Mechanical Reasoning Guide

Levers & Pulleys

Balance a beam, then a mobile; find the force a rope system needs and how far its load rises. Engineers, soldiers and technicians are tested on seeing how. Can you?

Which weight balances the mobile?
And how much force actually holds the load?

Two simple principles are all it takes. Read on, then try the test.

Where it appears

Levers and pulleys are fundamental simple machines tested in mechanical reasoning (or mechanical comprehension) exams, measuring practical physical intuition. You will meet them in:

Bennett Mechanical Comprehension Test (BMCT)The gold-standard test of mechanical aptitude used in industrial, technical, and engineering recruitment.

ASVAB (Armed Services Vocational Aptitude Battery)The Mechanical Comprehension subtest required for US military mechanical, aviation, and engineering trades.

Differential Aptitude Tests (DAT)Its Mechanical Reasoning subtest, widely used in technical career guidance and school assessment.

Technician & trade apprenticeship testsApprenticeship selection for electrical (IBEW), pipefitter, millwright, mechanic, and plant operator roles.

These tests reward precise physical reasoning over visual guesswork. Calculating turning effects and counting rope lines link by link avoids the common visual traps.

Part 1: Levers & Balance

A beam on a central pivot balances when the turning effect (moment) is equal on both sides. Distance is measured in numbered notches (1 to 6) from the central pivot (0):

turning effect = weight × distance from pivot

For the beam to balance horizontally:

Σ (weight × distance) on the left = Σ (weight × distance) on the right

1Finding the unknown weight

Multiply each weight by its distance. Add up all turning effects on the left, subtract any known turning effects on the right, and divide the remainder by the distance where the question mark sits:

weight = needed turning effect ÷ distance

The commonest slip: calculating the missing turning effect (e.g. 12) and choosing 12 kg, forgetting to divide by the distance notch!

6 kg at 2 = 12 · 3 kg at 4 = 12

2Placing a weight

When asked where a given weight must go to balance the beam (spots A, B, C, or D), divide the required turning effect by the given weight:

distance = needed turning effect ÷ weight to place

The mirror trap: choosing the mirror notch of the opposite weight. That is only right when the two weights are identical!

Place the 6 kg weight on letter B (notch 2) to balance 3 kg at 4

3Mobiles: hanging beams

In a mobile, one or more balanced beams hang from the top beam. The rule is simple and exact:

A hanging balanced beam acts on the beam above as its whole combined weight, concentrated at the single point where it hangs.

Beams themselves weigh nothing in these questions. Add the weights on the hanging beam together (e.g. 3 + 6 = 9 kg) and treat it as a single 9 kg load at that hanging notch.

The sub-beam weighs 3 + 6 = 9 kg at notch 3; balanced by 9 kg at 3

Part 2: Pulleys — Force & Distance

A rope system distributes the load across multiple supporting segments of rope, reducing the effort needed to hold or lift it:

force needed = load ÷ n

where n is the number of rope segments directly holding the moving block.

4Downward pull: free end does not count

When the free end goes over a top fixed pulley and is pulled downward, it only redirects your effort. It does not support the moving block.

Count only the segments running to the moving block below.

The trap: counting the pulled end when pulling down. If 2 vertical segments hold the block and the free end pulls down, n is 2, not 3.

Downward pull: 2 holding segments · 120 N ÷ 2 = 60 N

5Upward pull: free end DOES count

When the rope is pulled upward directly from the moving block, your hands are actively lifting the block. The pulled end is itself one of the holding segments.

Here n includes the pulled line in your hand.

Upward pull: 3 holding segments · 180 N ÷ 3 = 60 N

6Rope pulled vs. load rise

Work is conserved: effort force is divided by n, so the rope must move n times farther than the load:

load rise = rope pulled ÷ n

If n = 3 and you pull 12 metres of rope, the load rises 12 ÷ 3 = 4 metres.

Pull 12 m of rope through 3 segments · load rises 4 m

7Comparing systems: which needs least force?

When comparing four systems (A, B, C, D), always compute load ÷ n for each. Never guess by "most pulleys" or "lightest load" alone:

Trap A: The system with the most rope segments may carry a far heavier load.
Trap B: The system with the lightest load may only have 1 rope segment, requiring full force.

Always compute: Force = Load ÷ n for each lettered option, then choose the smallest resulting number.

Two questions, solved

1A lever question

Which weight balances the beam?

The question

Try it first, then open the answer.

Show the answer: 3 kg

Calculate the left turning effect (anticlockwise moment): 1×6 + 1×3 = 9.
The right side must also equal 9 to balance.
The unknown weight '?' sits at distance 3.
Weight needed = 9 ÷ 3 = 3 kg.

The solution and calculated values

2A pulley question

What force holds the 180 N load?

The question

Try it first, then open the answer.

Show the answer: 36 N

Count the rope segments supporting the moving block: 5 segments.
The free end is pulled upward directly from the moving block, so it counts as one of the 5 supporting segments.
Force required = Load ÷ segments = 180 N ÷ 5 = 36 N.

The solution and calculated values

How the practice test runs

3:00 on the clock, and it only runs while a question is on screen.
Adaptive ladder: single weights first, then placement questions, multi-weight combinations, mobiles with hanging sub-beams, and complex pulley systems.
The ladder climb: until your first miss, every right answer jumps a whole level; after it, three right answers in a row jump a level and a miss drops one.
Scoring: a right answer earns difficulty points; an incorrect answer costs half as many, so blind guessing does not pay.
Every question is uniquely generated with exact integer values, and the review screen provides full mathematical proofs.

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