24 Mechanical Reasoning Practice Questions & Answers

Every Mechanical Reasoning practice question from the Firefighter Written Exam Practice Test, with the correct answer and a short explanation.

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1. A water tank's surface sits 90 vertical feet above a pump gauge at ground level. Using 0.433 psi per vertical foot of water, what static (head) pressure will the gauge read with no water flowing?
- A.About 90 psi
- B.About 208 psi
- C.About 21 psi
- D.About 39 psi✓ Answer
Head pressure equals vertical height times 0.433 psi per foot: 90 x 0.433 = 38.97, about 39 psi. The pressure comes from the weight of the water column above the gauge, not from the pump or the tank's size.
Source: Hydrostatic head rule: 1 vertical foot of water = 0.433 psiReport a problem with this question
2. A gauge at the base of a standpipe reads 60 psi of static water pressure. Using 2.31 vertical feet of water per 1 psi, how high above the gauge does the water stand?
- A.About 138.6 feet✓ Answer
- B.About 231 feet
- C.About 60 feet
- D.About 26 feet
Feet of head equals psi times 2.31: 60 x 2.31 = 138.6 feet. This is simply the inverse of the 0.433 psi-per-foot rule, so multiply when converting psi to feet and divide when converting feet to psi.
Source: Hydrostatic head rule: 1 psi = 2.31 vertical feet of waterReport a problem with this question
3. A wide open reservoir and a narrow vertical pipe both hold fresh water to a depth of 30 feet. How does the water pressure at the very bottom of the narrow pipe compare with the pressure at the bottom of the reservoir?
- A.Equal, because pressure depends only on the vertical depth✓ Answer
- B.Higher in the pipe, because the same water is squeezed into a smaller area
- C.Higher in the reservoir, because it holds far more water
- D.It cannot be determined without knowing both diameters
Hydrostatic pressure depends on the vertical height of the liquid column and its density, not on container shape, width, or total volume. Thirty feet of water produces the same pressure at the bottom whether the column is an inch wide or a mile wide.
Source: Hydrostatics: pressure at a point = height x density; independent of container shapeReport a problem with this question
4. Four glass tubes of different widths and shapes — one straight and narrow, one wide, one bent, one flared like a funnel — all open at the top and joined at the bottom by a single horizontal pipe. Water is poured in until it settles. Where does the water stand?
- A.Highest in the narrowest tube
- B.At the same level in all four tubes✓ Answer
- C.Highest in the funnel-shaped tube
- D.Highest in the widest tube
In communicating vessels a liquid seeks a common level, because pressure at the shared bottom connection must be equal and pressure depends only on vertical height. Shape and width change how much water each tube holds, not how high it stands.
Source: Principle of communicating vessels: connected open liquid columns equalize in levelReport a problem with this question
5. A pump discharges into a hose line at a fixed pressure. The crew replaces the line with one that is twice as long and of smaller inside diameter, using the same nozzle. What happens?
- A.Flow increases, because a smaller hose holds less water
- B.Nozzle pressure falls, because friction loss grows with length and shrinking diameter✓ Answer
- C.Nozzle pressure rises, because narrower pipe speeds water up
- D.Nothing changes, because the pump pressure is the same
Friction loss in a hose or pipe increases directly with length and rises sharply as inside diameter decreases, so more of the pump's pressure is consumed moving water through the line and less is left at the nozzle.
Source: Fluid friction: pressure loss increases with line length and decreases sharply with larger diameterReport a problem with this question
6. A sealed empty drum is pushed part way under water and released; it floats. The upward buoyant force acting on the drum is equal to which of the following?
- A.The total volume of the drum expressed in gallons
- B.The drum's weight only if the drum sinks
- C.The weight of the water the drum pushes aside✓ Answer
- D.The atmospheric pressure pressing on the drum's top
Buoyant force equals the weight of the fluid displaced by the submerged part of the object. An object floats when it can displace water weighing as much as itself, which is why a hollow steel drum floats while a solid steel bar of the same weight sinks.
Source: Archimedes' principle: buoyant force = weight of displaced fluidReport a problem with this question
7. An 8-inch pulley turning at 150 rpm drives a 2-inch pulley through a snug, uncrossed belt with no slipping. How fast does the 2-inch pulley turn?
- A.37.5 rpm
- B.300 rpm
- C.600 rpm✓ Answer
- D.150 rpm
Belt-driven speed is inversely proportional to diameter: N1 x D1 = N2 x D2, so 150 x 8 = N2 x 2 and N2 = 600 rpm. The smaller wheel always turns faster, which is the point candidates most often get backwards.
Source: Belt drive ratio: N_A x D_A = N_B x D_B (speed inverse to pulley diameter)Report a problem with this question
8. Two equal-diameter pulleys are linked by a belt that is crossed in a figure eight between them. The driving pulley turns clockwise. How does the driven pulley turn?
- A.Counterclockwise, at the same speed✓ Answer
- B.Clockwise, but more slowly
- C.Clockwise, at the same speed
- D.It cannot turn at all with a crossed belt
A crossed (twisted) belt reverses the direction of the driven wheel, while an open belt keeps both wheels turning the same way. Crossing changes direction only; with equal diameters the speed ratio stays 1 to 1.
Source: Belt drive direction rule: open belt = same direction, crossed belt = opposite directionReport a problem with this question
9. Pulley A is 3 inches across and turns at 600 rpm. An open belt links A to pulley B, which is 9 inches across. Pulley C, 6 inches across, is keyed to the same shaft as B, and a second open belt links C to pulley D, which is 2 inches across. How fast does D turn?
- A.200 rpm
- B.67 rpm
- C.1,800 rpm
- D.600 rpm✓ Answer
Work the chain one stage at a time: A drives B, so 600 x 3 / 9 = 200 rpm at B; C shares B's shaft, so C also turns 200 rpm; C drives D, so 200 x 6 / 2 = 600 rpm. Wheels fixed on a common shaft always share the same rpm regardless of their diameters.
Source: Belt drive ratio applied stage by stage; pulleys on a common shaft share rpmReport a problem with this question
10. Three gears sit in a row, each meshing directly with the next: gear A meshes with gear B, and gear B meshes with gear C. Gear A is turned clockwise. Which describes the rotation of B and C?
- A.B clockwise, C counterclockwise
- B.B clockwise, C clockwise
- C.B counterclockwise, C clockwise✓ Answer
- D.All three turn the same direction
Directly meshed gears always turn in opposite directions, so each mesh flips the rotation: A clockwise makes B counterclockwise, which makes C clockwise again. With an odd number of gears in a simple train, the last gear turns the same way as the first.
Source: Gear mesh rule: directly meshed gears rotate in opposite directionsReport a problem with this question
11. A driving gear with 20 teeth meshes with a driven gear with 60 teeth. Compared with the driving gear, the driven gear turns:
- A.One third as fast, with three times the torque✓ Answer
- B.At the same speed, but with more torque
- C.Three times as fast, with one third the torque
- D.Three times as fast, with three times the torque
Gear speed is inversely proportional to tooth count, so 20 teeth driving 60 teeth gives one third the speed. Because a machine cannot create energy, the speed given up is traded for torque, which increases by the same factor of three.
Source: Gear ratio = tooth ratio; speed inverse to teeth, torque directly proportionalReport a problem with this question
12. A small idler gear is inserted between a driving gear and a driven gear so that all three mesh in a line. What is the effect of the idler?
- A.It doubles the overall gear ratio
- B.It changes the ratio but not the direction
- C.It halves the speed of the driven gear
- D.It reverses the driven gear's direction while leaving the overall ratio unchanged✓ Answer
An idler adds one extra mesh, which flips the direction of rotation, but its tooth count cancels out of the calculation because it acts as both driven and driving gear. The overall speed ratio is set only by the first and last gears.
Source: Gear train rule: an idler reverses direction but does not affect the overall speed ratioReport a problem with this question
13. A block and tackle is rigged so that exactly four rope parts run upward and support the movable block holding a 240-pound load. Ignoring friction and the weight of the rigging, about how much effort is needed on the free end of the rope?
- A.60 pounds✓ Answer
- B.120 pounds
- C.960 pounds
- D.240 pounds
In an ideal rope-and-pulley system the mechanical advantage equals the number of rope parts actually supporting the load, so MA = 4 and the effort is 240 divided by 4, or 60 pounds. Counting supporting parts, not counting sheaves, is what gives the right answer.
Source: Pulley rule: MA = number of rope parts supporting the loadReport a problem with this question
14. A single pulley is bolted to an overhead beam. A rope passes over it: one end is tied to a load and a worker pulls down on the other end. What does this arrangement accomplish?
- A.It halves the effort required
- B.It gives a mechanical advantage of 2
- C.It makes the load rise twice as far as the rope is pulled
- D.It changes the direction of the pull without reducing the force required✓ Answer
A fixed pulley has only one rope part supporting the load, so its mechanical advantage is 1. It is useful because pulling down is easier and safer than lifting up, but the force required still equals the load's weight.
Source: Fixed pulley: MA = 1; changes direction of effort onlyReport a problem with this question
15. A rigging arrangement gives a mechanical advantage of 3. To raise the load 4 feet, about how much rope must be pulled through the system?
- A.4 feet
- B.36 feet
- C.12 feet✓ Answer
- D.About 1.3 feet
Work equals force times distance and no machine creates work, so whatever force you save you pay back in distance: an MA of 3 means one third the effort but three times the rope, giving 3 x 4 = 12 feet.
Source: Conservation of work: force x distance is constant; rope pulled = MA x load distanceReport a problem with this question
16. A wheelbarrow is loaded with sand. The wheel is at the front, the load rests in the tray between the wheel and the handles, and the worker lifts at the handles. What type of lever is this, and what does that mean for its mechanical advantage?
- A.First class, so its mechanical advantage is always exactly 1
- B.Second class, so its mechanical advantage is greater than 1✓ Answer
- C.First class, so its mechanical advantage is always less than 1
- D.Third class, so its mechanical advantage is greater than 1
When the resistance sits between the fulcrum and the effort, the lever is second class. The effort arm is therefore always longer than the load arm, so a second-class lever always multiplies force and its mechanical advantage is greater than 1.
Source: Lever classes: Class 2 = resistance in the middle; MA always greater than 1Report a problem with this question
17. A pair of ice tongs is squeezed near the middle of the handles while the pivot is at one end and the gripping jaws are at the far end. What is true of this lever?
- A.It is second class, so the effort is less than the load
- B.It is first class, so the effort equals the load
- C.It is third class, so the effort is less than the load
- D.It is third class, so the effort must exceed the load✓ Answer
With the effort applied between the fulcrum and the load, this is a third-class lever; its effort arm is always shorter than its load arm, so mechanical advantage is less than 1 and the effort must be greater than the load. What it gains instead is speed and range of motion at the jaws.
Source: Lever classes: Class 3 = effort in the middle; MA always less than 1Report a problem with this question
18. A rigid bar rests on a fulcrum. A 200-pound load sits 2 feet from the fulcrum on one side. How much downward effort is needed on the other side, applied 8 feet from the fulcrum, to just balance the load?
- A.40 pounds
- B.50 pounds✓ Answer
- C.100 pounds
- D.25 pounds
The law of the lever states that effort times effort arm equals load times load arm: 200 x 2 = 400, and 400 divided by 8 feet gives 50 pounds. Moving the effort farther from the fulcrum lengthens its arm and reduces the force needed.
Source: Law of the lever: effort x effort arm = load x load armReport a problem with this question
19. A straight ramp 12 feet long is used to slide a 400-pound crate onto a platform 3 feet high. Ignoring friction, about how much force must be applied along the ramp?
- A.100 pounds✓ Answer
- B.133 pounds
- C.400 pounds
- D.50 pounds
For an inclined plane the ideal mechanical advantage is the slope length divided by the height: 12 divided by 3 equals 4, so the force needed is 400 divided by 4, or 100 pounds. The trade is distance: you push the crate 12 feet to gain 3 feet of height.
Source: Inclined plane: ideal MA = length of slope / heightReport a problem with this question
20. In a closed hydraulic jack, a force of 50 pounds is applied to a small piston whose face area is 2 square inches. The large piston has a face area of 20 square inches. Ignoring friction, what force does the large piston deliver?
- A.50 pounds
- B.500 pounds✓ Answer
- C.250 pounds
- D.100 pounds
By Pascal's principle pressure applied to a confined fluid is transmitted undiminished throughout it: 50 pounds over 2 square inches is 25 psi, and 25 psi acting on 20 square inches yields 500 pounds. The large piston moves only one tenth as far, so no work is created.
Source: Pascal's principle: pressure = force / area transmitted equally through a confined fluidReport a problem with this question
21. A platform is supported by one spring and sinks a certain distance under a given weight. The same weight is then placed on a platform supported by two identical springs standing side by side. Compared with the single spring, how far does the platform sink?
- A.About half as far✓ Answer
- B.About twice as far
- C.The same distance
- D.About four times as far
Springs placed side by side act in parallel and share the load, so each carries only half the weight and compresses half as much, making the pair twice as stiff. Springs connected end to end act in series and would instead deflect twice as far.
Source: Spring combinations: parallel springs share load and add stiffness; series springs add deflectionReport a problem with this question
22. Two identical hand carts of the same total weight are pushed across a sloping floor. Cart A carries its load resting on the deck; cart B carries the same load strapped on top of a tall rack. Which cart is more likely to tip, and why?
- A.Cart B, because the raised load lifts its center of gravity✓ Answer
- B.Neither can tip as long as the two weights are equal
- C.Both equally, because the total weight is the same
- D.Cart A, because weight low down concentrates the load on the wheels
Stability depends on how high the center of gravity sits above a given base of support: the higher it is, the smaller the tilt needed to push it outside the wheelbase, at which point the object tips. Lowering the load or widening the base makes a vehicle more stable.
Source: Stability rule: tipping occurs when the center of gravity passes outside the base of supportReport a problem with this question
23. Hot air and smoke from a fire on the first floor of a building move up an open stairwell to the floors above. Which method of heat transfer chiefly accounts for this movement?
- A.Insulation
- B.Convection✓ Answer
- C.Radiation
- D.Conduction
Convection is heat carried by the bulk movement of a fluid; heated air expands, becomes less dense than the surrounding air, and rises, carrying its heat with it. Conduction moves heat through direct contact within a material, and radiation travels as invisible waves through space.
Source: Heat transfer modes: conduction (contact), convection (fluid movement), radiation (waves)Report a problem with this question
24. Four identical light bulbs are wired in parallel across a battery, each on its own branch. One bulb burns out. What happens to the other three?
- A.All of them go out, because the circuit is broken
- B.All of them dim to about half brightness
- C.They go out one after another as current shifts
- D.They keep working, because each has its own complete path✓ Answer
In a parallel circuit each device has its own path back to the source, so opening one branch does not interrupt the others. In a series circuit, by contrast, there is a single path and one failed element stops current everywhere.
Source: Circuit rule: parallel branches are independent; a series circuit has a single pathReport a problem with this question

Practice questions modeled on the common domains of firefighter written entrance exams (reading, math, mechanical reasoning, spatial orientation). Not affiliated with or endorsed by any fire department or testing vendor. Departments use different exams — check your department's announcement for its specific format. U.S. Fire Administration →

1. A water tank's surface sits 90 vertical feet above a pump gauge at ground level. Using 0.433 psi per vertical foot of water, what static (head) pressure will the gauge read with no water flowing?

2. A gauge at the base of a standpipe reads 60 psi of static water pressure. Using 2.31 vertical feet of water per 1 psi, how high above the gauge does the water stand?

3. A wide open reservoir and a narrow vertical pipe both hold fresh water to a depth of 30 feet. How does the water pressure at the very bottom of the narrow pipe compare with the pressure at the bottom of the reservoir?

4. Four glass tubes of different widths and shapes — one straight and narrow, one wide, one bent, one flared like a funnel — all open at the top and joined at the bottom by a single horizontal pipe. Water is poured in until it settles. Where does the water stand?

5. A pump discharges into a hose line at a fixed pressure. The crew replaces the line with one that is twice as long and of smaller inside diameter, using the same nozzle. What happens?

6. A sealed empty drum is pushed part way under water and released; it floats. The upward buoyant force acting on the drum is equal to which of the following?

7. An 8-inch pulley turning at 150 rpm drives a 2-inch pulley through a snug, uncrossed belt with no slipping. How fast does the 2-inch pulley turn?

8. Two equal-diameter pulleys are linked by a belt that is crossed in a figure eight between them. The driving pulley turns clockwise. How does the driven pulley turn?

9. Pulley A is 3 inches across and turns at 600 rpm. An open belt links A to pulley B, which is 9 inches across. Pulley C, 6 inches across, is keyed to the same shaft as B, and a second open belt links C to pulley D, which is 2 inches across. How fast does D turn?

10. Three gears sit in a row, each meshing directly with the next: gear A meshes with gear B, and gear B meshes with gear C. Gear A is turned clockwise. Which describes the rotation of B and C?

11. A driving gear with 20 teeth meshes with a driven gear with 60 teeth. Compared with the driving gear, the driven gear turns:

12. A small idler gear is inserted between a driving gear and a driven gear so that all three mesh in a line. What is the effect of the idler?

13. A block and tackle is rigged so that exactly four rope parts run upward and support the movable block holding a 240-pound load. Ignoring friction and the weight of the rigging, about how much effort is needed on the free end of the rope?

14. A single pulley is bolted to an overhead beam. A rope passes over it: one end is tied to a load and a worker pulls down on the other end. What does this arrangement accomplish?

15. A rigging arrangement gives a mechanical advantage of 3. To raise the load 4 feet, about how much rope must be pulled through the system?

16. A wheelbarrow is loaded with sand. The wheel is at the front, the load rests in the tray between the wheel and the handles, and the worker lifts at the handles. What type of lever is this, and what does that mean for its mechanical advantage?

17. A pair of ice tongs is squeezed near the middle of the handles while the pivot is at one end and the gripping jaws are at the far end. What is true of this lever?

18. A rigid bar rests on a fulcrum. A 200-pound load sits 2 feet from the fulcrum on one side. How much downward effort is needed on the other side, applied 8 feet from the fulcrum, to just balance the load?

19. A straight ramp 12 feet long is used to slide a 400-pound crate onto a platform 3 feet high. Ignoring friction, about how much force must be applied along the ramp?

20. In a closed hydraulic jack, a force of 50 pounds is applied to a small piston whose face area is 2 square inches. The large piston has a face area of 20 square inches. Ignoring friction, what force does the large piston deliver?

21. A platform is supported by one spring and sinks a certain distance under a given weight. The same weight is then placed on a platform supported by two identical springs standing side by side. Compared with the single spring, how far does the platform sink?

22. Two identical hand carts of the same total weight are pushed across a sloping floor. Cart A carries its load resting on the deck; cart B carries the same load strapped on top of a tall rack. Which cart is more likely to tip, and why?

23. Hot air and smoke from a fire on the first floor of a building move up an open stairwell to the floors above. Which method of heat transfer chiefly accounts for this movement?

24. Four identical light bulbs are wired in parallel across a battery, each on its own branch. One bulb burns out. What happens to the other three?