A-Level Modelling in mechanics Practice Questions

Free A-Level Modelling in mechanics practice questions with full step-by-step worked solutions. Covers modelling, particle, light-string, inextensible. Practise exam-style problems and check your method.

modellingparticlelight-stringinextensiblesmoothuniform-rod
A-Level70 questionsStep-by-step solutions
Question 1
2 markseasy
In mechanics modelling, what does the assumption of a particle mean?
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Worked solution

  1. Recall the modelling term

    particle

    This is a standard assumption in A-Level mechanics.

  2. State what may be ignored

    The object has no rotational effects and all its mass acts at a single point.

    The assumption simplifies the model by ignoring a complicating effect.

  3. Select the correct meaning

    The object has no rotational effects and all its mass acts at a single point.

    This is the standard interpretation.

Answer
The object has no rotational effects and all its mass acts at a single point.
Question 2
2 markseasy
Convert 90 km/h90\,\text{km/h} to m/s\text{m/s}.
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Worked solution

  1. Write the conversion factor

    Convert using 1000 m1000\,\text{m} per km and 3600 s3600\,\text{s} per hour

    Use the standard SI relationship.

  2. Apply the conversion

    90×10003600=25 m s−190\times\dfrac{1000}{3600}=25\,\text{m s}^{-1}

    This gives the value in the required unit.

  3. State the converted value

    25 m s−125\,\text{m s}^{-1}

    This is the required value.

Answer
25 m s−125\,\text{m s}^{-1}
Question 3
3 marksintermediate
Find the magnitude of the vector a=11i+60j\mathbf{a}=11\mathbf{i}+60\mathbf{j}.
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Worked solution

  1. Write the magnitude formula

    ∣a∣=a2+b2|\mathbf{a}|=\sqrt{a^2+b^2}

    The magnitude is the length of the vector.

  2. Substitute the components

    ∣a∣=112+602=61|\mathbf{a}|=\sqrt{11^2+60^2}=61

    Evaluate the square root.

  3. Check using a known triple

    Verify the components.\text{Verify the components.}

    Common Pythagorean triples help check the answer.

  4. State the units if required

    Same units as the components.\text{Same units as the components.}

    Magnitude inherits the component units.

  5. Check using a known triple

    Verify the components.\text{Verify the components.}

    Common Pythagorean triples help check the answer.

  6. State the magnitude

    6161

    This is the length of the vector.

Answer
6161
Question 4
5 markshard
A model treats a car as a particle. What is being ignored?
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Worked solution

  1. Recall definitions

    Use standard mechanics terminology.\text{Use standard mechanics terminology.}

    Each option tests a different concept.

  2. Eliminate incorrect options

    Check units and definitions.\text{Check units and definitions.}

    Several distractors are plausible.

  3. Select the best match

    The size and shape of the car

    This is the correct answer.

  4. Confirm uniqueness

    Only one option fits.\text{Only one option fits.}

    The correct option is unambiguous.

  5. Select the best match

    The size and shape of the car

    This is the correct answer.

  6. Confirm uniqueness

    Only one option fits.\text{Only one option fits.}

    The correct option is unambiguous.

  7. Select the best match

    The size and shape of the car

    This is the correct answer.

  8. Confirm uniqueness

    Only one option fits.\text{Only one option fits.}

    The correct option is unambiguous.

  9. Select the best match

    The size and shape of the car

    This is the correct answer.

  10. State the answer

    The size and shape of the car

    Done.

Answer
The size and shape of the car
Question 5
8 markschallenging
Which list contains only base SI units?
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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

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