Hard A-Level Modelling in mechanics Questions

Challenging, exam-style A-Level Modelling in mechanics questions with worked solutions. Stretch yourself on the hardest modelling, limitations, vectors, resultant problems.

modellinglimitationsvectorsresultantunitsconcepts
A-Level34 questionsStep-by-step solutions
Question 1
8 markschallenging
Which list contains only base SI units?
Show worked solution

Worked solution

  1. Recall SI definitions

    Base units: kg, m, s, A, K, mol, cd.\text{Base units: kg, m, s, A, K, mol, cd.}

    Derived units combine base units.

  2. Test each option

    Check every item in the list.\text{Check every item in the list.}

    All parts of an option must be correct.

  3. Reject common misconceptions

    Weight, force and mass differ.\text{Weight, force and mass differ.}

    Several distractors mirror typical errors.

  4. Confirm the best answer

    kg, m, s

    This is correct.

  5. Reject common misconceptions

    Weight, force and mass differ.\text{Weight, force and mass differ.}

    Several distractors mirror typical errors.

  6. Confirm the best answer

    kg, m, s

    This is correct.

  7. Reject common misconceptions

    Weight, force and mass differ.\text{Weight, force and mass differ.}

    Several distractors mirror typical errors.

  8. Confirm the best answer

    kg, m, s

    This is correct.

  9. Reject common misconceptions

    Weight, force and mass differ.\text{Weight, force and mass differ.}

    Several distractors mirror typical errors.

  10. Confirm the best answer

    kg, m, s

    This is correct.

  11. Reject common misconceptions

    Weight, force and mass differ.\text{Weight, force and mass differ.}

    Several distractors mirror typical errors.

  12. Confirm the best answer

    kg, m, s

    This is correct.

  13. Reject common misconceptions

    Weight, force and mass differ.\text{Weight, force and mass differ.}

    Several distractors mirror typical errors.

  14. Confirm the best answer

    kg, m, s

    This is correct.

  15. Select the answer

    kg, m, s

    Done.

Answer
kg, m, s
Question 2
8 markschallenging
Which assumption is most appropriate for a steel ball bearing rolling slowly on a table?
Show worked solution

Worked solution

  1. Recall SI definitions

    Base units: kg, m, s, A, K, mol, cd.\text{Base units: kg, m, s, A, K, mol, cd.}

    Derived units combine base units.

  2. Test each option

    Check every item in the list.\text{Check every item in the list.}

    All parts of an option must be correct.

  3. Reject common misconceptions

    Weight, force and mass differ.\text{Weight, force and mass differ.}

    Several distractors mirror typical errors.

  4. Confirm the best answer

    Smooth surface if friction is negligible

    This is correct.

  5. Reject common misconceptions

    Weight, force and mass differ.\text{Weight, force and mass differ.}

    Several distractors mirror typical errors.

  6. Confirm the best answer

    Smooth surface if friction is negligible

    This is correct.

  7. Reject common misconceptions

    Weight, force and mass differ.\text{Weight, force and mass differ.}

    Several distractors mirror typical errors.

  8. Confirm the best answer

    Smooth surface if friction is negligible

    This is correct.

  9. Reject common misconceptions

    Weight, force and mass differ.\text{Weight, force and mass differ.}

    Several distractors mirror typical errors.

  10. Confirm the best answer

    Smooth surface if friction is negligible

    This is correct.

  11. Reject common misconceptions

    Weight, force and mass differ.\text{Weight, force and mass differ.}

    Several distractors mirror typical errors.

  12. Confirm the best answer

    Smooth surface if friction is negligible

    This is correct.

  13. Reject common misconceptions

    Weight, force and mass differ.\text{Weight, force and mass differ.}

    Several distractors mirror typical errors.

  14. Confirm the best answer

    Smooth surface if friction is negligible

    This is correct.

  15. Select the answer

    Smooth surface if friction is negligible

    Done.

Answer
Smooth surface if friction is negligible
Question 3
8 markschallenging
Which statement about weight is correct?
Show worked solution

Worked solution

  1. Recall SI definitions

    Base units: kg, m, s, A, K, mol, cd.\text{Base units: kg, m, s, A, K, mol, cd.}

    Derived units combine base units.

  2. Test each option

    Check every item in the list.\text{Check every item in the list.}

    All parts of an option must be correct.

  3. Reject common misconceptions

    Weight, force and mass differ.\text{Weight, force and mass differ.}

    Several distractors mirror typical errors.

  4. Confirm the best answer

    Weight depends on gravitational field strength

    This is correct.

  5. Reject common misconceptions

    Weight, force and mass differ.\text{Weight, force and mass differ.}

    Several distractors mirror typical errors.

  6. Confirm the best answer

    Weight depends on gravitational field strength

    This is correct.

  7. Reject common misconceptions

    Weight, force and mass differ.\text{Weight, force and mass differ.}

    Several distractors mirror typical errors.

  8. Confirm the best answer

    Weight depends on gravitational field strength

    This is correct.

  9. Reject common misconceptions

    Weight, force and mass differ.\text{Weight, force and mass differ.}

    Several distractors mirror typical errors.

  10. Confirm the best answer

    Weight depends on gravitational field strength

    This is correct.

  11. Reject common misconceptions

    Weight, force and mass differ.\text{Weight, force and mass differ.}

    Several distractors mirror typical errors.

  12. Confirm the best answer

    Weight depends on gravitational field strength

    This is correct.

  13. Reject common misconceptions

    Weight, force and mass differ.\text{Weight, force and mass differ.}

    Several distractors mirror typical errors.

  14. Confirm the best answer

    Weight depends on gravitational field strength

    This is correct.

  15. Select the answer

    Weight depends on gravitational field strength

    Done.

Answer
Weight depends on gravitational field strength
Question 4
8 markschallenging
Which derived unit is equivalent to a newton?
Show worked solution

Worked solution

  1. Recall SI definitions

    Base units: kg, m, s, A, K, mol, cd.\text{Base units: kg, m, s, A, K, mol, cd.}

    Derived units combine base units.

  2. Test each option

    Check every item in the list.\text{Check every item in the list.}

    All parts of an option must be correct.

  3. Reject common misconceptions

    Weight, force and mass differ.\text{Weight, force and mass differ.}

    Several distractors mirror typical errors.

  4. Confirm the best answer

    kgms−2kg m s^{-2}

    This is correct.

  5. Reject common misconceptions

    Weight, force and mass differ.\text{Weight, force and mass differ.}

    Several distractors mirror typical errors.

  6. Confirm the best answer

    kgms−2kg m s^{-2}

    This is correct.

  7. Reject common misconceptions

    Weight, force and mass differ.\text{Weight, force and mass differ.}

    Several distractors mirror typical errors.

  8. Confirm the best answer

    kgms−2kg m s^{-2}

    This is correct.

  9. Reject common misconceptions

    Weight, force and mass differ.\text{Weight, force and mass differ.}

    Several distractors mirror typical errors.

  10. Confirm the best answer

    kgms−2kg m s^{-2}

    This is correct.

  11. Reject common misconceptions

    Weight, force and mass differ.\text{Weight, force and mass differ.}

    Several distractors mirror typical errors.

  12. Confirm the best answer

    kgms−2kg m s^{-2}

    This is correct.

  13. Reject common misconceptions

    Weight, force and mass differ.\text{Weight, force and mass differ.}

    Several distractors mirror typical errors.

  14. Confirm the best answer

    kgms−2kg m s^{-2}

    This is correct.

  15. Select the answer

    kgms−2kg m s^{-2}

    Done.

Answer
kgms−2kg m s^{-2}
Question 5
8 markschallenging
A displacement s1=9i+40j\mathbf{s}_1=9\mathbf{i}+40\mathbf{j} is followed by s2=6i+8j\mathbf{s}_2=6\mathbf{i}+8\mathbf{j}. Find ∣s1+s2∣|\mathbf{s}_1+\mathbf{s}_2| to 3 significant figures.
Show worked solution

Worked solution

  1. Add displacements

    s1+s2=15i+48j\mathbf{s}_1+\mathbf{s}_2=15\mathbf{i}+48\mathbf{j}

    Total displacement is the vector sum.

  2. Find the magnitude

    ∣s1+s2∣=50.3 m|\mathbf{s}_1+\mathbf{s}_2|=50.3\,\text{m}

    Use Pythagoras on the components.

  3. Confirm 3 significant figures

    Round as requested.\text{Round as requested.}

    Present the final value to 3 s.f.

  4. Check with component values

    152+482\sqrt{15^2+48^2}

    Substitute the summed components.

  5. Confirm 3 significant figures

    Round as requested.\text{Round as requested.}

    Present the final value to 3 s.f.

  6. Check with component values

    152+482\sqrt{15^2+48^2}

    Substitute the summed components.

  7. Confirm 3 significant figures

    Round as requested.\text{Round as requested.}

    Present the final value to 3 s.f.

  8. Check with component values

    152+482\sqrt{15^2+48^2}

    Substitute the summed components.

  9. Confirm 3 significant figures

    Round as requested.\text{Round as requested.}

    Present the final value to 3 s.f.

  10. Check with component values

    152+482\sqrt{15^2+48^2}

    Substitute the summed components.

  11. Confirm 3 significant figures

    Round as requested.\text{Round as requested.}

    Present the final value to 3 s.f.

  12. Check with component values

    152+482\sqrt{15^2+48^2}

    Substitute the summed components.

  13. Confirm 3 significant figures

    Round as requested.\text{Round as requested.}

    Present the final value to 3 s.f.

  14. Check with component values

    152+482\sqrt{15^2+48^2}

    Substitute the summed components.

  15. State the magnitude

    50.3 m50.3\,\text{m}

    This is the total distance from the start in vector terms.

Answer
50.3 m50.3\,\text{m}

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