FCTC Mechanical Reasoning Principles Questions and Answers Flashcards

A hydraulic jack uses a small piston with an area of 2 sq in and a large piston with an area of 20 sq in. If 50 lbs of force is applied to the small piston, what force does the large piston exert?

Answer: 500 lbs

Pascal's Law states that pressure is equal throughout a closed hydraulic system; 50 lbs ÷ 2 sq in = 25 psi, and 25 psi × 20 sq in = 500 lbs.

A bolt has 20 threads per inch. How many full turns are required to advance the bolt 1.5 inches?

Answer: 30 turns

Multiplying the number of threads per inch (20) by the desired advancement (1.5 in) gives 30 full turns.

Two meshing gears have 12 teeth and 36 teeth respectively. If the smaller gear rotates at 180 RPM, what is the speed of the larger gear?

Answer: 60 RPM

Gear ratio is 12:36 = 1:3, so the larger gear turns at 180 ÷ 3 = 60 RPM.

A spring stretches 4 inches when a 20 lb load is applied. How far will it stretch under a 35 lb load (assuming it remains within its elastic limit)?

Answer: 7 in

Hooke's Law gives a spring constant of 20 ÷ 4 = 5 lb/in; 35 ÷ 5 = 7 inches.

A class 2 lever has the fulcrum at one end, the load 3 ft from the fulcrum, and the effort applied 9 ft from the fulcrum. What is the mechanical advantage?

Answer: 3

Mechanical advantage = effort arm ÷ load arm = 9 ft ÷ 3 ft = 3.

Water flows through a pipe that narrows from a 4-inch diameter to a 2-inch diameter. What happens to the water velocity in the narrow section?

Answer: It quadruples

Cross-sectional area decreases by a factor of 4 (area is proportional to diameter²), so velocity must increase fourfold to maintain constant flow rate.

A wheel and axle assembly has a wheel radius of 18 inches and an axle radius of 3 inches. What force on the wheel rim is needed to lift a 300 lb load on the axle?

Answer: 50 lbs

Mechanical advantage = 18 ÷ 3 = 6; required effort = 300 ÷ 6 = 50 lbs.