3.3 Pulleys and Mechanical Advantage

A pulley is a grooved wheel (a sheave) that a rope, cable, or halyard runs over. On Mechanical Reasoning figures, pulleys do two jobs, and you must not mix them. A fixed pulley is anchored to a beam, a ladder head, or a rescue anchor. Its axle does not travel with the load. It changes the direction of your pull — typically so you can pull down to lift up — and its ideal mechanical advantage (MA) is 1. You still support the full load. A movable pulley has its axle attached to the load. The sheave travels as the load travels. A single movable pulley is supported by two rope segments, so its ideal MA is 2: the load is shared between the two strands.

A block and tackle is a set of fixed and movable sheaves reeved together. The aptitude rule is: count the supporting strands — the rope segments that actually hold up the moving block and load — and that count is the ideal MA. Do not count a coil of 65 mm hose drawn as scenery. Do not count a tag line that is not on the sheaves. Do not count the hauling part as a supporting strand if you are pulling down on a rope that has already left the movable block and gone over a separate fixed sheave; that downward free end is a direction change, not an extra support.

QFD's pack lists mechanical concepts and principles among Mechanical Reasoning topics. Pulley figures are a standard way those concepts are tested on cognitive batteries. Independent OpenExamPrep examples below use a rescue line and a tool bag so the geometry is easy to see. They are not official QFD items.

Fixed, movable, and why the haul feels different

Picture a tool bag hanging from a single sheave shackled to a ladder beam. You pull down on the free end and the bag rises. Direction reversed, force not multiplied: if the bag and contents weigh 200 N (a convenient 20 kg at g = 10 N/kg for diagram arithmetic), you still pull about 200 N. That is a fixed pulley.

Now shackle the sheave to the tool bag instead, anchor one end of the rope to the beam, run the rope down to the sheave and back up, and pull up on the free end. Two strands now share the 200 N, so each strand (and your pull) is about 100 N. The sheave rises with the bag. That is a movable pulley. You pay in distance: to lift the bag 1 m you pull about 2 m of rope.

Add a fixed sheave at the beam so you can pull down instead of up, without adding a third supporting strand, and you have the common fireground arrangement: a movable block on the load plus a fixed direction-change at the head. Still MA 2 if only two strands support the bag.

Strand-count table

Ideal means ignore friction, rope stiffness, and the weight of the blocks unless the figure labels them. If a stem says "frictionless" or shows no extra marks, use the table. If a stem shows a brake, a snatch, or a labelled friction, you cannot treat MA as a free gift — but most cognitive figures stay ideal.

Worked rescue-line example

A four-strand block and tackle hangs from a mezzanine beam. The movable block is hooked to a 240 N bag of breaking-in tools. Ideal effort is 240 / 4 = 60 N. To raise the bag 0.50 m you pull 2.0 m of rope (distance traded at the same ratio as MA). If the figure's options include "60 N and 2 m of rope" versus "240 N and 0.50 m of rope," the first pair is the block and tackle and the second pair is a straight lift with no advantage.

A second figure shows the same bag on a single fixed pulley at the head of a 13.5 m ladder. Pulling down 0.50 m of halyard-style rope raises the bag 0.50 m and still costs about 240 N. Candidates who always divide by two because "pulleys help" will pick a 120 N option that the figure does not earn.

A third figure shows a firefighter pulling up on the free end of a two-strand movable pulley (no extra fixed sheave). That free end is a supporting strand, so MA is 2. Change the figure so the free end comes over a high fixed sheave and the firefighter pulls down: still two strands on the movable block, still MA 2. The extra sheave only turned the haul. The trap is adding 1 to the MA every time you see another wheel, including a wheel that does not support the load.

Keep this list of pulley traps:

• Counting every drawn wheel as a force multiplier, including a pure direction-change sheave
• Counting hose coils, tag lines, or a second unused rope as strands
• Forgetting the distance trade-off (you cannot get MA 4 and also pull only 1 m of rope to lift 1 m)
• Treating a movable sheave as fixed because it "looks attached to the beam" when the hook is on the load
• Importing wet-rope friction when the figure is unmarked
• Spending time converting the bag's mass with a calculator you are not allowed to use; the figure will give friendly numbers or ask only for more/less, not a precise newton value

Fluids in hoses, nozzle reaction, and kinetic energy of a moving bag after it is dropped are pack topics, but they are not pulley MA. They wait for Chapter 4. If the stem asks what happens after the bag is released and falls, you have left simple machines.