ASVAB Mechanical Comprehension (MC) Practice Test (2026) covers ASVAB Mechanical Comprehension (MC) practice test in a four-choice format with a “Show Answer” toggle for review. Each item includes the correct answer, a concise explanation, and official citations where applicable so you can verify what the test is targeting. Use it to practice forces, machines, fluids, heat, and everyday mechanical principles.
FAQ
What should I know for ASVAB Mechanical Comprehension (MC) on the ASVAB?
Focus on the recurring concepts that appear in many forms, not one-off trivia. Learn the key terms, practice mixed sets, and use explanations to build a quick recognition habit so you don’t overthink simple items.
Where can I take an ASVAB Mechanical Comprehension (MC) practice test?
Use a practice set that matches real wording and keeps you answering before you peek. After each question, open “Show Answer,” compare your reasoning to the explanation, and retake missed concepts later to confirm retention.
What should I know for ASVAB Mechanical Comprehension (MC) on the ASVAB (part 2)?
Focus on the recurring concepts that appear in many forms, not one-off trivia. Learn the key terms, practice mixed sets, and use explanations to build a quick recognition habit so you don’t overthink simple items.
What should an ASVAB Mechanical Comprehension (MC) study guide cover?
A solid guide focuses on the core terms, common situations, and definitions that show up repeatedly. Pair reading with practice runs, and use explanations to learn why wrong options are wrong, not just which option is right.
What should an ASVAB Mechanical Comprehension (MC) study guide cover (part 2)?
A solid guide focuses on the core terms, common situations, and definitions that show up repeatedly. Pair reading with practice runs, and use explanations to learn why wrong options are wrong, not just which option is right.
ASVAB Mechanical Comprehension MC Practice Test
Explanation: Mechanical advantage for a lever equals effort arm ÷ load arm. Effort arm is 3 ft (from fulcrum to effort), load arm is 1 ft, so MA = 3 ÷ 1 = 3.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: lever mechanical advantage (moment arms).
Explanation: Pressure is transmitted equally in a closed fluid. Output force scales with area: 120 N × (50 ÷ 2) = 120 × 25 = 3,000 N.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: Pascal’s principle (hydraulics).
Explanation: Meshed gears spin in opposite directions. Identical gears have the same speed ratio, so Gear B is 60 rpm counterclockwise.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: gear direction and speed ratio.
Explanation: Constant speed means net force is zero. The friction must balance the applied 40 lb force in the opposite direction.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: Newton’s first law (equilibrium of forces).
Explanation: A fixed pulley changes direction of force but does not multiply it. Ideal mechanical advantage is 1, so effort equals load: 200 lb.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: pulley mechanical advantage (fixed pulley).
Explanation: Parallel component is W·sin(θ). With W = 10 lb and θ = 30°, sin(30°) = 0.5, so 10 × 0.5 = 5 lb.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: resolving forces on an incline.
Explanation: Thermal expansion depends on coefficient of linear expansion. Aluminum’s coefficient is larger than steel’s, so it expands more for the same temperature rise.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: thermal expansion of solids.
Explanation: Newton’s second law: F = m·a = 6 × 2 = 12 N.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: Newton’s second law.
Explanation: Ideal MA for a wheel and axle is wheel radius ÷ axle radius. 12 ÷ 3 = 4.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: wheel-and-axle mechanical advantage.
Explanation: For incompressible flow, continuity applies: A₁v₁ = A₂v₂. Area scales with diameter squared, so halving diameter makes area 1/4, requiring speed to be 4×.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: continuity equation (fluid flow).
Explanation: Torque equals force × perpendicular distance from pivot. A longer handle increases the moment arm, increasing torque for the same force.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: torque and moment arm.
Explanation: Friction in braking converts motion (kinetic energy) into heat (thermal energy) in pads and rotors.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: energy conversion (friction).
Explanation: A single movable pulley has ideal mechanical advantage 2 because two rope segments support the load. Effort = 20 ÷ 2 = 10 lb.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: pulley mechanical advantage (movable pulley).
Explanation: Parallel springs share the load and their spring constants add: k_total = k₁ + k₂, so two identical springs give 2k.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: spring constants in parallel.
Explanation: Even distribution means each tire supports one-fourth the weight: 1,500 ÷ 4 = 375 lb.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: normal force and load distribution.
Explanation: An object floats if it is less dense than the fluid. Floating in mercury but sinking in water means its density lies between the two fluids.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: buoyancy and density.
Explanation: The fan accelerates air particles, increasing their speed and therefore kinetic energy.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: work and kinetic energy.
Explanation: With a centered load and symmetric supports, the load is shared equally: each support carries half the load (idealized).
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: static equilibrium (balanced supports).
Explanation: Ohm’s law: R = V ÷ I = 12 ÷ 3 = 4 Ω.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: Ohm’s law (basic electrical relationships).
Explanation: The compression stroke moves the piston upward with valves closed, compressing the mixture before ignition.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: four-stroke engine cycle.
Explanation: Efficiency = useful output ÷ input = 400 ÷ 500 = 0.8 = 80%.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: machine efficiency.
Explanation: Centripetal force is F = m·v²/r. With the same mass and radius, increasing speed increases force with v².
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: centripetal force relationship.
Explanation: Reducing waste heat means a larger fraction of input heat becomes useful work, so efficiency increases.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: energy conservation and heat-engine efficiency.
Explanation: Effort equals load ÷ MA. 240 ÷ 4 = 60 lb (ideal).
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: mechanical advantage (pulleys).
Explanation: The side that expands more becomes effectively longer, so the strip bends toward the side that expands less (shorter side on the inside of the curve).
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: differential thermal expansion (bimetal bending).
Explanation: Ideal effort equals load ÷ MA. 300 ÷ 6 = 50 lb.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: mechanical advantage (ideal machines).
Explanation: Ideal MA for an inclined plane is length ÷ height. 12 ÷ 3 = 4.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: inclined plane mechanical advantage.
Explanation: Speed is inversely proportional to teeth count. 90 × (12 ÷ 36) = 30 rpm (opposite direction).
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: gear ratio (teeth and speed).
Explanation: Torque = force × lever arm = 25 × 8 = 200 lb·in.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: torque calculation.
Explanation: Kinetic energy = ½mv² = 0.5×5×(4²)=2.5×16=40 J.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: kinetic energy.
Explanation: Power = work ÷ time = 900 ÷ 3 = 300 W.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: power (work rate).
Explanation: Force scales with area: 40 × (32 ÷ 4) = 40 × 8 = 320 lb.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: Pascal’s principle.
Explanation: Density = 2.0 kg ÷ 1.0 L = 2.0 kg/L, which is greater than water, so it sinks.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: density and buoyancy.
Explanation: For a uniform beam, its weight acts at the center of mass, halfway along its length.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: center of mass (uniform objects).
Explanation: Constant speed means net force is zero, so friction balances the applied 30 lb.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: friction and equilibrium.
Explanation: For identical springs in series, k_eq = k/2. 200/2 = 100 N/m.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: springs in series.
Explanation: Power P = V×I = 12×2.5 = 30 W.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: electrical power.
Explanation: Copper’s thermal conductivity is much higher, so it conducts heat faster.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: thermal conductivity.
Explanation: Hydrostatic pressure increases with depth (p = ρgh), not container shape.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: fluid pressure with depth.
Explanation: Distance tradeoff equals MA. With 4 supporting segments, MA = 4, so load rises 8/4 = 2 ft.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: work conservation in pulleys.
Explanation: MA = wheel radius ÷ axle radius = 10 ÷ 2 = 5.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: wheel-and-axle MA.
Explanation: Hooke’s law: F = kx = 300×0.20 = 60 N.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: Hooke’s law.
Explanation: For steady flow, higher speed is commonly associated with lower static pressure (Bernoulli effect).
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: Bernoulli principle (qualitative).
Explanation: Rolling friction is typically much less than sliding friction, so bearings reduce resistive torque.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: friction types (rolling vs sliding).
Explanation: Effort arm is 9 ft and load arm is 3 ft, so MA = 9 ÷ 3 = 3.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: lever mechanical advantage (moment arms).
Explanation: Efficiency ≈ AMA ÷ IMA = 8 ÷ 10 = 0.8 = 80%.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: machine efficiency.
Explanation: Work = F×d = 60×5 = 300 J.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: work.
Explanation: Advance = pitch × turns = 0.25×8 = 2 inches.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: screw motion (pitch).
Explanation: In a third-class lever, the effort is between fulcrum and load, giving speed advantage but MA < 1.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: lever classes.
Explanation: Only the perpendicular component produces torque: τ = rF sinθ = 2×100×sin30° = 200×0.5 = 100 N·m.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: torque with angle.
Explanation: Speed ratio is inverse of teeth: 120×(10/30)=40 rpm.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: sprocket/gear ratio.
Explanation: Braking work must remove kinetic energy, which scales with v², so distance tends to scale with v².
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: kinetic energy and braking work.
Explanation: Force = load × (height/length) = 200×(2/10)=200×0.2=40 lb.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: inclined plane (work conservation).
Explanation: Convection transfers heat via moving fluid (air/water) carrying energy.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: heat transfer modes.
Explanation: Materials expand/contract with temperature; joints allow movement to avoid stress damage.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: thermal expansion in structures.
Explanation: Pressure at depth comes from the weight of fluid above: p = ρgh.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: hydrostatic pressure.
Explanation: With 3 supporting segments, MA = 3, so effort = 150 ÷ 3 = 50 lb.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: pulley mechanical advantage.
Explanation: A large handle radius compared with small axle radius provides substantial torque multiplication.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: wheel-and-axle torque multiplication.
Explanation: A longer wedge has a smaller slope, increasing ideal mechanical advantage.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: wedge as inclined plane.
Explanation: Efficiency = ideal/actual for same output. Actual ≈ ideal ÷ 0.70 = 200/0.70 ≈ 286 N.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: efficiency calculation.
Explanation: For two equal resistors in parallel, R_eq = R/2.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: parallel resistance.
Explanation: Series resistance is 6+3=9 Ω. Current I = V/R = 18/9=2 A.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: Ohm’s law (series circuit).
Explanation: A flywheel’s inertia stores energy and resists speed changes, smoothing motion.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: rotational inertia.
Explanation: Perpendicular component is 0.60×20=12 N. Torque = 12×0.5 = 6 N·m.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: torque from perpendicular component.
Explanation: The disk has smaller rotational inertia than a ring, so more energy goes to translational speed, arriving first.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: rotational inertia and rolling motion.
Explanation: Pressure equals force divided by area: 400 ÷ 20 = 20 psi.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: pressure (force/area).
Explanation: Pressure = 600 ÷ 30 = 20 psi.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: pressure (force/area).
Explanation: 1 horsepower is defined as about 746 watts.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: power unit conversion.
Explanation: An odd number of gear meshes reverses direction; adding an idler makes two meshes, so driver and driven rotate the same direction.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: gear direction with idler.
Explanation: Linear speed v = rω = 0.30×10 = 3 m/s.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: angular to linear speed.
Explanation: Impulse equals force times time: 2,000×0.05 = 100 N·s.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: impulse-momentum.
Explanation: Yield strength is where deformation transitions from elastic to plastic (permanent).
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: stress–strain (material behavior).
Explanation: At the neutral axis, bending stress changes sign and is zero.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: beam bending basics.
Explanation: Buoyant force equals weight of displaced fluid: 62.4×0.12 ≈ 7.49 lb.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: Archimedes’ principle.
Explanation: Continuity: A₁v₁ = A₂v₂. If area halves, speed doubles.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: continuity equation.
Explanation: Evaporation of refrigerant absorbs heat from the inside (latent heat).
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: phase change and heat transfer.
Explanation: Effort = 250 ÷ 5 = 50 lb.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: pulley mechanical advantage.
Explanation: Normal force ≈ W cos20° ≈ 120×0.94 ≈ 113 lb. Friction = μN ≈ 0.20×113 ≈ 23 lb.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: friction on an incline.
Explanation: Net force = 30−10=20 N. a = F/m = 20/10 = 2 m/s².
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: Newton’s second law with friction.
Explanation: Centripetal acceleration a = v²/r. Tripling v makes a 9 times larger.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: centripetal acceleration.
Explanation: Potential energy mgh becomes kinetic: v = √(2gh)=√(2×9.8×5)=√98≈9.9 m/s.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: energy conservation.
Explanation: τ = F r ⇒ F = τ/r = 60/2 = 30 lb.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: torque and lever arm.
Explanation: Speed ratio = 48/16 = 3. Driven cog rotates 3×: 60×3=180 rpm.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: sprocket ratio.
Explanation: Volume conserved: A_in d_in = A_out d_out. d_out = 3×8 / 24 = 1 inch.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: hydraulic displacement (volume conservation).
Explanation: Potential energy increase = weight × height = 50×6 = 300 ft·lb.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: work against gravity.
Explanation: Work removed equals kinetic energy: ½mv² = 0.5×1000×225 = 112,500 J.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: kinetic energy and work.
Explanation: Energy U = ½kx² ⇒ k = 2U/x² = 24 / 0.01 = 2,400 N/m.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: spring potential energy.
Explanation: For no rotation, the sum of torques about any point must be zero.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: static equilibrium (torque balance).
Explanation: Each tire supports 400 lb. Pressure = 400 ÷ 20 = 20 psi.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: pressure (force/area).
Explanation: Shear stress acts parallel to a surface, promoting sliding between layers.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: types of stress.
Explanation: Moving fulcrum toward the load increases effort arm relative to load arm, increasing MA.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: lever moment arms.
Explanation: In an ideal system, input distance = MA × output distance. 8×3 = 24 ft.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: work conservation in machines.
Explanation: Efficiency = output/input ⇒ input = 520/0.65 ≈ 800 J.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: efficiency (energy).
Explanation: IMA ≈ (2πr)/pitch = (2π×10)/0.25 ≈ (62.8)/0.25 ≈ 251.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: screw mechanical advantage.
Explanation: MA = input distance ÷ output distance = 16 ÷ 2 = 8.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: mechanical advantage from distance ratio.
Explanation: Each mesh reverses direction. Two reversals (A→B, B→C) make C rotate opposite A.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: gear direction (multiple meshes).
Explanation: The movable pulley provides MA; the fixed pulley mainly redirects the effort direction.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: pulley function (fixed vs movable).
Explanation: Copper has higher thermal conductivity than stainless steel, so heat flows faster.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: thermal conductivity (materials).
Explanation: Static friction adjusts up to a maximum; the threshold pull equals the maximum static friction.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: static friction threshold.
Explanation: Volume conserved: A_in d_in = A_out d_out ⇒ d_in = (50×1)/2 = 25 cm.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: hydraulic displacement (volume conservation).
Explanation: Work against gravity equals W = mgh = 8×9.8×3 ≈ 235.2 J.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: work against gravity (mgh).
Explanation: Work against gravity equals W = mgh = 9×9.8×4 ≈ 352.8 J.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: work against gravity (mgh).
Explanation: Work against gravity equals W = mgh = 10×9.8×5 ≈ 490.0 J.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: work against gravity (mgh).
Explanation: Work against gravity equals W = mgh = 11×9.8×3 ≈ 323.4 J.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: work against gravity (mgh).
Explanation: Work against gravity equals W = mgh = 12×9.8×4 ≈ 470.4 J.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: work against gravity (mgh).
Explanation: Work against gravity equals W = mgh = 13×9.8×5 ≈ 637.0 J.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: work against gravity (mgh).
Explanation: Work against gravity equals W = mgh = 14×9.8×3 ≈ 411.6 J.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: work against gravity (mgh).
Explanation: Work against gravity equals W = mgh = 15×9.8×4 ≈ 588.0 J.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: work against gravity (mgh).
Explanation: Work against gravity equals W = mgh = 16×9.8×5 ≈ 784.0 J.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: work against gravity (mgh).
Explanation: Work against gravity equals W = mgh = 17×9.8×3 ≈ 499.8 J.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: work against gravity (mgh).
Explanation: Ideal MA = effort arm ÷ load arm = 18/3 ≈ 6.00.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: lever mechanical advantage (moment arms).
Explanation: Ideal MA = effort arm ÷ load arm = 17/4 ≈ 4.25.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: lever mechanical advantage (moment arms).
Explanation: Ideal MA = effort arm ÷ load arm = 16/5 ≈ 3.20.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: lever mechanical advantage (moment arms).
Explanation: Ideal MA = effort arm ÷ load arm = 15/6 ≈ 2.50.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: lever mechanical advantage (moment arms).
Explanation: Ideal MA = effort arm ÷ load arm = 14/3 ≈ 4.67.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: lever mechanical advantage (moment arms).
Explanation: Ideal MA = effort arm ÷ load arm = 13/4 ≈ 3.25.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: lever mechanical advantage (moment arms).
Explanation: Ideal MA = effort arm ÷ load arm = 12/5 ≈ 2.40.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: lever mechanical advantage (moment arms).
Explanation: Ideal MA = effort arm ÷ load arm = 11/6 ≈ 1.83.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: lever mechanical advantage (moment arms).
Explanation: Ideal MA = effort arm ÷ load arm = 10/3 ≈ 3.33.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: lever mechanical advantage (moment arms).
Explanation: Ideal MA = effort arm ÷ load arm = 9/4 ≈ 2.25.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: lever mechanical advantage (moment arms).
Explanation: Ideal MA equals supporting segments (2), so effort = 120/2 ≈ 60.0 lb.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: pulley mechanical advantage.
Explanation: Ideal MA equals supporting segments (3), so effort = 130/3 ≈ 43.3 lb.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: pulley mechanical advantage.
Explanation: Ideal MA equals supporting segments (4), so effort = 140/4 ≈ 35.0 lb.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: pulley mechanical advantage.
Explanation: Ideal MA equals supporting segments (5), so effort = 150/5 ≈ 30.0 lb.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: pulley mechanical advantage.
Explanation: Ideal MA equals supporting segments (6), so effort = 160/6 ≈ 26.7 lb.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: pulley mechanical advantage.
Explanation: Ideal MA equals supporting segments (2), so effort = 170/2 ≈ 85.0 lb.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: pulley mechanical advantage.
Explanation: Ideal MA equals supporting segments (3), so effort = 180/3 ≈ 60.0 lb.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: pulley mechanical advantage.
Explanation: Ideal MA equals supporting segments (4), so effort = 190/4 ≈ 47.5 lb.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: pulley mechanical advantage.
Explanation: Ideal MA equals supporting segments (5), so effort = 200/5 ≈ 40.0 lb.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: pulley mechanical advantage.
Explanation: Ideal MA equals supporting segments (6), so effort = 210/6 ≈ 35.0 lb.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: pulley mechanical advantage.
Explanation: F_out = F_in × (A_out/A_in) = 80×(20/2) ≈ 800.0 N.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: Pascal’s principle (force-area scaling).
Explanation: F_out = F_in × (A_out/A_in) = 90×(25/3) ≈ 750.0 N.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: Pascal’s principle (force-area scaling).
Explanation: F_out = F_in × (A_out/A_in) = 100×(30/4) ≈ 750.0 N.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: Pascal’s principle (force-area scaling).
Explanation: F_out = F_in × (A_out/A_in) = 80×(35/5) ≈ 560.0 N.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: Pascal’s principle (force-area scaling).
Explanation: F_out = F_in × (A_out/A_in) = 90×(40/2) ≈ 1800.0 N.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: Pascal’s principle (force-area scaling).
Explanation: F_out = F_in × (A_out/A_in) = 100×(45/3) ≈ 1500.0 N.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: Pascal’s principle (force-area scaling).
Explanation: F_out = F_in × (A_out/A_in) = 80×(50/4) ≈ 1000.0 N.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: Pascal’s principle (force-area scaling).
Explanation: F_out = F_in × (A_out/A_in) = 90×(55/5) ≈ 990.0 N.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: Pascal’s principle (force-area scaling).
Explanation: F_out = F_in × (A_out/A_in) = 100×(60/2) ≈ 3000.0 N.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: Pascal’s principle (force-area scaling).
Explanation: F_out = F_in × (A_out/A_in) = 80×(65/3) ≈ 1733.3 N.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: Pascal’s principle (force-area scaling).
Explanation: F_f = μ_kN with N = Wcosθ. N ≈ 150·cos(15°) ≈ 144.9 lb, so F_f ≈ 0.15×144.9 ≈ 21.7 lb.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: kinetic friction on an incline (μN).
Explanation: F_f = μ_kN with N = Wcosθ. N ≈ 155·cos(20°) ≈ 145.7 lb, so F_f ≈ 0.16×145.7 ≈ 23.3 lb.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: kinetic friction on an incline (μN).
Explanation: F_f = μ_kN with N = Wcosθ. N ≈ 160·cos(25°) ≈ 145.0 lb, so F_f ≈ 0.17×145.0 ≈ 24.7 lb.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: kinetic friction on an incline (μN).
Explanation: F_f = μ_kN with N = Wcosθ. N ≈ 165·cos(30°) ≈ 142.9 lb, so F_f ≈ 0.18×142.9 ≈ 25.7 lb.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: kinetic friction on an incline (μN).
Explanation: F_f = μ_kN with N = Wcosθ. N ≈ 170·cos(35°) ≈ 139.3 lb, so F_f ≈ 0.19×139.3 ≈ 26.5 lb.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: kinetic friction on an incline (μN).
Explanation: F_f = μ_kN with N = Wcosθ. N ≈ 175·cos(40°) ≈ 134.1 lb, so F_f ≈ 0.15×134.1 ≈ 20.1 lb.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: kinetic friction on an incline (μN).
Explanation: F_f = μ_kN with N = Wcosθ. N ≈ 180·cos(15°) ≈ 173.9 lb, so F_f ≈ 0.16×173.9 ≈ 27.8 lb.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: kinetic friction on an incline (μN).
Explanation: F_f = μ_kN with N = Wcosθ. N ≈ 185·cos(20°) ≈ 173.8 lb, so F_f ≈ 0.17×173.8 ≈ 29.6 lb.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: kinetic friction on an incline (μN).
Explanation: F_f = μ_kN with N = Wcosθ. N ≈ 190·cos(25°) ≈ 172.2 lb, so F_f ≈ 0.18×172.2 ≈ 31.0 lb.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: kinetic friction on an incline (μN).
Explanation: F_f = μ_kN with N = Wcosθ. N ≈ 195·cos(30°) ≈ 168.9 lb, so F_f ≈ 0.19×168.9 ≈ 32.1 lb.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: kinetic friction on an incline (μN).
Explanation: rpm_driven = rpm_driver × (teeth_driver/teeth_driven) = 60×(12/36) ≈ 20.0 rpm.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: gear ratio (teeth and speed).
Explanation: rpm_driven = rpm_driver × (teeth_driver/teeth_driven) = 70×(16/38) ≈ 29.5 rpm.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: gear ratio (teeth and speed).
Explanation: rpm_driven = rpm_driver × (teeth_driver/teeth_driven) = 80×(20/40) ≈ 40.0 rpm.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: gear ratio (teeth and speed).
Explanation: rpm_driven = rpm_driver × (teeth_driver/teeth_driven) = 90×(24/42) ≈ 51.4 rpm.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: gear ratio (teeth and speed).
Explanation: rpm_driven = rpm_driver × (teeth_driver/teeth_driven) = 100×(28/44) ≈ 63.6 rpm.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: gear ratio (teeth and speed).
Explanation: rpm_driven = rpm_driver × (teeth_driver/teeth_driven) = 110×(12/46) ≈ 28.7 rpm.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: gear ratio (teeth and speed).
Explanation: rpm_driven = rpm_driver × (teeth_driver/teeth_driven) = 120×(16/48) ≈ 40.0 rpm.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: gear ratio (teeth and speed).
Explanation: rpm_driven = rpm_driver × (teeth_driver/teeth_driven) = 130×(20/50) ≈ 52.0 rpm.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: gear ratio (teeth and speed).
Explanation: rpm_driven = rpm_driver × (teeth_driver/teeth_driven) = 140×(24/52) ≈ 64.6 rpm.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: gear ratio (teeth and speed).
Explanation: rpm_driven = rpm_driver × (teeth_driver/teeth_driven) = 150×(28/54) ≈ 77.8 rpm.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: gear ratio (teeth and speed).
Explanation: τ = rF sinθ = 0.4×120×sin(20°) ≈ 16.4 N·m.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: torque from perpendicular force component.
Explanation: τ = rF sinθ = 0.5×135×sin(30°) ≈ 33.7 N·m.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: torque from perpendicular force component.
Explanation: τ = rF sinθ = 0.6×150×sin(40°) ≈ 57.9 N·m.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: torque from perpendicular force component.
Explanation: τ = rF sinθ = 0.7×165×sin(50°) ≈ 88.5 N·m.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: torque from perpendicular force component.
Explanation: τ = rF sinθ = 0.4×180×sin(60°) ≈ 62.4 N·m.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: torque from perpendicular force component.
Explanation: τ = rF sinθ = 0.5×195×sin(20°) ≈ 33.3 N·m.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: torque from perpendicular force component.
Explanation: τ = rF sinθ = 0.6×210×sin(30°) ≈ 63.0 N·m.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: torque from perpendicular force component.
Explanation: τ = rF sinθ = 0.7×225×sin(40°) ≈ 101.2 N·m.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: torque from perpendicular force component.
Explanation: τ = rF sinθ = 0.4×240×sin(50°) ≈ 73.5 N·m.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: torque from perpendicular force component.
Explanation: τ = rF sinθ = 0.5×255×sin(60°) ≈ 110.4 N·m.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: torque from perpendicular force component.
Explanation: F = mv²/r = 900×10²/40 ≈ 2250 N ≈ 2.2 kN.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: centripetal force (mv²/r).
Explanation: F = mv²/r = 950×11²/45 ≈ 2554 N ≈ 2.6 kN.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: centripetal force (mv²/r).
Explanation: F = mv²/r = 1000×12²/50 ≈ 2880 N ≈ 2.9 kN.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: centripetal force (mv²/r).
Explanation: F = mv²/r = 1050×13²/55 ≈ 3226 N ≈ 3.2 kN.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: centripetal force (mv²/r).
Explanation: F = mv²/r = 1100×14²/40 ≈ 5390 N ≈ 5.4 kN.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: centripetal force (mv²/r).
Explanation: F = mv²/r = 1150×15²/45 ≈ 5750 N ≈ 5.8 kN.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: centripetal force (mv²/r).
Explanation: F = mv²/r = 1200×16²/50 ≈ 6144 N ≈ 6.1 kN.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: centripetal force (mv²/r).
Explanation: F = mv²/r = 1250×17²/55 ≈ 6568 N ≈ 6.6 kN.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: centripetal force (mv²/r).
Explanation: F = mv²/r = 1300×18²/40 ≈ 10530 N ≈ 10.5 kN.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: centripetal force (mv²/r).
Explanation: F = mv²/r = 1350×19²/45 ≈ 10830 N ≈ 10.8 kN.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: centripetal force (mv²/r).
Explanation: σ = F/A. A = 50 mm² = 0.000050 m². σ ≈ 4000/0.000050 ≈ 80.0 MPa.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: stress = force/area (tension).
Explanation: σ = F/A. A = 57 mm² = 0.000057 m². σ ≈ 4500/0.000057 ≈ 78.9 MPa.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: stress = force/area (tension).
Explanation: σ = F/A. A = 64 mm² = 0.000064 m². σ ≈ 5000/0.000064 ≈ 78.1 MPa.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: stress = force/area (tension).
Explanation: σ = F/A. A = 71 mm² = 0.000071 m². σ ≈ 5500/0.000071 ≈ 77.5 MPa.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: stress = force/area (tension).
Explanation: σ = F/A. A = 78 mm² = 0.000078 m². σ ≈ 6000/0.000078 ≈ 76.9 MPa.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: stress = force/area (tension).
Explanation: σ = F/A. A = 85 mm² = 0.000085 m². σ ≈ 6500/0.000085 ≈ 76.5 MPa.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: stress = force/area (tension).
Explanation: σ = F/A. A = 92 mm² = 0.000092 m². σ ≈ 7000/0.000092 ≈ 76.1 MPa.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: stress = force/area (tension).
Explanation: σ = F/A. A = 99 mm² = 0.000099 m². σ ≈ 7500/0.000099 ≈ 75.8 MPa.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: stress = force/area (tension).
Explanation: σ = F/A. A = 106 mm² = 0.000106 m². σ ≈ 8000/0.000106 ≈ 75.5 MPa.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: stress = force/area (tension).
Explanation: σ = F/A. A = 113 mm² = 0.000113 m². σ ≈ 8500/0.000113 ≈ 75.2 MPa.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: stress = force/area (tension).
Explanation: p = ρgh = 1000×9.8×0.80 ≈ 7.8 kPa.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: hydrostatic pressure (ρgh).
Explanation: p = ρgh = 1000×9.8×1.15 ≈ 11.3 kPa.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: hydrostatic pressure (ρgh).
Explanation: p = ρgh = 1000×9.8×1.50 ≈ 14.7 kPa.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: hydrostatic pressure (ρgh).
Explanation: p = ρgh = 1000×9.8×1.85 ≈ 18.1 kPa.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: hydrostatic pressure (ρgh).
Explanation: p = ρgh = 1000×9.8×2.20 ≈ 21.6 kPa.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: hydrostatic pressure (ρgh).
Explanation: p = ρgh = 1000×9.8×2.55 ≈ 25.0 kPa.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: hydrostatic pressure (ρgh).
Explanation: p = ρgh = 1000×9.8×2.90 ≈ 28.4 kPa.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: hydrostatic pressure (ρgh).
Explanation: p = ρgh = 1000×9.8×3.25 ≈ 31.9 kPa.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: hydrostatic pressure (ρgh).
Explanation: p = ρgh = 1000×9.8×3.60 ≈ 35.3 kPa.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: hydrostatic pressure (ρgh).
Explanation: p = ρgh = 1000×9.8×3.95 ≈ 38.7 kPa.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: hydrostatic pressure (ρgh).
Explanation: Impulse equals change in momentum: F_avg·Δt = mΔv. Here Δv = 8→0, so F_avg = m v / Δt = 0.6×8/0.04 ≈ 120.0 N.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: impulse–momentum (FΔt = mΔv).
Explanation: Impulse equals change in momentum: F_avg·Δt = mΔv. Here Δv = 9→0, so F_avg = m v / Δt = 0.7×9/0.05 ≈ 126.0 N.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: impulse–momentum (FΔt = mΔv).
Explanation: Impulse equals change in momentum: F_avg·Δt = mΔv. Here Δv = 10→0, so F_avg = m v / Δt = 0.8×10/0.06 ≈ 133.3 N.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: impulse–momentum (FΔt = mΔv).
Explanation: Impulse equals change in momentum: F_avg·Δt = mΔv. Here Δv = 11→0, so F_avg = m v / Δt = 0.9×11/0.07 ≈ 141.4 N.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: impulse–momentum (FΔt = mΔv).
Explanation: Impulse equals change in momentum: F_avg·Δt = mΔv. Here Δv = 12→0, so F_avg = m v / Δt = 1.0×12/0.04 ≈ 300.0 N.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: impulse–momentum (FΔt = mΔv).
Explanation: Impulse equals change in momentum: F_avg·Δt = mΔv. Here Δv = 13→0, so F_avg = m v / Δt = 1.1×13/0.05 ≈ 286.0 N.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: impulse–momentum (FΔt = mΔv).
Explanation: Impulse equals change in momentum: F_avg·Δt = mΔv. Here Δv = 14→0, so F_avg = m v / Δt = 1.2×14/0.06 ≈ 280.0 N.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: impulse–momentum (FΔt = mΔv).
Explanation: Impulse equals change in momentum: F_avg·Δt = mΔv. Here Δv = 15→0, so F_avg = m v / Δt = 1.3×15/0.07 ≈ 278.6 N.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: impulse–momentum (FΔt = mΔv).
Explanation: Impulse equals change in momentum: F_avg·Δt = mΔv. Here Δv = 16→0, so F_avg = m v / Δt = 1.4×16/0.04 ≈ 560.0 N.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: impulse–momentum (FΔt = mΔv).
Explanation: Impulse equals change in momentum: F_avg·Δt = mΔv. Here Δv = 17→0, so F_avg = m v / Δt = 1.5×17/0.05 ≈ 510.0 N.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: impulse–momentum (FΔt = mΔv).
Explanation: Rotational KE = ½Iω². Convert speed: ω = 180×2π/60 ≈ 18.8 rad/s. KE ≈ 0.5×0.45×(18.8)² ≈ 80 J.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: rotational kinetic energy (½Iω²).
Explanation: Rotational KE = ½Iω². Convert speed: ω = 200×2π/60 ≈ 20.9 rad/s. KE ≈ 0.5×0.50×(20.9)² ≈ 110 J.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: rotational kinetic energy (½Iω²).
Explanation: Rotational KE = ½Iω². Convert speed: ω = 220×2π/60 ≈ 23.0 rad/s. KE ≈ 0.5×0.55×(23.0)² ≈ 146 J.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: rotational kinetic energy (½Iω²).
Explanation: Rotational KE = ½Iω². Convert speed: ω = 240×2π/60 ≈ 25.1 rad/s. KE ≈ 0.5×0.60×(25.1)² ≈ 189 J.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: rotational kinetic energy (½Iω²).
Explanation: Rotational KE = ½Iω². Convert speed: ω = 260×2π/60 ≈ 27.2 rad/s. KE ≈ 0.5×0.65×(27.2)² ≈ 241 J.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: rotational kinetic energy (½Iω²).
Explanation: Rotational KE = ½Iω². Convert speed: ω = 280×2π/60 ≈ 29.3 rad/s. KE ≈ 0.5×0.70×(29.3)² ≈ 301 J.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: rotational kinetic energy (½Iω²).
Explanation: Rotational KE = ½Iω². Convert speed: ω = 300×2π/60 ≈ 31.4 rad/s. KE ≈ 0.5×0.75×(31.4)² ≈ 370 J.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: rotational kinetic energy (½Iω²).
Explanation: Rotational KE = ½Iω². Convert speed: ω = 320×2π/60 ≈ 33.5 rad/s. KE ≈ 0.5×0.80×(33.5)² ≈ 449 J.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: rotational kinetic energy (½Iω²).
Explanation: Rotational KE = ½Iω². Convert speed: ω = 340×2π/60 ≈ 35.6 rad/s. KE ≈ 0.5×0.85×(35.6)² ≈ 539 J.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: rotational kinetic energy (½Iω²).
Explanation: Rotational KE = ½Iω². Convert speed: ω = 360×2π/60 ≈ 37.7 rad/s. KE ≈ 0.5×0.90×(37.7)² ≈ 640 J.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: rotational kinetic energy (½Iω²).
Explanation: Torques add with sign. τ_net = r(F1 − F2) = 0.35×(80−30) ≈ 17.5 N·m (clockwise).
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: net torque (sum of torques).
Explanation: Torques add with sign. τ_net = r(F1 − F2) = 0.40×(90−35) ≈ 22.0 N·m (clockwise).
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: net torque (sum of torques).
Explanation: Torques add with sign. τ_net = r(F1 − F2) = 0.45×(100−40) ≈ 27.0 N·m (clockwise).
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: net torque (sum of torques).
Explanation: Torques add with sign. τ_net = r(F1 − F2) = 0.50×(110−45) ≈ 32.5 N·m (clockwise).
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: net torque (sum of torques).
Explanation: Torques add with sign. τ_net = r(F1 − F2) = 0.55×(120−30) ≈ 49.5 N·m (clockwise).
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: net torque (sum of torques).
Explanation: Torques add with sign. τ_net = r(F1 − F2) = 0.35×(130−35) ≈ 33.2 N·m (clockwise).
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: net torque (sum of torques).
Explanation: Torques add with sign. τ_net = r(F1 − F2) = 0.40×(140−40) ≈ 40.0 N·m (clockwise).
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: net torque (sum of torques).
Explanation: Torques add with sign. τ_net = r(F1 − F2) = 0.45×(150−45) ≈ 47.2 N·m (clockwise).
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: net torque (sum of torques).
Explanation: Torques add with sign. τ_net = r(F1 − F2) = 0.50×(160−30) ≈ 65.0 N·m (clockwise).
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: net torque (sum of torques).
Explanation: Torques add with sign. τ_net = r(F1 − F2) = 0.55×(170−35) ≈ 74.2 N·m (clockwise).
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: net torque (sum of torques).
Explanation: An idler gear changes direction but not the overall speed ratio. Overall ratio = teeth_A/teeth_C, so rpm_C = 120×(14/21) ≈ 80.0 rpm.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: gear trains with idlers (ratio depends on first and last gears).
Explanation: An idler gear changes direction but not the overall speed ratio. Overall ratio = teeth_A/teeth_C, so rpm_C = 130×(16/24) ≈ 86.7 rpm.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: gear trains with idlers (ratio depends on first and last gears).
Explanation: An idler gear changes direction but not the overall speed ratio. Overall ratio = teeth_A/teeth_C, so rpm_C = 140×(18/27) ≈ 93.3 rpm.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: gear trains with idlers (ratio depends on first and last gears).
Explanation: An idler gear changes direction but not the overall speed ratio. Overall ratio = teeth_A/teeth_C, so rpm_C = 150×(20/30) ≈ 100.0 rpm.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: gear trains with idlers (ratio depends on first and last gears).
Explanation: An idler gear changes direction but not the overall speed ratio. Overall ratio = teeth_A/teeth_C, so rpm_C = 160×(22/21) ≈ 167.6 rpm.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: gear trains with idlers (ratio depends on first and last gears).
Explanation: An idler gear changes direction but not the overall speed ratio. Overall ratio = teeth_A/teeth_C, so rpm_C = 170×(24/24) ≈ 170.0 rpm.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: gear trains with idlers (ratio depends on first and last gears).
Explanation: An idler gear changes direction but not the overall speed ratio. Overall ratio = teeth_A/teeth_C, so rpm_C = 180×(26/27) ≈ 173.3 rpm.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: gear trains with idlers (ratio depends on first and last gears).
Explanation: An idler gear changes direction but not the overall speed ratio. Overall ratio = teeth_A/teeth_C, so rpm_C = 190×(28/30) ≈ 177.3 rpm.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: gear trains with idlers (ratio depends on first and last gears).
Explanation: An idler gear changes direction but not the overall speed ratio. Overall ratio = teeth_A/teeth_C, so rpm_C = 200×(30/21) ≈ 285.7 rpm.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: gear trains with idlers (ratio depends on first and last gears).
Explanation: An idler gear changes direction but not the overall speed ratio. Overall ratio = teeth_A/teeth_C, so rpm_C = 210×(32/24) ≈ 280.0 rpm.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: gear trains with idlers (ratio depends on first and last gears).
Explanation: In a belt drive (no slip), rim speeds match: rpm₁D₁ = rpm₂D₂. So rpm₂ = rpm₁(D₁/D₂) = 900×(4/10) ≈ 360.0 rpm.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: belt/pulley speed ratio (equal rim speed).
Explanation: In a belt drive (no slip), rim speeds match: rpm₁D₁ = rpm₂D₂. So rpm₂ = rpm₁(D₁/D₂) = 950×(5/12) ≈ 395.8 rpm.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: belt/pulley speed ratio (equal rim speed).
Explanation: In a belt drive (no slip), rim speeds match: rpm₁D₁ = rpm₂D₂. So rpm₂ = rpm₁(D₁/D₂) = 1000×(6/14) ≈ 428.6 rpm.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: belt/pulley speed ratio (equal rim speed).
Explanation: In a belt drive (no slip), rim speeds match: rpm₁D₁ = rpm₂D₂. So rpm₂ = rpm₁(D₁/D₂) = 1050×(7/16) ≈ 459.4 rpm.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: belt/pulley speed ratio (equal rim speed).
Explanation: In a belt drive (no slip), rim speeds match: rpm₁D₁ = rpm₂D₂. So rpm₂ = rpm₁(D₁/D₂) = 1100×(4/18) ≈ 244.4 rpm.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: belt/pulley speed ratio (equal rim speed).
Explanation: In a belt drive (no slip), rim speeds match: rpm₁D₁ = rpm₂D₂. So rpm₂ = rpm₁(D₁/D₂) = 1150×(5/20) ≈ 287.5 rpm.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: belt/pulley speed ratio (equal rim speed).
Explanation: In a belt drive (no slip), rim speeds match: rpm₁D₁ = rpm₂D₂. So rpm₂ = rpm₁(D₁/D₂) = 1200×(6/22) ≈ 327.3 rpm.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: belt/pulley speed ratio (equal rim speed).
Explanation: In a belt drive (no slip), rim speeds match: rpm₁D₁ = rpm₂D₂. So rpm₂ = rpm₁(D₁/D₂) = 1250×(7/24) ≈ 364.6 rpm.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: belt/pulley speed ratio (equal rim speed).
Explanation: In a belt drive (no slip), rim speeds match: rpm₁D₁ = rpm₂D₂. So rpm₂ = rpm₁(D₁/D₂) = 1300×(4/26) ≈ 200.0 rpm.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: belt/pulley speed ratio (equal rim speed).
Explanation: In a belt drive (no slip), rim speeds match: rpm₁D₁ = rpm₂D₂. So rpm₂ = rpm₁(D₁/D₂) = 1350×(5/28) ≈ 241.1 rpm.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: belt/pulley speed ratio (equal rim speed).
Explanation: Spring energy U = ½kx² = 0.5×150×(0.08)² ≈ 0.48 J.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: spring potential energy (½kx²).
Explanation: Spring energy U = ½kx² = 0.5×175×(0.09)² ≈ 0.71 J.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: spring potential energy (½kx²).
Explanation: Spring energy U = ½kx² = 0.5×200×(0.10)² ≈ 1.00 J.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: spring potential energy (½kx²).
Explanation: Spring energy U = ½kx² = 0.5×225×(0.11)² ≈ 1.36 J.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: spring potential energy (½kx²).
Explanation: Spring energy U = ½kx² = 0.5×250×(0.12)² ≈ 1.80 J.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: spring potential energy (½kx²).
Explanation: Spring energy U = ½kx² = 0.5×275×(0.08)² ≈ 0.88 J.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: spring potential energy (½kx²).
Explanation: Spring energy U = ½kx² = 0.5×300×(0.09)² ≈ 1.21 J.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: spring potential energy (½kx²).
Explanation: Spring energy U = ½kx² = 0.5×325×(0.10)² ≈ 1.62 J.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: spring potential energy (½kx²).
Explanation: Spring energy U = ½kx² = 0.5×350×(0.11)² ≈ 2.12 J.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: spring potential energy (½kx²).
Explanation: Spring energy U = ½kx² = 0.5×375×(0.12)² ≈ 2.70 J.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: spring potential energy (½kx²).
Explanation: Series resistance R = 4+10 = 14 Ω. Current I = V/R = 24/14 ≈ 1.71 A. Power P = VI ≈ 24×1.71 ≈ 41.1 W.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: series circuits (Ohm’s law, P = VI).
Explanation: Series resistance R = 5+9 = 14 Ω. Current I = V/R = 24/14 ≈ 1.71 A. Power P = VI ≈ 24×1.71 ≈ 41.1 W.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: series circuits (Ohm’s law, P = VI).
Explanation: Series resistance R = 6+8 = 14 Ω. Current I = V/R = 24/14 ≈ 1.71 A. Power P = VI ≈ 24×1.71 ≈ 41.1 W.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: series circuits (Ohm’s law, P = VI).
Explanation: Series resistance R = 7+7 = 14 Ω. Current I = V/R = 24/14 ≈ 1.71 A. Power P = VI ≈ 24×1.71 ≈ 41.1 W.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: series circuits (Ohm’s law, P = VI).
Explanation: Series resistance R = 8+10 = 18 Ω. Current I = V/R = 24/18 ≈ 1.33 A. Power P = VI ≈ 24×1.33 ≈ 32.0 W.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: series circuits (Ohm’s law, P = VI).
Explanation: Series resistance R = 9+9 = 18 Ω. Current I = V/R = 24/18 ≈ 1.33 A. Power P = VI ≈ 24×1.33 ≈ 32.0 W.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: series circuits (Ohm’s law, P = VI).
Explanation: Series resistance R = 10+8 = 18 Ω. Current I = V/R = 24/18 ≈ 1.33 A. Power P = VI ≈ 24×1.33 ≈ 32.0 W.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: series circuits (Ohm’s law, P = VI).
Explanation: Series resistance R = 11+7 = 18 Ω. Current I = V/R = 24/18 ≈ 1.33 A. Power P = VI ≈ 24×1.33 ≈ 32.0 W.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: series circuits (Ohm’s law, P = VI).
Explanation: Series resistance R = 12+10 = 22 Ω. Current I = V/R = 24/22 ≈ 1.09 A. Power P = VI ≈ 24×1.09 ≈ 26.2 W.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: series circuits (Ohm’s law, P = VI).
Explanation: Series resistance R = 13+9 = 22 Ω. Current I = V/R = 24/22 ≈ 1.09 A. Power P = VI ≈ 24×1.09 ≈ 26.2 W.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: series circuits (Ohm’s law, P = VI).
Explanation: Buoyant force equals weight of displaced fluid: F_b = ρgV = 1000×9.8×0.015 ≈ 147 N.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: Archimedes’ principle (ρgV).
Explanation: Buoyant force equals weight of displaced fluid: F_b = ρgV = 1000×9.8×0.017 ≈ 167 N.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: Archimedes’ principle (ρgV).
Explanation: Buoyant force equals weight of displaced fluid: F_b = ρgV = 1000×9.8×0.019 ≈ 186 N.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: Archimedes’ principle (ρgV).
Explanation: Buoyant force equals weight of displaced fluid: F_b = ρgV = 1000×9.8×0.021 ≈ 206 N.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: Archimedes’ principle (ρgV).
Explanation: Buoyant force equals weight of displaced fluid: F_b = ρgV = 1000×9.8×0.023 ≈ 225 N.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: Archimedes’ principle (ρgV).
Explanation: Buoyant force equals weight of displaced fluid: F_b = ρgV = 1000×9.8×0.025 ≈ 245 N.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: Archimedes’ principle (ρgV).
Explanation: Buoyant force equals weight of displaced fluid: F_b = ρgV = 1000×9.8×0.027 ≈ 265 N.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: Archimedes’ principle (ρgV).
Explanation: Buoyant force equals weight of displaced fluid: F_b = ρgV = 1000×9.8×0.029 ≈ 284 N.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: Archimedes’ principle (ρgV).
Explanation: Buoyant force equals weight of displaced fluid: F_b = ρgV = 1000×9.8×0.031 ≈ 304 N.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: Archimedes’ principle (ρgV).
Explanation: Buoyant force equals weight of displaced fluid: F_b = ρgV = 1000×9.8×0.033 ≈ 323 N.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: Archimedes’ principle (ρgV).
Explanation: Bernoulli (same height): pressure drop ΔP ≈ ½ρ(v₂²−v₁²) = 0.5×1000×(4.0²−2.0²) ≈ 6.0 kPa.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: Bernoulli principle (pressure–velocity tradeoff).
Explanation: Bernoulli (same height): pressure drop ΔP ≈ ½ρ(v₂²−v₁²) = 0.5×1000×(4.3²−2.2²) ≈ 6.8 kPa.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: Bernoulli principle (pressure–velocity tradeoff).
Explanation: Bernoulli (same height): pressure drop ΔP ≈ ½ρ(v₂²−v₁²) = 0.5×1000×(4.6²−2.4²) ≈ 7.7 kPa.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: Bernoulli principle (pressure–velocity tradeoff).
Explanation: Bernoulli (same height): pressure drop ΔP ≈ ½ρ(v₂²−v₁²) = 0.5×1000×(4.9²−2.6²) ≈ 8.6 kPa.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: Bernoulli principle (pressure–velocity tradeoff).
Explanation: Bernoulli (same height): pressure drop ΔP ≈ ½ρ(v₂²−v₁²) = 0.5×1000×(5.2²−2.8²) ≈ 9.6 kPa.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: Bernoulli principle (pressure–velocity tradeoff).
Explanation: Bernoulli (same height): pressure drop ΔP ≈ ½ρ(v₂²−v₁²) = 0.5×1000×(5.5²−3.0²) ≈ 10.6 kPa.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: Bernoulli principle (pressure–velocity tradeoff).
Explanation: Bernoulli (same height): pressure drop ΔP ≈ ½ρ(v₂²−v₁²) = 0.5×1000×(4.0²−3.2²) ≈ 2.9 kPa.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: Bernoulli principle (pressure–velocity tradeoff).
Explanation: Bernoulli (same height): pressure drop ΔP ≈ ½ρ(v₂²−v₁²) = 0.5×1000×(4.3²−3.4²) ≈ 3.5 kPa.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: Bernoulli principle (pressure–velocity tradeoff).
Explanation: Bernoulli (same height): pressure drop ΔP ≈ ½ρ(v₂²−v₁²) = 0.5×1000×(4.6²−3.6²) ≈ 4.1 kPa.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: Bernoulli principle (pressure–velocity tradeoff).
Explanation: Bernoulli (same height): pressure drop ΔP ≈ ½ρ(v₂²−v₁²) = 0.5×1000×(4.9²−3.8²) ≈ 4.8 kPa.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: Bernoulli principle (pressure–velocity tradeoff).
Explanation: Efficiency η = W_out/Q_in = 175/500 ≈ 0.350 → about 35%.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: efficiency (η = W/Q).
Explanation: Efficiency η = W_out/Q_in = 202/550 ≈ 0.368 → about 37%.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: efficiency (η = W/Q).
Explanation: Efficiency η = W_out/Q_in = 230/600 ≈ 0.383 → about 38%.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: efficiency (η = W/Q).
Explanation: Efficiency η = W_out/Q_in = 227/650 ≈ 0.350 → about 35%.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: efficiency (η = W/Q).
Explanation: Efficiency η = W_out/Q_in = 255/700 ≈ 0.364 → about 36%.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: efficiency (η = W/Q).
Explanation: Efficiency η = W_out/Q_in = 282/750 ≈ 0.377 → about 38%.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: efficiency (η = W/Q).
Explanation: Efficiency η = W_out/Q_in = 280/800 ≈ 0.350 → about 35%.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: efficiency (η = W/Q).
Explanation: Efficiency η = W_out/Q_in = 308/850 ≈ 0.362 → about 36%.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: efficiency (η = W/Q).
Explanation: Efficiency η = W_out/Q_in = 335/900 ≈ 0.372 → about 37%.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: efficiency (η = W/Q).
Explanation: Efficiency η = W_out/Q_in = 332/950 ≈ 0.350 → about 35%.
Citation: ASVAB content domain — Mechanical Comprehension; underlying principle: efficiency (η = W/Q).
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