⚙️ Forces, Work and Energy

Part 1 of 7 — Mechanical Comprehension on the ASVAB

What the Mechanical Comprehension subtest is

Mechanical Comprehension (MC) tests "knowledge of mechanical and physical principles": how forces, machines, gears, fluids and structures behave. Almost every question shows a picture: a box on a ramp, a lever with weights, a pulley system, a gear train, a beam on two posts. Your job is to read the picture and apply one or two principles.

On the paper enlistment test it is $25$ questions in $19$ minutes. No calculator is allowed, and the numbers are chosen so the arithmetic is quick by hand.

Why MC matters

MC is not part of the AFQT, but it shows up in many job line scores:

• Marine Corps GT (General Technical) $= \text{AR} + \text{MC} + \text{VE}$. Unlike the Army GT, the Marine GT includes MC, and GT opens a lot of Marine jobs.
• Air Force M (Mechanical) $= \text{AR} + \text{MC} + \text{AS} + 2 \cdot \text{VE}$
• Marine Corps MM $= \text{AR} + \text{MC} + \text{EI} + \text{AS}$
• Navy MEC $= \text{AR} + \text{MC} + \text{AS}$, MEC2 $= \text{AR} + \text{MC} + \text{AO}$, NUC $= \text{AR} + \text{MK} + \text{MC} + \text{VE}$
• The Army's MM area is a weighted blend driven mostly by AS, MC and EI
• On the high-school CEP, MC is part of the Science/Technical score ($\text{GS} + \text{EI} + \text{MC}$)

Cutoffs differ by job and change over time, so ask your recruiter which scores your target jobs use.

⚙️ Forces, Work and Energy

Part 2 of 7 — Forces, Weight and Center of Gravity

Forces and net force

A force is a push or a pull. On the ASVAB, forces are usually given in pounds (lb). When several forces act on one object, what matters is the net force:

• Forces in the same direction add.
• Forces in opposite directions subtract, and the net force points the way of the bigger one.
• If the forces cancel (net force $= 0$), the forces are balanced: the object stays at rest, or keeps moving at a steady speed in a straight line.

Worked example. Two soldiers pull a sled to the right with $40$ lb and $25$ lb, and friction pulls left with $15$ lb. Net force $= 40 + 25 - 15 = 50$ lb to the right.

Newton's three laws in plain words

Mass and weight

Mass is how much matter an object has; it is the same everywhere. Weight is the force of gravity on that mass. On the Moon, gravity is weaker, so the same toolbox weighs less but has the same mass.

⚙️ Forces, Work and Energy

Part 3 of 7 — Friction and Motion

Friction always fights sliding

Friction is the force between two surfaces that resists them sliding past each other.

• It acts along the surface (parallel to it).
• It points opposite to the sliding, or opposite to the way the object would slide if friction were not there.

What changes the amount of friction

• Rougher surfaces give more friction; smoother or lubricated surfaces (oil, grease) give less.
• Pressing the surfaces together harder (a heavier load) gives more friction.
• Contact area matters very little: a brick slides about as easily on its side as on its end.
• Static friction (before sliding starts) is larger than kinetic friction (while sliding). That is why a heavy crate is hardest to get moving.
• Rolling friction is far smaller than sliding friction. That is why we use wheels, rollers and ball bearings.

Friction is not always the enemy: tire tread, brake pads and boot soles all depend on it. Spreading sand on ice increases friction so tires and boots can grip.

Worked example. Why does oil in an engine reduce wear? It puts a thin film between metal parts, so they slide on the oil instead of grinding on each other. Less friction means less heat and less wear.

⚙️ Forces, Work and Energy

Part 4 of 7 — Work, Energy and Power

Work

In physics, work is done only when a force moves something in the direction of the force:

$\text{Work} = \text{Force} \times \text{distance}$

With force in pounds and distance in feet, work is in foot-pounds (ft·lb).

• Push a cart with $50$ lb for $20$ ft: $W = 50 \times 20 = 1{,}000$ ft·lb.
• Lift a $60$-lb ammo can $4$ ft onto a truck bed: the force needed is its weight, so $W = 60 \times 4 = 240$ ft·lb.
• No movement, no work. Holding a heavy box perfectly still, or pushing on a wall that does not move, does zero work, even though you get tired.
• Carrying a box across a level floor at a steady height does no work against gravity: the lifting force is up, but the motion is sideways.

Energy

Energy is the ability to do work, and it is measured in the same units.

Conservation of energy: energy is not created or destroyed; it changes form. A swinging pendulum or a roller coaster trades potential energy (high up) for kinetic energy (low down, fast) and back. Friction turns some of it into heat, which is why a real swing slowly stops.

⚙️ Forces, Work and Energy

Part 5 of 7 — Pressure and Properties of Materials

Pressure is force spread over an area

$\text{Pressure} = \frac{\text{Force}}{\text{Area}}$

With force in pounds and area in square inches, pressure is in pounds per square inch (psi).

• The same force on a smaller area makes more pressure: a sharp knife, a nail point, a narrow chisel edge.
• The same force on a larger area makes less pressure: snowshoes, wide tires on sand, a tank's long tracks, a board laid across thin ice.

Worked example. A $180$-lb soldier stands in boots with a total sole area of $60$ square inches. Pressure on the ground $= 180 \div 60 = 3$ psi. On snowshoes with $360$ square inches of area, it drops to $180 \div 360 = 0.5$ psi, so she does not sink.

Gas pressure

• A gas fills its whole container and pushes on every wall.
• Squeeze a gas into a smaller volume and its pressure goes up (pumping up a tire).
• Heat a sealed gas and its pressure goes up (tire pressure rises after a long drive; that is why aerosol cans warn against heat).
• At sea level the air presses on everything with about $14.7$ psi.

One-way valves

Pumps use check valves that let air or water through in only one direction. In a simple hand pump, pushing the piston down squeezes the air below it: the higher pressure pushes the outlet valve open (air goes to the tire) and holds the inlet valve shut. Pulling the piston up lowers the pressure inside: the outlet valve closes and outside air pushes the inlet valve open to refill the cylinder.

⚙️ Forces, Work and Energy

Part 6 of 7 — Forces and Energy Test Strategy and Traps

Your clock: about 1½ minutes a question

Mechanical Comprehension gives you $15$ questions in $22$ minutes, about $88$ seconds each. That is more time per question than Shop or Auto, because you have to study a picture. Use it, but don't overspend:

• Concept questions (which way friction points, where a pendulum is fastest) should take 30 to 45 seconds.
• Calculation questions (work, power, pressure) take a line or two of scratch work. Write the formula first, then plug in.
• You cannot go back. Answer each question before moving on, and treat every question as scored, because tryout questions look the same.
• If time runs short, keep reading and answering for real. A string of wrong answers at the end of a subtest is penalized heavily on the CAT.

A four-step routine for picture questions

1. Label the forces in your head: weight (down), support (perpendicular to the surface), friction (along the surface, against sliding), pushes and pulls.
2. Circle the numbers that matter and ignore the ones that don't (a weight is irrelevant to the work done by a horizontal push).
3. Pick the principle: net force, center of gravity, friction, $W = Fd$, energy trade, $P = W/t$, $P = F/A$.
4. Check with an extreme case. If the rope were almost flat, would the tension be huge? (Yes.) If the area shrank to a point, would the pressure soar? (Yes.)

⚙️ Forces, Work and Energy

Part 7 of 7 — Forces, Work and Energy Mastery Set

This set mixes net force, center of gravity, friction, motion, work, energy, power, pressure and materials, the way the Mechanical Comprehension subtest does. Give yourself about $1\frac{1}{2}$ minutes per question and use scratch paper for the arithmetic.