Forces, Work and Energy

⚙️ 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.

The three Mechanical Comprehension lessons

The plan for this lesson

How to read an MC picture

1. Name every force you can see: weight pulling down, a push, a rope pulling, friction, a support pushing up.
2. Look at the numbers and where they are: a weight $3$ feet from a pivot is different from the same weight $1$ foot away.
3. Ask what the question wants: a direction, a comparison ("which is greater?"), or a number.

Warm-up 1. Use the figure. 🎯

Warm-up 2. Use the figure. 🎯

Key Takeaways — Part 1

• MC on the CAT-ASVAB: 15 questions in 22 minutes, about $1\frac{1}{2}$ minutes each, almost all with a picture
• MC feeds Marine GT (AR + MC + VE), Air Force M, Marine MM, Navy MEC/MEC2/NUC, and the Army MM area
• Read every picture the same way: name the forces, note the numbers and distances, then answer the exact question

Up Next: Part 2 — forces, weight and center of gravity.

⚙️ 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.

Net force. ✍️ Use the figure.

A crate is pulled to the right by a $30$-lb rope and to the left by a $12$-lb rope.

1) The size of the net force on the crate, in pounds (number only):

2) A second $20$-lb pull to the left is added. Now what is the size of the net force, in pounds (number only)?

Newton's laws and weight. 🎯

Center of gravity and stability

The center of gravity (CG) is the point where an object's weight can be treated as acting: its balance point.

• An object tips over when its CG moves outside the edge of its base of support.
• Lower CG and a wider base = more stable. That is why race cars sit low, why heavy cargo is loaded on the bottom of a truck, and why you spread your feet on a moving deck.
• Adding weight high up raises the CG and makes tipping easier: a ladder rack full of steel on top of a van, or a load lifted high on a forklift.

Cranes and counterweights

A crane lifting a load out on its boom is like a seesaw with the tipping edge at its front wheels or outriggers. The farther out the load and the heavier it is, the more it tends to tip the crane forward. A counterweight at the back, outriggers that widen the base, and a shorter reach all keep the combined CG inside the base.

Tension and compression

• A rope or cable can only pull: it is in tension.
• A post, column or strut that is pushed on from both ends is in compression.
• When a load hangs from two ropes, the more nearly horizontal the ropes, the greater the tension in each one. Steep, nearly vertical ropes share the weight with the least tension. Two vertical ropes holding a centered load each carry half of it.

The crane. Use the figure. 🎯

Two ways to hang a sign. Use the figure. 🎯

Stability, tension and compression. 🔽

Key Takeaways — Part 2

• Net force: same direction adds, opposite directions subtract; balanced forces = no change in motion
• Newton: inertia; $F = ma$ (more mass, less acceleration); equal and opposite reaction
• Mass stays the same everywhere; weight depends on gravity
• Tipping happens when the center of gravity passes the edge of the base: keep it low, keep the base wide
• Load farther out on a crane boom = more tipping; counterweights and outriggers fight it
• Ropes are in tension, posts in compression; shallow ropes carry more tension than steep ones

Up Next: Part 3 — friction and motion.

⚙️ 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.

The skier. Use the figure. 🎯

Friction checks. 🎯

Speed, acceleration, momentum and inertia

Worked example. A convoy covers $120$ miles in $3$ hours. Its average speed is $120 \div 3 = 40$ miles per hour.

Worked example. A jeep goes from $0$ to $30$ miles per hour in $6$ seconds. Its acceleration is $30 \div 6 = 5$ miles per hour each second.

Momentum example. A loaded dump truck and a pickup are both going $30$ mph. The dump truck has far more mass, so it has more momentum and needs much more braking force (or distance) to stop.

Moving in a circle

An object moving in a circle is constantly being pulled toward the center (by a string, the road's friction, a track). If that pull disappears, inertia takes over and the object moves off in a straight line in the direction it was moving at that instant, tangent to the circle. It does not keep curving, and it does not fly straight outward from the center.

Let go of the string. Use the figure. 🎯

Speed and acceleration. ✍️

1) A supply truck drives $150$ miles in $3$ hours. Its average speed, in miles per hour (number only):

2) A motorcycle speeds up from $10$ mph to $40$ mph in $6$ seconds. Its acceleration, in miles per hour per second (number only):

3) At an average of $45$ mph, how many hours does a $180$-mile trip take? (number only)

Key Takeaways — Part 3

• Friction acts along the surface, opposite the sliding (or the would-be sliding)
• Skier sliding down: friction points up the slope; a box at rest on a ramp: friction points up the ramp
• More friction: rougher surfaces, heavier loads. Less: lubrication, rolling instead of sliding. Area barely matters
• Static friction > kinetic friction: starting is hardest
• Speed = distance ÷ time; acceleration = change in speed ÷ time; momentum = mass × velocity
• Release an object moving in a circle and it goes straight, tangent to the circle

Up Next: Part 4 — work, energy and power.

⚙️ 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.

Work. ✍️

1) A mechanic pushes a $250$-lb engine stand across the floor with a steady $40$-lb force for $15$ feet. How much work does the push do, in foot-pounds? (number only)

2) A $150$-lb crate is lifted $5$ feet straight up. How much work is done, in foot-pounds? (number only)

3) A soldier holds a $30$-lb pack perfectly still above her head for $10$ seconds. How much work does she do on the pack during that time, in foot-pounds? (number only)

The pendulum. Use the figure. 🎯

The roller coaster. Use the figure. 🎯

Power and efficiency

Power is how fast work is done:

$\text{Power} = \frac{\text{Work}}{\text{time}}$

With work in foot-pounds and time in seconds, power is in ft·lb per second. Engines and motors are rated in horsepower:

$1 \text{ horsepower} = 550 \text{ ft·lb per second}$

Worked example. A winch lifts a $1{,}100$-lb load $10$ feet in $20$ seconds. Work $= 1{,}100 \times 10 = 11{,}000$ ft·lb. Power $= 11{,}000 \div 20 = 550$ ft·lb/s $= 1$ horsepower.

Two soldiers each carry identical crates up the same stairs. The one who gets to the top faster did the same work but used more power.

Efficiency

No real machine puts out as much work as you put in; some is always lost to friction as heat.

$\text{Efficiency} = \frac{\text{work out}}{\text{work in}} \times 100\%$

A machine that takes in $800$ ft·lb and delivers $600$ ft·lb is $\frac{600}{800} = 75\%$ efficient. An efficiency over 100% is impossible: that answer choice is always wrong.

Power, energy and efficiency. 🎯

Key Takeaways — Part 4

• Work = force × distance (in the direction of the force), in foot-pounds; no movement = no work
• Lifting work = weight × height
• Potential energy grows with height; kinetic energy grows with speed squared
• Energy changes form but is conserved: fastest at the lowest point, stopped at the highest points of a swing
• Power = work ÷ time; 1 hp = 550 ft·lb/s
• Efficiency = work out ÷ work in; never over $100\%$

Up Next: Part 5 — pressure and the properties of materials.

⚙️ 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.

Same brick, three ways. ✍️ Use the figure.

An $8$-lb block measures $8$ in. $\times$ $4$ in. $\times$ $2$ in. It can rest on its $8 \times 4$ face (position 1), its $8 \times 2$ face (position 2) or its $4 \times 2$ end (position 3).

1) The pressure under the block in position 1, in psi (decimal or fraction):

2) The pressure under the block in position 3, in psi (number only):

3) Which position (1, 2 or 3) puts the most pressure on the floor? (number only)

The hand pump. Use the figure. 🎯

Properties of materials

Thermal expansion

Most materials expand when heated and contract when cooled. Different materials expand by different amounts.

• Bridges have expansion joints and railroad rails have small gaps so they can grow on hot days without buckling.
• Running hot water over a stuck metal jar lid loosens it: the metal lid expands more than the glass jar.
• A bimetallic strip (two metals bonded together) bends when heated, because one metal grows more than the other. The strip curves toward the metal that expands less. Thermostats use this to switch a furnace on and off.

The bimetallic strip. Use the figure. 🎯

Name the property. 🔽

Key Takeaways — Part 5

• Pressure = force ÷ area (psi): small area = high pressure, large area = low pressure
• Same object, smallest face down = most pressure
• Squeezing or heating a sealed gas raises its pressure
• One-way valves: the push stroke opens the outlet, the pull stroke opens the inlet
• Brittle (glass), ductile (copper wire), elastic (springs), hard (diamond), malleable (foil)
• Heat makes things expand; a bimetallic strip bends toward the metal that expands less

Up Next: Part 6 — test strategy and the classic traps in forces and energy questions.

⚙️ 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.)

The traps test writers like

Trap 1. Use the figure. 🎯

Traps 2 to 4. 🎯

Speed drill. Under 30 seconds each. ⏱️

Key Takeaways — Part 6

• MC: 15 questions, 22 minutes, about 88 seconds each; concept questions in 30 to 45 seconds
• Routine: label forces → circle the numbers → pick the principle → check an extreme case
• Friction opposes sliding or would-be sliding (a crate at rest on a ramp feels friction up the ramp)
• No movement along the force = no work; use the push, not the weight, for horizontal work
• Same weight on a smaller area = more pressure; efficiency is never over $100\%$

Up Next: Part 7 — a mixed mastery set for forces, work and energy.

⚙️ 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.

Question 1. Use the figure. 🎯

Question 2. Use the figure. 🎯

Question 3. Use the figure. 🎯

Questions 4 and 5. ✍️

4) A team drags a sled with a steady $60$-lb pull along the ground for $50$ feet. How much work does the pull do, in foot-pounds? (number only)

5) A hoist does $27{,}500$ ft·lb of work in $10$ seconds. What is its power in horsepower? ($1$ hp $= 550$ ft·lb/s; number only)

Questions 6 to 10. 🎯

Lesson Wrap-Up

Next steps: take the exit quiz for this topic, then go on to Levers, Pulleys, Inclined Planes and Screws.