What this section covers: Mechanical and physical principles.
15 free practice questions
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Question 1A worker uses a 6-foot steel bar as a lever to lift a 300-pound rock. A small block under the bar serves as the fulcrum, 1 foot from the end under the rock; the worker pushes down on the other end, 5 feet from the fulcrum. Ignoring the weight of the bar, how much force must the worker apply to balance the rock?
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Answer: B — 60 pounds.
For a lever, effort × effort distance = load × load distance: F × 5 ft = 300 lb × 1 ft, so F = 60 pounds. The lever's mechanical advantage is 5 ÷ 1 = 5.
Checked against: Official ASVAB — Mechanical Comprehension (MC): knowledge of mechanical and physical principles; OpenStax College Physics 2e, 9.5 Simple Machines (levers, MA = distance ratio)
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Question 2A wheelbarrow carries a 120-pound load whose weight acts 1.5 feet from the wheel's axle. The worker lifts the handles at a point 4.5 feet from the axle. Ignoring the weight of the wheelbarrow, what upward force must the worker apply?
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Answer: B — 40 pounds.
The axle is the pivot, and the load and the lifting force are on the same side of it. Balancing torques: F × 4.5 ft = 120 lb × 1.5 ft, so F = 180 ÷ 4.5 = 40 pounds.
Checked against: Official ASVAB — Mechanical Comprehension (MC): knowledge of mechanical and physical principles; OpenStax College Physics 2e, 9.5 Simple Machines (wheelbarrow)
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Question 3A 200-pound load hangs from a single movable pulley. One end of the rope is tied to a ceiling beam, and a worker pulls straight up on the other end, so two rope segments support the pulley. Ignoring friction and the weight of the pulley, how hard must the worker pull to hold the load?
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Answer: D — 100 pounds.
The two rope segments share the load equally, so each carries 200 ÷ 2 = 100 pounds, and the worker's pull equals the tension in one segment. A single movable pulley has a mechanical advantage of about 2.
Checked against: Official ASVAB — Mechanical Comprehension (MC): knowledge of mechanical and physical principles; OpenStax College Physics 2e, 9.5 Simple Machines (pulley systems)
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Question 4A block and tackle supports a 480-pound engine with 4 rope segments running to the lower (movable) block. Ignoring friction, the worker needs a 120-pound pull. How many feet of rope must the worker pull through to raise the engine 2 feet?
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Answer: C — 8 feet.
Each of the 4 supporting segments must shorten by 2 feet, so 4 × 2 = 8 feet of rope must be pulled. The machine trades distance for force: 120 lb × 8 ft = 480 lb × 2 ft = 960 foot-pounds of work either way.
Checked against: Official ASVAB — Mechanical Comprehension (MC): knowledge of mechanical and physical principles; OpenStax College Physics 2e, 9.5 Simple Machines (pulley systems, MA about 4)
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Question 5A driving gear with 20 teeth turns at 90 revolutions per minute (rpm) and meshes directly with a driven gear that has 60 teeth. How fast does the driven gear turn?
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Answer: A — 30 rpm.
Meshing gears move the same number of teeth past the contact point each minute: 20 × 90 = 1,800 teeth per minute, and 1,800 ÷ 60 = 30 rpm. The larger gear turns more slowly, in proportion to its extra teeth.
Checked against: Official ASVAB — Mechanical Comprehension (MC): knowledge of mechanical and physical principles; OpenStax College Physics 2e, 6.1 Rotation Angle and Angular Velocity (v = rω: equal edge speed at the contact point)
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Question 6Three gears are mounted in a straight row so that gear A meshes with gear B, and gear B meshes with gear C. Gear A turns clockwise. Which way does gear C turn?
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Answer: B — Clockwise.
Each pair of meshing gears turns in opposite directions: A clockwise makes B counterclockwise, and B counterclockwise makes C clockwise. In a simple row, every second gear turns the same way as the first.
Checked against: Official ASVAB — Mechanical Comprehension (MC): knowledge of mechanical and physical principles; OpenStax College Physics 2e, 6.1 Rotation Angle and Angular Velocity (meshing gears share the edge speed at the contact point)
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Question 7A 4-inch-diameter pulley on a motor turns at 600 rpm. An open (uncrossed) belt connects it to a 12-inch-diameter pulley on a machine. How fast, and in which direction, does the 12-inch pulley turn?
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Answer: C — 200 rpm, same direction as the motor pulley.
The belt moves both rims at the same speed, so rpm × diameter is the same for both pulleys: 600 × 4 = rpm × 12, giving 200 rpm. An open belt turns both pulleys the same way; only a crossed belt reverses the direction.
Checked against: Official ASVAB — Mechanical Comprehension (MC): knowledge of mechanical and physical principles; OpenStax College Physics 2e, 6.1 Rotation Angle and Angular Velocity (v = rω)
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Question 8A 300-pound crate is pushed up a frictionless ramp that is 12 feet long and rises 3 feet. What force, applied parallel to the ramp, is needed to push the crate up at a steady speed?
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Answer: D — 75 pounds.
Without friction, the work along the ramp equals the work of lifting the crate straight up: F × 12 ft = 300 lb × 3 ft = 900 foot-pounds, so F = 75 pounds. The ramp's mechanical advantage is 12 ÷ 3 = 4.
Checked against: Official ASVAB — Mechanical Comprehension (MC): knowledge of mechanical and physical principles; OpenStax College Physics 2e, 9.5 Simple Machines (inclined plane) and 7.1 Work
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Question 9A soldier holds a 40-pound pack perfectly still at shoulder height for 5 minutes. How much work, in the scientific sense, does the soldier do on the pack during that time?
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Answer: C — Zero.
Work is force times the distance moved in the direction of the force. The pack does not move, so no work is done on it, even though the soldier's muscles tire.
Checked against: Official ASVAB — Mechanical Comprehension (MC): knowledge of mechanical and physical principles; OpenStax College Physics 2e, 7.1 Work: The Scientific Definition
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Question 10A motor lifts a 1,000-newton load straight up 5 meters in 10 seconds at a steady speed. What is the motor's average power output?
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Answer: B — 500 watts.
Work = force × distance = 1,000 N × 5 m = 5,000 joules. Power is work divided by time: 5,000 J ÷ 10 s = 500 watts (1 watt = 1 joule per second). 5,000 is the work, not the power.
Checked against: Official ASVAB — Mechanical Comprehension (MC): knowledge of mechanical and physical principles; OpenStax College Physics 2e, 7.7 Power
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Question 11In a hydraulic jack, the small piston has an area of 2 square inches and the large piston an area of 40 square inches. A force of 50 pounds is applied to the small piston. Ignoring friction, what force does the large piston exert?
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Answer: C — 1,000 pounds.
Pascal's principle: the pressure is the same throughout the enclosed fluid. The pressure is 50 lb ÷ 2 in² = 25 pounds per square inch, and on the large piston 25 × 40 = 1,000 pounds.
Checked against: Official ASVAB — Mechanical Comprehension (MC): knowledge of mechanical and physical principles; OpenStax College Physics 2e, 11.5 Pascal's Principle (hydraulic systems)
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Question 12A 2,400-pound machine rests evenly on a flat base 4 feet long and 3 feet wide. What pressure does it exert on the floor?
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Answer: A — 200 pounds per square foot.
Pressure is force divided by area. The base area is 4 × 3 = 12 square feet, so the pressure is 2,400 ÷ 12 = 200 pounds per square foot.
Checked against: Official ASVAB — Mechanical Comprehension (MC): knowledge of mechanical and physical principles; OpenStax College Physics 2e, 11.3 Pressure (P = F/A)
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Question 13A metal part weighs 50 newtons in air. Hung from a spring scale and fully under water, it reads 30 newtons. What buoyant force does the water exert on the part?
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Answer: A — 20 newtons.
The water pushes up on the part with a buoyant force equal to the weight it seems to lose: 50 N - 30 N = 20 newtons. By Archimedes' principle, this also equals the weight of the water the part displaces.
Checked against: Official ASVAB — Mechanical Comprehension (MC): knowledge of mechanical and physical principles; OpenStax College Physics 2e, 11.7 Archimedes' Principle
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Question 14A bolt must be tightened to 90 foot-pounds of torque. The mechanic pushes at a right angle on the end of a wrench whose handle is 18 inches long, measured from the center of the bolt. What force is needed?
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Answer: C — 60 pounds.
Torque = force × lever arm. The lever arm is 18 inches = 1.5 feet, so F = 90 ÷ 1.5 = 60 pounds. Using 18 as feet or multiplying instead of dividing gives the wrong answers; a longer handle would need even less force.
Checked against: Official ASVAB — Mechanical Comprehension (MC): knowledge of mechanical and physical principles; OpenStax College Physics 2e, 9.2 The Second Condition for Equilibrium (torque = lever arm × force)
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Question 15A spring stretches 2 inches when a 10-pound weight hangs from it. If the spring stays within its elastic limit, how far will it stretch with a 25-pound weight?
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Answer: A — 5 inches.
By Hooke's law the stretch is proportional to the force. The spring stretches 2 ÷ 10 = 0.2 inch per pound, so 25 pounds stretch it 25 × 0.2 = 5 inches.
Checked against: Official ASVAB — Mechanical Comprehension (MC): knowledge of mechanical and physical principles; OpenStax College Physics 2e, 16.1 Hooke's Law: Stress and Strain Revisited
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