from the energy measurements?

  16. Practice problem / FREE SAMPLE

    Infer time from a remaining fraction →

    Intermediate · Find a missing quantity. An eightfold reduction requires three successive halvings.

  17. Practice problem

    Infer two beams from their brightest and dimmest readings →

    Intermediate · Read graphs & measurements. What is the ratio of the stronger beam intensity to the weaker one?

  18. Practice problem

    Insert a dielectric after disconnecting →

    Intermediate · Compare cases. Find its new voltage.

  19. Practice problem

    Insert a dielectric with the battery connected →

    Intermediate · Compare cases. Find its final free plate-charge magnitude.

  20. Practice problem

    Inside a uniformly charged shell →

    Intermediate · Compare cases. Find the electric-field magnitude at a point 0.20 m from its centre.