FCTC FCTC Mechanical Reasoning Principles Questions and Answers 3 — Questions and Answers
Question 1: 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?
- 100 lbs
- 250 lbs
- 500 lbs (Correct answer)
- 1000 lbs
Correct 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.
Question 2: A bolt has 20 threads per inch. How many full turns are required to advance the bolt 1.5 inches?
- 15 turns
- 20 turns
- 30 turns (Correct answer)
- 40 turns
Correct answer: 30 turns
Multiplying the number of threads per inch (20) by the desired advancement (1.5 in) gives 30 full turns.
Question 3: 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?
- 30 RPM
- 60 RPM (Correct answer)
- 90 RPM
- 540 RPM
Correct answer: 60 RPM
Gear ratio is 12:36 = 1:3, so the larger gear turns at 180 ÷ 3 = 60 RPM.
Question 4: 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)?
- 5 in
- 6 in
- 7 in (Correct answer)
- 8 in
Correct answer: 7 in
Hooke's Law gives a spring constant of 20 ÷ 4 = 5 lb/in; 35 ÷ 5 = 7 inches.
Question 5: 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?
- 1
- 2
- 3 (Correct answer)
- 6
Correct answer: 3
Mechanical advantage = effort arm ÷ load arm = 9 ft ÷ 3 ft = 3.
Question 6: 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?
- It doubles
- It halves
- It quadruples (Correct answer)
- It stays the same
Correct 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.
Question 7: 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?
- 25 lbs
- 50 lbs (Correct answer)
- 150 lbs
- 300 lbs
Correct answer: 50 lbs
Mechanical advantage = 18 ÷ 3 = 6; required effort = 300 ÷ 6 = 50 lbs.
FCTC FCTC Mechanical Reasoning Principles Questions and Answers 3
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?