⚙️ Gears, Fluids and Structures

Part 1 of 7 — Gears, Fluids and Structures on the ASVAB

The rest of Mechanical Comprehension

Mechanical Comprehension (MC) is $15$ questions in $22$ minutes on the CAT-ASVAB, about $1\frac{1}{2}$ minutes each. Besides forces and simple machines, the official topic list includes "mechanical motion," "fluid dynamics" and "structural support." In practice that means pictures like these:

• a gear train: which way does the last gear turn, and how fast?
• belt-driven pulleys of different sizes: which one spins fastest?
• a cam pushing a rod up and down, or springs stretched by weights
• a hydraulic lift or a pump with valves
• objects floating in water
• a beam on two posts (which post holds more?), or shelves and brackets (which holds the most weight?)

Why these are good points

Each picture type has one rule behind it. Learn the rule once and every version of the picture becomes a 30-to-60-second question:

⚙️ Gears, Fluids and Structures

Part 2 of 7 — Gears and Gear Trains

Rule 1: direction alternates

Two meshed gears always turn in opposite directions. In a chain of gears in a row, the direction alternates:

Shortcut: odd-numbered gears turn the same way as the first; even-numbered gears turn the opposite way.

An idler gear is a gear placed between two others just so they turn the same direction. It does not change the speed ratio between the first and last gear.

Gears fixed on the same shaft turn together: same direction, same rpm.

Rule 2: teeth × rpm is the same for meshed gears

Every tooth that passes on one gear pushes one tooth on the other, so

$\text{teeth}_1 \times \text{rpm}_1 = \text{teeth}_2 \times \text{rpm}_2$

• The smaller gear turns faster; the larger gear turns slower.
• Speed and turning force trade off: a small gear driving a big gear gives less speed and more torque (a low gear for climbing); a big gear driving a small one gives more speed and less torque.

Worked example. A $10$-tooth gear at $300$ rpm drives a $30$-tooth gear. $10 \times 300 = 30 \times \text{rpm}$, so the big gear turns at $100$ rpm, one-third as fast but with three times the torque.

Worked example. In a row of three gears, $A$ ($20$ teeth) drives idler $B$ ($8$ teeth), which drives $C$ ($40$ teeth). Skip the idler for speed: $20 \times \text{rpm}_A = 40 \times \text{rpm}_C$. If $A$ turns at $60$ rpm, $C$ turns at $30$ rpm, in the same direction as $A$.

⚙️ Gears, Fluids and Structures

Part 3 of 7 — Belts, Chains, Cams, Cranks and Springs

Belt-driven pulleys

A belt connects two pulleys so they turn together. Every inch of belt that runs off one pulley runs onto the other, so

$\text{diameter}_1 \times \text{rpm}_1 = \text{diameter}_2 \times \text{rpm}_2$

• The smallest pulley in a belt system turns fastest.
• An open belt (a simple loop) turns both pulleys the same direction.
• A crossed belt (a figure 8) turns them in opposite directions.
• Pulleys fixed on the same shaft turn together, at the same rpm.

Worked example. A motor turns a $3$-inch pulley at $1{,}200$ rpm. A belt drives a $9$-inch pulley. $3 \times 1{,}200 = 9 \times \text{rpm}$, so the big pulley turns at $400$ rpm.

Chains and sprockets

A chain works exactly like a belt, but with teeth: teeth × rpm is the same for both sprockets, and both turn the same direction. On a bicycle with a $48$-tooth front sprocket and a $16$-tooth rear sprocket, the rear wheel turns $48 \div 16 = 3$ times for each turn of the pedals.

⚙️ Gears, Fluids and Structures

Part 4 of 7 — Fluids, Pascal's Principle and Hydraulics

Pressure in a liquid grows with depth

The deeper you go in a liquid, the more liquid is stacked above you, so the pressure increases with depth.

• At the same depth, the pressure is the same in every direction and does not depend on the shape or width of the container. A narrow pipe and a wide tank filled to the same height have the same pressure at the bottom.
• A water tower is tall so the water at the bottom has high pressure to push through the town's pipes.
• Water squirts out of a hole near the bottom of a tank faster and farther than out of a hole near the top.
• Dams are built thicker at the bottom, where the water pressure is greatest.

Pascal's principle

Pressure applied to a confined fluid is passed on equally to every part of the fluid and the walls of its container.

Liquids barely compress, so a push on one end of a sealed system shows up instantly at the other end. That is how hydraulic brakes, jacks and lifts work. Air bubbles ruin the effect, because gas does compress: air in brake lines makes the pedal feel spongy.

⚙️ Gears, Fluids and Structures

Part 5 of 7 — Buoyancy and Structural Support

Buoyancy: Archimedes' principle

Any object in a fluid is pushed up by a buoyant force equal to the weight of the fluid it pushes aside (displaces).

• If the object is less dense than the fluid, it floats. It sinks only until it has displaced its own weight of fluid.
• If it is denser, it sinks, but it still weighs less in the fluid than in air: its apparent weight = real weight − buoyant force.
• A steel ship floats because its hollow hull pushes aside a huge volume of water, enough to weigh as much as the ship.
• Salt water is denser than fresh water, so a boat floats higher in the ocean than in a lake.
• Of several same-size blocks floating in the same water, the one that sits deepest is the densest (heaviest).

Worked example. A $50$-lb block is lowered completely into water and pushes aside $30$ lb of water. The buoyant force is $30$ lb, so the block's apparent weight is $50 - 30 = 20$ lb, and it sinks. A $20$-lb log that would displace $30$ lb of water if pushed under instead floats, sinking only until it displaces $20$ lb.

⚙️ Gears, Fluids and Structures

Part 6 of 7 — Gears, Fluids and Structures Test Strategy and Traps

Timing

Mechanical Comprehension: $15$ questions in $22$ minutes, about $88$ seconds each. Gear-direction, belt and float questions are often answerable in 20 to 40 seconds once you know the rule; save your time for the multi-step ones (compound gears, hydraulic distances, beam shares).

• You must answer each question to move on, and you cannot go back.
• Treat every question as scored; tryout items look identical.
• If time runs short, keep working real answers. A string of wrong answers at the end of a subtest is penalized heavily on the CAT.

Fast routines

⚙️ Gears, Fluids and Structures

Part 7 of 7 — Gears, Fluids and Structures Mastery Set

This set mixes gear trains, belts, chains, cams, springs, hydraulics, buoyancy and structures. Use the fast routines from Part 6, and give yourself about $1\frac{1}{2}$ minutes per question.