How Do Pulleys Work? A Firefighter Mechanical Aptitude Question, Worked Step by Step

A drawing full of rope and wheels can look complicated, but under ideal conditions a single-rope pulley question comes down to one counting rule, applied carefully.

Below is one original question, the reasoning worked through in order, and the mistake behind each wrong answer.

How does a pulley make a load easier to lift?

A pulley reduces the pull you need only when it moves, because then whatever it pulls on hangs from more than one rope segment and each segment carries a share. In a system threaded with one continuous rope, count the rope segments pulling up on whatever moves with the load: that count is the ideal mechanical advantage, and the pull you need is the load divided by it. A pulley that stays in place changes the direction of your pull, not its size.

It helps to separate the two kinds before any numbers appear.

• A fixed pulley is attached to something that does not move, such as a beam or an anchor. The rope runs over it and the wheel turns, but the pulley stays put. On its own it has a mechanical advantage of 1: you pull with a force equal to the load, in a more convenient direction, such as downward with your body weight behind it.
• A movable pulley is attached to the load and rises with it. The rope runs down one side of the wheel and up the other, so both sides hold the load up. On its own, with both sides vertical, it has a mechanical advantage of 2.

A pulley system is some combination of the two. The part that travels with the load is the moving block, and every question about pulley advantage depends on it. The mechanical syllabus lists this with every other concept the section draws from, and its first lesson, on levers, is open to free accounts.

What does "ideal" mean in a pulley question?

It means the question has removed everything that makes a real rig behave differently from the arithmetic: friction, the weight of the gear, rope stretch, angled rope and acceleration. Under those conditions the tension is the same all the way along a single rope, which is what makes the counting rule exact rather than approximate.

Spelled out, the assumptions are:

• The pulleys turn without friction.
• The pulleys and the rope weigh nothing.
• The rope does not stretch.
• The rope segments are parallel to one another (in this post, all vertical).
• The load moves at a steady speed, so the pull balances the weight instead of accelerating it.

When a question says to ignore friction and gives no pulley weight or rope angle, work inside these rules; if it gives a moving pulley's weight, add that weight to the load.

Can you solve this pulley question?

You can, if you count rope segments rather than pulleys. Try it before you read the working: the question was written for this post, and its numbers are chosen to keep the arithmetic clean.

A firefighter on a balcony is raising a hose bundle that weighs 660 N (newtons, the metric unit of force). Two pulleys are in use. Pulley A is fixed to a beam above. Pulley B is clipped to the bundle. One end of the rope is tied to the frame of pulley B. From that knot the rope runs up and over pulley A, back down and around pulley B, then straight up to the firefighter, who pulls upward. Every rope segment hangs vertically. Ignoring friction and the weight of the pulleys and rope, what pull raises the bundle at a steady speed?

• A. 660 N
• B. 330 N
• C. 220 N
• D. 165 N

How do you work out the answer?

The answer is C, 220 N. Three rope segments pull up on pulley B, so the ideal mechanical advantage is 3, and 660 N divided by 3 is 220 N. Here is the reasoning in order.

Step 1: Find what moves. Pulley B is clipped to the bundle, so it rises with it. Pulley A stays on the beam. Only rope segments pulling on pulley B can share the bundle's weight.

Step 2: Follow the rope and count. Start at the tied end and follow the rope to the firefighter's hands, noting every segment that pulls up on pulley B.

Segment	Runs from	Pulls up on pulley B?
1	The knot on B's frame, up to pulley A	Yes
2	Pulley A, down and under the wheel of pulley B	Yes
3	The wheel of pulley B, up to the firefighter	Yes

That is three segments. The third is the one being pulled, and it still counts, because it leaves the moving pulley heading upward and lifts on it.

Step 3: Use the tension. This is one continuous rope under ideal conditions, so every segment carries the same tension, and that tension is exactly the pull in the firefighter's hands. Three equal tensions hold up 660 N at a steady speed, so three times the pull equals 660 N, and the pull is 220 N.

Step 4: Check the rope length. A pulley system reduces the force but not the work. To raise the bundle 6 metres, each of the three segments has to shorten by 6 metres, so the firefighter pulls 18 metres of rope through their hands. Check it with work, which is force multiplied by distance: 220 N over 18 metres is 3,960 joules, and 660 N raised 6 metres is also 3,960 joules. The two agree, as they must in an ideal system. A pulley trades force for distance; it never reduces the work.

Why are the other answers wrong?

Each wrong answer comes from a specific counting mistake. Knowing the mistakes by name makes them easier to catch in your own working.

• 660 N treats the whole rig as fixed pulleys, with a mechanical advantage of 1. That would only be true if the load hung from a single rope segment.
• 330 N counts pulleys instead of segments: two pulleys, so divide by 2. The same number appears if you count the two segments wrapped around pulley B's wheel and miss the tied end on its frame.
• 165 N assumes each pulley doubles the advantage, giving 2 times 2. Advantages multiply only when one separate pulley system pulls on the rope of another. With a single rope, you count segments rather than multiply.

Does moving the knot change the answer?

Yes, and this shows why you count segments instead of pulleys. Tie the rope to the beam beside pulley A instead of to pulley B, and only two segments pull up on the moving pulley, so the same two pulleys give an ideal mechanical advantage of 2 and a pull of 330 N.

In that version the rope runs from the beam down around pulley B, up over pulley A, and down to the firefighter. The line in the firefighter's hands now leaves the fixed pulley, so it redirects the pull but holds up nothing. A 6 metre lift takes 12 metres of rope instead of 18.

Adding a pulley can also change nothing at all. Go back to the original rig, run the line leaving pulley B up over a third pulley on the beam, and bring it down to a firefighter on the ground. Pulley B still has three segments pulling up on it, so the pull is still 220 N and a 6 metre lift still takes 18 metres of rope. The third pulley changes the pulling direction to downward but adds no advantage, and the beam now carries the full weight of the bundle plus the firefighter's pull.

Why does a real pulley system need more pull than the ideal answer?

Because a real system has the friction and weight that the ideal question removes. Friction at each sheave (the grooved wheel), the stiffness of rope bending around it, and the weight of the moving pulley all add to the pull, so the ideal figure is the least a real rig could need to raise the load, not what it will need.

The same logic explains why stacking pulleys has limits in practice. Every pulley added for advantage also adds friction, so on a raise a real system gives less advantage than its segment count suggests.

Do firefighter aptitude tests ask about pulleys?

Not by name in the description we checked: the National Testing Network's published description of the FireTEAM mechanical test does not mention pulleys. It describes the test as a multiple-choice test presented on video, with an animated brick-making factory that candidates answer questions about, and says most questions concern basic mechanical objects and principles, giving valves and water pressure as its examples.

So treat pulley practice as general practice in mechanical reasoning. It is not a preview of any particular test. The habit it builds, working out what carries a load before doing arithmetic, applies beyond pulleys.

How should you handle a pulley question under time pressure?

Use the same three steps every time, then run one check before you choose an answer. The check catches the first mistake above, an answer equal to the load, but it cannot tell 330 N or 165 N from 220 N, which is why the count in step 2 matters.

1. In a single-rope system, find the pulley that moves with the load.
2. Count the rope segments pulling up on it, including the pulled line if it leaves that pulley heading upward.
3. Divide the load by that count.
4. Check: if two or more segments pull up on the moving pulley, rule out any option where the pull is not less than the load or the rope pulled is not longer than the rise.

Where can you practise more pulley questions?

Semparo's mechanical aptitude practice bank has 500 original questions on levers, pulleys, gears, hydraulics, tools, valves and pressure. Each comes with an explanation of the reasoning, and a free account includes 10 of them as samples.

The full bank and every lesson, including the one on pulleys and block and tackle, come with the Aptitude section or with Pro, and you can compare what each plan includes before choosing.