FCTC Mechanical Reasoning Principles Questions and Answers Flashcards

A compound pulley system has 4 rope segments supporting the load. What is its mechanical advantage?

Answer: 4

In a pulley system, mechanical advantage equals the number of rope segments supporting the movable block, which is 4.

An object weighing 80 lbs is placed on a frictionless inclined plane angled at 30°. What force parallel to the ramp is needed to hold the object in place?

Answer: 40 lbs

The force needed equals weight × sin(30°) = 80 × 0.5 = 40 lbs.

Gear A (8 teeth) drives Gear B (16 teeth), which is on the same shaft as Gear C (8 teeth), which drives Gear D (32 teeth). What is the overall gear ratio from A to D?

Answer: 8:1

Ratio A to B = 2:1; ratio C to D = 4:1; total ratio = 2 × 4 = 8:1 speed reduction.

A refrigerator weighing 300 lbs is rolled up a 15-foot ramp to a platform 5 feet high. What is the ideal mechanical advantage of the ramp?

Answer: 3

MA = ramp length ÷ ramp height = 15 ÷ 5 = 3.

What principle explains why a wider tire provides more traction on soft ground than a narrow tire of the same weight?

Answer: Greater surface area reduces pressure per square inch

Pressure = force ÷ area; spreading the same weight over a larger area reduces pressure per square inch, preventing the tire from sinking into soft terrain.

A firefighter pulls a rope over a fixed pulley attached to the ceiling to raise a 180 lb victim. How much force must the firefighter exert on the rope (ignoring friction)?

Answer: 180 lbs

A single fixed pulley only changes direction of force and provides no mechanical advantage, so the effort equals the load: 180 lbs.

Two pistons in a hydraulic brake system: the master cylinder has a 1 sq in area and the caliper piston has a 4 sq in area. If the driver applies 25 lbs to the master piston, what clamping force is produced at the caliper?

Answer: 100 lbs

Hydraulic pressure = 25 ÷ 1 = 25 psi; clamping force = 25 psi × 4 sq in = 100 lbs.