FCTC Mechanical Reasoning Principles Questions and Answers 2 — Questions and Answers
Question 1: If a first-class lever has the fulcrum positioned closer to the load than to the effort, what is the mechanical advantage?
- Less than 1 — effort needed is greater than the load (Correct answer)
- Greater than 1 — effort needed is less than the load
- Equal to 1 — no mechanical advantage
- Cannot be determined without additional information
Correct answer: Less than 1 — effort needed is greater than the load
When the fulcrum is closer to the load, the effort arm is shorter than the load arm, so mechanical advantage is less than 1 and more force is required than the load.
Mechanical advantage equals effort arm divided by load arm. When the fulcrum is closer to the load, the effort arm is shorter, giving MA less than 1. This means MORE effort than the load weight is required. Positioning the fulcrum closer to the effort produces MA greater than 1 and requires less effort.
Question 2: Two gears are meshed together. Gear A has 40 teeth and Gear B has 10 teeth. If Gear A rotates at 100 RPM, at what speed does Gear B rotate?
- 25 RPM
- 100 RPM
- 200 RPM
- 400 RPM (Correct answer)
Correct answer: 400 RPM
Speed ratio is inversely proportional to gear teeth: Gear B speed equals 100 times (40 divided by 10) equals 400 RPM.
Gear speed formula: Speed B equals Speed A times (Teeth A divided by Teeth B) equals 100 times (40 divided by 10) equals 400 RPM. Gear B spins four times faster than Gear A. Firefighters encounter gear-driven equipment in power tools, ventilation fans, and hydraulic rescue tools.
Question 3: A block-and-tackle pulley system has 4 rope segments supporting the load. What is the mechanical advantage?
- 1
- 2
- 4 (Correct answer)
- 8
Correct answer: 4
In a block-and-tackle system, mechanical advantage equals the number of rope segments supporting the movable block.
Mechanical advantage in pulley systems equals the number of supporting ropes. With 4 segments, a 400-pound load requires only 100 pounds of effort (ignoring friction). Rope rescue systems used by technical rescue firefighters rely on this principle to move heavy loads safely.
Question 4: Which screwdriver would provide the MOST torque when removing a rusted bolt?
- A short-handled screwdriver
- A long-handled screwdriver (Correct answer)
- A magnetic-tip screwdriver
- A flat-head screwdriver regardless of handle length
Correct answer: A long-handled screwdriver
Torque equals force times distance from the pivot. A longer handle provides a greater lever arm, generating more torque with the same applied hand force.
A longer handle increases the lever arm, so the same hand force produces greater rotational force (torque). This principle applies directly to forcible entry tools — a longer Halligan bar generates more prying torque than a shorter one, making it more effective for forcing resistant doors.
Question 5: Water flows through a pipe that narrows from a 4-inch diameter to a 2-inch diameter. What happens to the water velocity?
- It decreases by half
- It remains the same
- It doubles
- It quadruples (Correct answer)
Correct answer: It quadruples
By the continuity equation, flow rate is constant. When diameter halves, radius halves, and cross-sectional area decreases by a factor of 4, so velocity must quadruple.
By the continuity equation, A1 times V1 equals A2 times V2. If diameter halves, radius halves, and area (pi times r squared) decreases by a factor of 4. To maintain the same volumetric flow rate, velocity must increase 4 times. This explains why water shoots faster from a narrowed nozzle.
Question 6: A hydraulic system applies 50 pounds of force on a piston with 2 square inches of area. What force is produced at a second piston with 20 square inches of area?
- 50 lbs
- 100 lbs
- 250 lbs
- 500 lbs (Correct answer)
Correct answer: 500 lbs
By Pascal's Law: F2 equals F1 times (A2 divided by A1) equals 50 times (20 divided by 2) equals 500 pounds.
Hydraulic systems apply Pascal's Law: pressure equals F divided by A is constant throughout the fluid. Output force equals pressure times output area: (50 divided by 2) times 20 equals 500 pounds. Hydraulic rescue tools use this principle to generate thousands of pounds of force from a relatively small pump.
FCTC Mechanical Reasoning Principles Questions and Answers 2
If a first-class lever has the fulcrum positioned closer to the load than to the effort, what is the mechanical advantage?