ASVAB — All Questions

A screw jack has threads with a pitch of 1/4 inch and is turned by a handle 14 inches long. Taking pi as 3.14 and ignoring friction, its mechanical advantage is about:

• a.about 14
• b.about 56
• c.about 88
• d.about 350✓

One turn moves the effort around a circle of 2 x 3.14 x 14 = about 88 inches while the load rises one pitch, 1/4 inch. Mechanical advantage is effort distance over load distance: 88 / 0.25 = about 350. Using the 14-inch handle instead of the circle it sweeps gives only about 56.

In a hydraulic jack the small piston has an area of 1 square inch and the large piston an area of 25 square inches. One stroke pushes the small piston down 5 inches. How far does the large piston rise on that stroke?

• a.0.20 inch✓
• b.125 inches
• c.5.0 inches
• d.1.25 inches

Liquid is nearly incompressible, so the volume leaving one cylinder arrives in the other: 1 x 5 = 25 x d, giving d = 0.2 inch. The 25-fold gain in force is paid for with 25 times less travel. Multiplying rather than dividing gives 125 inches and would create energy out of nothing.

In a hydraulic press the small piston is 2 inches in diameter and the large piston is 6 inches in diameter. A 100-pound force on the small piston produces what force at the large piston?

• a.100 pounds
• b.300 pounds
• c.600 pounds
• d.900 pounds✓

Pressure is the same throughout a closed fluid and force = pressure x area, so force scales with AREA, and area goes as the square of diameter. (6/2)^2 = 9, so 9 x 100 = 900 pounds. Using the diameter ratio of 3 directly gives 300; reading equal pressure as equal force gives 100.

A steel bar weighs 60 pounds hanging from a scale in air. Lowered until it is completely underwater, the same scale reads 52 pounds. The water the bar displaces weighs:

• a.60 pounds
• b.68 pounds
• c.52 pounds
• d.8 pounds✓

Archimedes' principle: the buoyant force equals the weight of fluid displaced, and it shows up as lost apparent weight. 60 - 52 = 8 pounds of water displaced. The submerged reading, 52, is what the scale still holds, and adding the loss back to the dry weight gives 68.

Standing water exerts about 0.43 pound per square inch of pressure for every foot of depth. A storage tank is filled with water to a depth of 30 feet. The water pressure on the tank floor is about:

• a.6.45 pounds per square inch
• b.12.9 pounds per square inch✓
• c.30.4 pounds per square inch
• d.69.8 pounds per square inch

Pressure in standing liquid is proportional to depth alone, so multiply the per-foot figure by the depth: 0.43 x 30 = 12.9 pounds per square inch. Dividing the depth by 0.43 gives about 69.8 and inverts the relation; adding the two numbers gives 30.4. The tank width never enters it.

A spring stretches 3 inches when a 12-pound weight hangs from it. Two identical springs are then joined end to end in a single line, and the same 12-pound weight is hung from the lower one. The total stretch is:

• a.3 inches
• b.1.5 inches
• c.6 inches✓
• d.12 inches

Springs joined end to end each carry the FULL load, so each stretches its own 3 inches and the stretches add: 3 + 3 = 6 inches. Springs side by side are the opposite case, splitting the load so each stretches 1.5 inches. Treating a series pair like a parallel pair produces that 1.5.

A spring stretches 2 inches under a 10-pound load. Still within its elastic limit, how far will the same spring stretch under a 25-pound load?

• a.12.5 inches
• b.4 inches
• c.2.5 inches
• d.5 inches✓

Within its elastic limit a spring's stretch is proportional to the load, so stretch per pound stays fixed: 2/10 = 0.2 inch per pound, and 25 x 0.2 = 5 inches. Taking the load ratio 25/10 = 2.5 as the answer reports the multiplier instead of multiplying the 2-inch stretch by it.

A seesaw 12 feet long pivots at its midpoint. A 90-pound child sits at one end. How far from the pivot must a 120-pound child sit on the other side to balance it?

• a.6.0 feet
• b.8.0 feet
• c.4.5 feet✓
• d.3.0 feet

Balance means matching moments: weight x distance on one side equals weight x distance on the other. 90 x 6 = 540, and 540 / 120 = 4.5 feet. The heavier child always sits closer to the pivot. Multiplying by the weight ratio instead of dividing pushes that child out to 8 feet.

A uniform beam 12 feet long weighs 200 pounds and rests on a support at each end. A 600-pound crate sits 3 feet from the left support. How much weight does the left support carry?

• a.450 pounds
• b.600 pounds
• c.550 pounds✓
• d.400 pounds

Take moments about the far support: a load 9 feet from it on a 12-foot span puts 600 x 9/12 = 450 pounds on the near support, and the beam's own 200 pounds acts at midspan, 100 to each end. 450 + 100 = 550. Splitting the crate evenly gives 400; ignoring the beam's weight leaves 450.

A loaded forklift is most likely to tip over when:

• a.its total weight exceeds the rated capacity
• b.its center of gravity moves outside the wheels✓
• c.the load weighs more than the counterweight
• d.its center of gravity is over the front axle

A body tips when a vertical line through its center of gravity falls outside the area enclosed by its supports. Raising a load raises that center, so a small tilt swings the line past the wheels. Weight by itself does not decide it: a heavy low load is steadier than a light high one.

A 250-pound crate rests on a floor where the coefficient of sliding friction is 0.4. Once it is moving, how much horizontal force keeps it sliding at a steady speed?

• a.150 pounds
• b.250 pounds
• c.100 pounds✓
• d.625 pounds

Sliding friction equals the coefficient times the force pressing the surfaces together: 0.4 x 250 = 100 pounds, and at steady speed the push only has to match friction. Dividing 250 by 0.4 gives 625; taking 250 minus 40 percent gives 150, which is what is left over, not what is needed.

Two identical steel blocks of equal weight are dragged across the same concrete floor, one resting on its wide face and the other standing on its narrow edge. The force needed to drag the block on its narrow edge is:

• a.about half that for the wide one
• b.about a quarter of the wide one
• c.about twice that for the wide one
• d.about the same as for the wide one✓

Sliding friction depends on the force pressing the surfaces together and on the two materials, not on how much area they share. Standing the block on edge raises the pressure but shrinks the contact area by the same factor, leaving the friction force unchanged. Weight, not footprint, sets it.

A hoist raises a 400-pound load 20 feet in 10 seconds. The power it delivers is:

• a.40 foot-pounds per second
• b.800 foot-pounds per second✓
• c.8,000 foot-pounds per second
• d.80 foot-pounds per second

Power is work divided by time, and work is force x distance: 400 x 20 = 8,000 foot-pounds, delivered in 10 seconds, is 800 foot-pounds per second. Quoting 8,000 reports the work and ignores the time, dividing by the 10 seconds a second time gives 80, and 40 never uses the 20-foot lift.

A pendulum bob is pulled to one side until it hangs 9 inches higher than its resting point, then released. Ignoring friction and air resistance, on the far side of its swing the bob rises:

• a.18 inches, twice as high
• b.6 inches, two thirds as high
• c.9 inches, the same height✓
• d.4.5 inches, half as high

With friction ignored, energy only trades between height and motion: the potential energy at release becomes kinetic energy at the bottom, then becomes height again. The bob returns to its starting height, 9 inches, no more and no less. Real pendulums fall short only because friction removes energy.

A windshield wiper is driven by a four-bar linkage whose motor crank turns steadily in complete circles. The wiper arm:

• a.rotates in full circles at the same speed
• b.turns in full circles at half that speed
• c.swings back and forth through a limited arc✓
• d.moves in a straight line at a steady pace

A linkage's output is set by the lengths of its bars. When the crank is short enough to rotate fully but the output bar cannot swing past its own pivot, steady rotation at the motor becomes a limited back-and-forth arc. That is how one motor turning one way sweeps a wiper both ways.