ASVAB Mechanical Comprehension study guide

All fifteen procedures this subtest draws on, a four-step inspection order for reading a mechanism, and fifteen worked examples — each one ending in the rule misapplied.

What this subtest actually asks of you

Mechanical Comprehension is 15 of the 135 scored questions on the computer ASVAB — 11% of the scored test. Like General Science and Electronics Information, it is not one of the four AFQT subtests, so it does not move the number that decides whether you can enlist — but it feeds the line scores that decide which jobs you qualify for (how the ASVAB is scored).

Almost nothing here is a fact to memorize. This subtest shows you a mechanism — or describes one — and asks which rule decides what happens: which gear turns which way, how much force the ramp saves, whether the block floats, where the beam bends. There are no dates and no vocabulary lists, and that is why it rewards a method rather than a memory.

Two consequences:

Name the mechanism class first. Lever, gear, pulley, belt, spring, pressure, floating, friction, momentum, flow. Almost every question announces its class in a word or a picture, and deciding that first is what stops you applying the pulley rule to a lever.
The wrong answers are real rules aimed at the wrong situation. More pulleys does not mean more force needed; pressure depends on area and not on weight alone; a thicker handle makes a screw turn slower, not faster. The list of those misapplications is half of this guide.

The fifteen procedures

Every Mechanical Comprehension question is one of these fifteen. Each one is worked out below — the rule, the steps, and the trap that costs points on it.

Levers. A lever balances when effort times the effort arm equals load times the load arm. A longer effort arm means less force, and the fulcrum — the pivot the bar turns on — sets both arms. → example 1
Gears. Meshed gears turn in opposite directions, so each mesh flips the direction. A large gear driven by a small one turns slower and delivers more torque; the tooth counts set the ratio. → example 2
Pulleys. The mechanical advantage is the number of rope segments holding the load up. A single fixed pulley changes only the direction of your pull; every extra supporting segment lowers the force and lengthens the rope you pull. → example 3
The wheel and axle. A big wheel fixed to a small axle multiplies turning force by the ratio of their diameters — which is why a large crank, a fat screwdriver handle and a barrow wheel all feel easier. → example 4
The inclined plane, the wedge and the screw. A ramp trades distance for force: its advantage is the length divided by the height, and the same idea makes a wedge and a screw's threads work. → example 5
Pressure and hydraulics. Pressure is force divided by area. In a hydraulic system the same pressure acts everywhere, so a larger piston delivers a larger force but moves a shorter distance. → example 6
Floating and sinking. An object floats when its density is less than the liquid's, and a floating object displaces its own weight of liquid. → example 7
Friction. Friction opposes motion and grows with the weight pressing the surfaces together and with how rough they are. Rolling friction is far smaller than sliding friction. → example 8
Momentum and inertia. Inertia is resistance to a change in motion, and it grows with mass. Momentum is mass times velocity, so a light fast object and a heavy slow one can carry the same momentum. → example 9
Work and power. Work is force times distance; power is work divided by time. A machine trades force for distance and never creates energy, so what you put in equals what the load gains. → example 10
Tension, compression and the rigid frame. A stretched member is in tension, a squeezed one is in compression, and a diagonal brace stiffens a frame because a triangle cannot lean. → example 11
Flow in pipes and straws. The same liquid passing a narrowing pipe must speed up, and a straw works because you lower the pressure inside it and the atmosphere pushes the drink up. → example 12
Belt drives. One pulley drives another through a belt: an open belt keeps both turning the same way, a crossed belt reverses the driven one, and the diameters set the speed — the smaller pulley turns faster. → example 13
Springs. A spring's stiffness is the force each inch of stretch needs, so a spring rated 5 pounds per inch needs 5 pounds to move it 1 inch. Two springs in parallel share a load and double the stiffness; two in series halve it. → example 14
The center of gravity and stability. An object behaves as if all its weight acts at one point, which is its center of gravity. An object tips once that point passes outside its base, which is why a low wide load is stable and a tall narrow one is not. → example 15

A four-step method

1. Name the mechanism class. Out loud: "this is a lever", "this is a gear train", "this is pressure". Step 1 is the whole defense against the error this subtest is built to catch — using a real rule on the wrong machine.

2. Find the two quantities the rule connects. A lever connects force and distance from the fulcrum. Gears connect tooth counts and turns. Pressure connects force and area. Write those down before you compute: a procedure written down can be checked, one done in your head cannot.

3. Apply the rule, and watch the direction of the trade. Every simple machine pays for its advantage somewhere: the ramp is longer, the rope is longer, the big piston moves less. If your answer has the load moving further and the force getting smaller, you have inverted the trade.

4. Check the answer against the mechanism. Does the load rise less than your hand moved? Does the narrow pipe carry the water faster? Does the denser water float the ship higher? Two seconds, and it catches the answer of the wrong direction — which is where most of the missed points on this subtest live.

The fifteen worked examples

Each example is one of the fifteen procedures above: the rule in action, the steps, and the trap that example is built to catch.

1. A lever, balanced on its two arms

A 60 lb load sits 2 feet from the fulcrum. How much effort is needed at 6 feet from the fulcrum, on the other side?

Name the class: a lever, with the fulcrum between the load and the effort.
Write the rule: effort × effort arm = load × load arm.
Substitute: effort × 6 = 60 × 2 = 120.
Divide: effort = 120 ÷ 6 = 20 lb.
Check the direction: the effort arm is three times the load arm, so the effort must be one third of the load — and 20 is a third of 60.
The trap: 60 lb, which ignores the arms entirely, and 180 lb, which multiplies by the three-to-one ratio instead of dividing by it.

2. Gears: direction first, then the ratio

Gear A has 12 teeth and drives gear B, which has 36 teeth. Gear A turns clockwise. Which way does B turn, and how many turns does B make for every 3 turns of A?

Direction first: meshed gears turn in opposite directions, so B turns counterclockwise.
Now the ratio. B has 36 ÷ 12 = 3 times as many teeth.
So B turns one third as fast: 3 turns of A gives 1 turn of B.
Torque goes the other way, so B delivers 3 times the torque that A supplies.
The trap: reporting B's answer as 3 turns (the input, not the output) and forgetting the direction flip. Direction and ratio are two separate questions, and a gear question usually asks both.

3. A pulley system: count the rope segments

A pulley block has four rope segments supporting the load. What is its mechanical advantage, and how much rope is pulled to raise the load 2 feet?

Count only the segments that hold the load up: 4.
Effort = load ÷ 4, so a 200 lb load needs 200 ÷ 4 = 50 lb of pull.
The distance trades the other way: to raise the load 2 feet you pull 4 × 2 = 8 feet of rope.
The single fixed pulley is the zero-advantage case: 1 supporting segment, so the effort equals the load and only the direction of your pull changes.
The trap: counting the rope that runs back to your hand as though it propped the load up, which turns four supporting segments into five.

4. The wheel and axle: a ratio of diameters

A wheel 24 inches in diameter is fixed to an axle 4 inches in diameter. What is the mechanical advantage, and what force at the rim lifts a 180 lb load?

Name the class: a wheel and axle, which is a lever whose two arms are radii.
Advantage = wheel diameter ÷ axle diameter = 24 ÷ 4 = 6.
So the force at the rim is the load ÷ 6: 180 ÷ 6 = 30 lb.
The rope carrying the load winds on the axle, so the load rises six times more slowly than your hand moves.
The trap: putting the radius against the diameter, or subtracting 24 − 4 = 20. An advantage is a ratio of two like measurements, never a difference.

5. The inclined plane: length over height

A ramp 12 feet long rises 3 feet. What is its advantage, and what force pushes a 600 lb crate up it?

Name the class: an inclined plane, which trades distance for force.
Advantage = length ÷ height = 12 ÷ 3 = 4.
Force = load ÷ advantage = 600 ÷ 4 = 150 lb.
Check it by work: 150 × 12 = 1800 foot-pounds up the ramp, and 600 × 3 = 1800 foot-pounds lifted straight up. The same work, spread over a longer push.
A wedge is two inclined planes back to back, and a screw is an inclined plane wrapped around a cylinder, so both obey the same rule.
The trap: dividing by the rise alone (600 ÷ 3 = 200) or multiplying by the advantage (2400). A gentler ramp is a longer ramp, so the force falls as the length rises.

6. Pressure, area and a hydraulic lift

A force of 20 lb acts on a piston of 2 square inches. What pressure is that, and what force does the same pressure produce on a 10 square inch piston?

Pressure = force ÷ area = 20 ÷ 2 = 10 pounds per square inch.
The same pressure acts throughout the fluid, so force = pressure × area = 10 × 10 = 100 lb.
The force grew 5 times (10 ÷ 2), so the distance shrinks 5 times: push the small piston down 10 inches and the large one rises 10 ÷ 5 = 2 inches.
Pressure is force over area, so a smaller area under the same force presses harder — which is the whole idea behind a sharp edge, a nail point and a narrow heel.
The trap: leaving the force unchanged because "it is the same fluid everywhere", or dividing by the area ratio instead of multiplying. Same pressure, bigger area, bigger force.

7. Floating: density and displaced weight

A 30 lb block floats. How much water does it displace, and why does a steel bolt of the same size sink?

A floating object displaces its own weight: a 30 lb block displaces 30 lb of water, which is why the level rises when it goes in.
Float or sink is a comparison of densities: wood is about 0.6 times as dense as water, so it floats, while steel is about 7.8 times as dense, so it sinks.
Denser liquid needs less volume for the same support: the same 30 lb of weight is displaced in a smaller volume of seawater, so the ship rides higher.
Check the direction every time: the denser the liquid, the higher the object floats — and the weight displaced never changes.
The trap: "heavy things sink". A steel ship floats because its shape encloses air, which brings its overall density below the water's, so the shape matters as much as the material.

8. Friction: what it depends on, and what it does not

A block slides across a level floor at a steady speed while you push it with 15 lb. What is the friction force, and what happens if a second identical block is stacked on top?

Steady speed means no net force, so friction equals your push: 15 lb backward against a 15 lb push.
Friction follows the weight pressing the surfaces together, so doubling the weight — one block to two identical blocks — roughly doubles the friction, from 15 lb to about 30 lb.
The surfaces matter too: wax, oil or a rubber sole change the friction several times over without changing the 15 lb of weight at all.
Rolling beats sliding every time: a cart's wheels cut the drag to a small fraction of the 15 lb it takes to slide the same crate across the floor.
The trap: "more contact area means more friction". Friction follows the force pressing the surfaces together, not how much surface is touching — which is why a wide tire and a narrow one grip about the same on a dry road.

9. Momentum and inertia: mass at speed

A 2,000 lb car at 30 mph and a 4,000 lb truck at 15 mph approach each other. Which has the greater momentum, and which is harder to stop?

Momentum is mass times velocity: 2,000 × 30 = 60,000 and 4,000 × 15 = 60,000.
The two momenta are equal, because the car's extra speed (30 ÷ 15 = 2) cancels the truck's extra mass (4,000 ÷ 2,000 = 2).
Inertia is a different question again: it follows mass alone, so the 4,000 lb truck resists a change in its motion twice as hard as the 2,000 lb car does.
Check the units: pounds times miles per hour on both sides, so 60,000 on each side is a like-for-like comparison.
The trap: choosing the faster vehicle on the assumption that speed decides momentum on its own, or choosing the heavier one on the same assumption about mass. Momentum needs both, multiplied.

10. Work and power: the same work at two speeds

A winch lifts a 300 lb crate 10 feet. How much work does it do? And if machine A does 1,000 foot-pounds of work in 5 seconds while machine B does the same in 2 seconds, which has more power?

Work is force times distance: 300 × 10 = 3,000 foot-pounds.
Power is work divided by time, so machine A delivers 1,000 ÷ 5 = 200 foot-pounds per second.
Machine B delivers the same work faster: 1,000 ÷ 2 = 500 foot-pounds per second, so B has the greater power.
A machine never creates energy, so what goes in equals what the load gains: a lever lifting a 400 lb load with 100 lb of effort must move your hand 4 feet to raise the load 1 foot (100 × 4 = 400 × 1).
The trap: reading a bigger power as more work done. Work is the total; power is only how fast it happens.

11. Tension, compression and the rigid triangle

A rope hangs a heavy sign. What force is the rope under, and where should a single brace go to stiffen a rectangular frame?

A rope is pulled from both ends, so it is in tension: a 200 lb sign hangs from 200 lb of pull along the rope.
A post being squeezed instead is in compression, and the same 200 lb pressing down a post is 200 lb of compression in it.
A rectangular frame can lean sideways into a parallelogram, so it is not rigid.
A brace running diagonally, corner to corner, makes two triangles, and a triangle cannot change shape without one of its sides changing length.
A beam supported at both ends bends most at the middle: carry 200 lb at the mid-span of a 10 ft beam and each support carries 200 ÷ 2 = 100 lb, while the bending is largest at the middle, furthest from what holds the ends up.
The trap: reading a hanging rope's curve as bending, or adding a brace parallel to a rail. Parallel members leave the rectangle a rectangle, and rectangles lean.

12. Flow: the same water through a narrower pipe

Water flows at a steady speed through a pipe that narrows from 4 square inches to 2 square inches of cross-section. What happens to the water in the narrow part?

The same volume has to pass every second, so area × speed stays constant: 4 square inches × 3 feet per second = 12 cubic inches per second.
The area halves, from 4 to 2 square inches, so the speed must double to keep the same 12 cubic inches per second: 12 ÷ 2 = 6 feet per second.
Going the other way works too: a pipe widening from 2 back to 4 square inches drops the speed from 6 to 3 feet per second.
A straw works the same way in reverse: drawing on it lowers the pressure inside, and the atmosphere pressing on the drink pushes it up the straw.
The trap: "the water must slow down because there is less room". Less room, same volume per second, so the speed has to rise.

13. A belt drive: direction first, then the speed the diameters set

A 6-inch pulley drives a 2-inch pulley through an open belt, and the driver turns at 300 r.p.m. Which way does the driven pulley turn, and how fast?

An open belt runs from one pulley straight across to the other, so both pulleys turn the same way: the 6-inch driver at 300 r.p.m. clockwise drives the 2-inch pulley clockwise as well.
A crossed belt — twisted once between the pulleys — reverses the driven pulley, so the same drive would turn the 2-inch pulley counter-clockwise.
The belt itself travels at one speed everywhere, so the pulley with the smaller circumference has to turn more often to keep up. The ratio comes from the diameters: 6 ÷ 2 = 3, and the driven pulley turns 3 times for each turn of the driver.
So the driven pulley turns 300 × 3 = 900 r.p.m.
The trade is the one the wheel and axle makes: the small pulley turns fast and delivers less turning force, and the large one turns slowly with more force.
The trap: reading a crossed belt's change of direction as a change of speed, or dividing the diameters the wrong way round and answering 100 r.p.m. Direction and ratio are two separate questions, and the belt's crossing answers only the first.

14. A spring: its rating, and how a pair of springs shares a load

A spring stretches 3 inches under a 15-pound load. What is its rating, and how far does it stretch under 40 pounds?

A spring's rating is the force needed for each inch of stretch: 15 ÷ 3 = 5 pounds per inch.
Under 40 pounds it stretches 40 ÷ 5 = 8 inches. Double the load, double the stretch — a spring's stretch is proportional to the force on it.
Two springs in parallel (side by side, sharing the same load bar) each take half: 40 ÷ 2 = 20 pounds each, so each stretches 20 ÷ 5 = 4 inches, and the pair carries 40 pounds with half the stretch of one spring alone.
Two in series (one hung below the other) each carry the whole 40 pounds, so the pair stretches 8 + 8 = 16 inches — half the stiffness, twice the travel.
The trap: reading a stiff spring as a strong one. The rating says how far it moves for a given force, not how much load it can survive; a spring taken past its rated stretch stays stretched and has to be replaced.

15. Center of gravity: where the weight acts, and when it tips

A uniform 6-foot beam weighs 60 pounds and rests on a support at its middle. A 30-pound weight is hung 2 feet to the right of the support. Where is the combined center of gravity?

A uniform beam acts as if its whole 60 pounds sits at its middle: 3 feet from the left end.
The hung weight sits 3 + 2 = 5 feet from the left end.
Add the moments about the left end: (60 × 3) + (30 × 5) = 180 + 150 = 330 foot-pounds, and the total weight is 60 + 30 = 90 pounds.
Divide the moment by the weight: 330 ÷ 90 = 3.67 feet from the left end, which is 0.67 feet right of the support — so the beam dips on the loaded side, and it tips once the weight hangs far enough out to carry the center of gravity past the support.
Stability is that same question for a whole object: it tips when its center of gravity passes outside the edge of its base, which is why a low, wide crate is steady and the same crate stood on end is not.
The trap: treating the two weights as a simple average. The 30 pounds acts twice as far from the support as the beam's own 60 pounds, and distance is half of a moment — weight alone decides nothing.

The misapplied rules, collected

These are not gaps in knowledge. Each one is a real rule used on the wrong mechanism, which is what this subtest is built to catch:

The right rule on the wrong machine — applying the pulley count to a lever, or the gear ratio to a wheel and axle. Name the class first, every time.
The trade inverted — a load that moves further and a force that gets smaller. No machine does both; the advantage is always paid for in distance.
Counting the rope in your hand — a pulley's advantage counts only the segments supporting the load.
Speed for force in a wheel and axle — a fat handle and a long crank turn things more slowly, not faster.
Using radius against diameter — an advantage is a ratio of two like measurements, and a difference (24 − 4) is not one.
Area swapped for force in pressure — same pressure, larger area, larger force; smaller area, higher pressure.
"Heavy things sink" — floating is a comparison of densities, which is why a steel ship floats and a steel bolt does not.
Contact area as the cause of friction — friction follows the weight pressing the surfaces together, plus how rough they are.
Speed or mass alone deciding momentum — momentum is mass times velocity; either one alone can be misleading.
Power read as work — more power only means the work happened faster.
A parallel brace — stiffening a frame means making triangles, not adding another rectangle.
"Narrower means slower" — the same flow through a smaller opening has to speed up.
A belt's crossing read as a gear ratio — an open belt and a crossed belt turn the driven pulley opposite ways, and neither changes the ratio, which the pulley diameters set.
Spring stiffness read as spring strength — the rating is pounds per inch; how much load the spring can survive is a different number.
Weight used where a moment belongs — a light weight acting far from the fulcrum can outweigh a heavy one close to it, and an object tips on where its center of gravity is, not on how heavy it is.

Notice how many of those are the mirror of the correct rule. On this subtest the facts are rarely the problem; the direction is.

How to practice this

Work the free Mechanical Comprehension practice set and read the figure before the prompt — on this subtest the picture usually tells you the class.
Draw the trade on your scratch paper: an arrow for the force and an arrow for the distance, with the big end on the side that loses.
Sort your errors by procedure, not by count. Missing three gear questions and three friction questions needs two different fixes.
Read the explanation on every question, including the ones you got right. A right answer reached for the wrong reason comes back on test day.

How to study for the ASVAB has the rest of the method, and what the pass adds.

Where to go next

Next topic — Assembling Objects
The exam itself — how the ASVAB is scored, how many questions, and what makes the ASVAB hard.

Mechanical Comprehension carries 15 of the 135 scored questions on the computer test — the published subtest table's count — and the AFQT score is not computed from it: that score comes from Arithmetic Reasoning, Mathematics Knowledge, Word Knowledge and Paragraph Comprehension.

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