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PN Sailor Initial Test study materials
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PN Sailor Initial Test: Mechanical Comprehension and Spatial Relations

PN Sailor Initial Test · Work through your exam, one topic at a time.

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Mechanical Comprehension and Spatial Relations

Mechanical Comprehension and Spatial Relations

This domain tests practical intuition about simple machines and the ability to rotate, fold, cut and view objects mentally. Formulas are minimal; the reasoning is what counts.

Simple machines

  • Levers. Class 1 has the fulcrum between load and effort; class 2 has the load between them; class 3 has the effort between them. Mechanical advantage (MA) = effort arm ÷ load arm.
  • Pulleys. A single fixed pulley changes direction only (MA = 1). A movable pulley halves the effort (MA = 2). With a block and tackle, count the rope segments supporting the load.
  • Gears and belts. Meshed gears turn in opposite directions; the larger gear turns slower and with more torque. Gear ratio = teeth on driven ÷ teeth on driver. A crossed belt reverses direction.
  • Inclined plane, wedge, screw. A gentler slope lowers effort but lengthens distance; the screw is an inclined plane wrapped around a cylinder.
  • Pressure and buoyancy. Pressure = force ÷ area, so a narrow area concentrates force. A floating object displaces its own weight in fluid.

Worked example

A lever has an effort arm of 2 m and a load arm of 0.5 m. What effort lifts a 40 N load?

MA = 2 ÷ 0.5 = 4. Therefore effort = load ÷ MA = 40 N ÷ 4 = 10 N. Check the sense of the answer: a long effort arm should reduce the effort, and 10 N is less than 40 N.

Spatial relations

  • Distinguish rotation (turning) from reflection (mirroring). A rotated letter keeps its handedness; a reflected one does not.
  • For cube-net items, opposite faces never touch when folded; identify the four faces forming the side band first.
  • For view problems, project the object onto the plane named - front, top or side - and drop hidden detail.
  • When folding paper, track each crease line and the layers it creates before punching or cutting.

Traps that cost marks

  • Confusing mechanical advantage with efficiency.
  • Assuming meshed gears turn the same way.
  • Treating a mirrored figure as a rotated one.
  • Forgetting to count the rope segment attached to the movable pulley.