Mechanical reasoning: guide and free practice

Mechanical reasoning applies basic principles of forces, motion and simple machines. Draw the system, identify the idealised assumptions and track how force or direction changes.

Start with the model

Practice questions often assume frictionless pulleys, rigid levers or gears without slipping. Those assumptions make a clean calculation possible. Real machines can have friction, losses and safety limits; the exercises below teach the simplified model rather than equipment operating instructions.

Three useful relationships

Direction and magnitude are different

An idler gear changes the rotation direction along a gear train but does not independently set the overall first-to-last speed ratio. A fixed pulley can change the pulling direction without reducing the required ideal force.

Draw before calculating

Label the pivot, rope supports or gear contacts. Use the same distance and force units throughout. For a spring or pressure problem, write the supplied relationship rather than importing extra assumptions. Our first set uses explicit text descriptions and simple arithmetic; it prepares underlying concepts rather than reproducing a provider's diagram library.

Your first practice session

Use the idealised assumptions stated in each question. No friction or mechanical loss is included unless specified. These are conceptual exercises, not practical operating instructions.

Try 10 questions with explanations

Worked examples

  1. 1. An ideal horizontal lever is balanced about its pivot. A downward 60 N force acts 2 m to the left. What downward force is needed 3 m to the right? Ignore the lever weight.
    1. 20 N
    2. 30 N
    3. 40 N
    4. 90 N

    Reference: q-f2822f9-172 · Report this question

    Show answer and solution

    Answer: C. 40 N

    Both forces act perpendicular to the horizontal lever and produce opposing moments. Balance gives 60 times 2 = F times 3, so F = 40 N.
  2. 2. External gear A meshes directly with external gear B on parallel fixed axes. A turns clockwise when viewed from one side. Viewed from the same side, which way does B turn?
    1. Clockwise
    2. Anticlockwise
    3. It cannot turn
    4. Direction is independent of A

    Reference: q-64a8c9b-172 · Report this question

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    Answer: B. Anticlockwise

    Directly meshed external gears on parallel axes turn in opposite directions when viewed from the same side. B therefore turns anticlockwise.
  3. 3. External gear A has 20 teeth and turns at 90 rpm. It meshes directly, without slipping, with a 60-tooth external gear B. What is B speed?
    1. 15 rpm
    2. 30 rpm
    3. 90 rpm
    4. 270 rpm

    Reference: q-60076370-138 · Report this question

    Show answer and solution

    Answer: B. 30 rpm

    Directly meshed tooth counts and speeds satisfy 20 times 90 = 60 times B speed. Thus B turns at 90 times 20/60 = 30 rpm.

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About this practice

These are independently written teaching questions. A practice score helps you review your answers; it is not a validated hiring prediction or an official employer score.