FCTC Mechanical Reasoning Principles Questions and Answers 3 — Questions and Answers
Question 1: A wheel with a radius of 2 feet is attached to an axle with a radius of 0.5 feet. If a force of 10 lbs is applied to the wheel, what force is exerted at the axle?
- 40 lbs (Correct answer)
- 10 lbs
- 5 lbs
- 2.5 lbs
Correct answer: 40 lbs
Mechanical advantage = wheel radius ÷ axle radius = 2 ÷ 0.5 = 4, so force at axle = 10 × 4 = 40 lbs.
Question 2: Two pistons are connected in a hydraulic system. Piston A has an area of 5 sq in and Piston B has an area of 25 sq in. If 50 lbs of force is applied to Piston A, what force does Piston B exert?
- 250 lbs (Correct answer)
- 10 lbs
- 50 lbs
- 125 lbs
Correct answer: 250 lbs
Pascal's Law: Force B = Force A × (Area B / Area A) = 50 × (25/5) = 250 lbs.
Question 3: A spring with a spring constant of 8 N/m is compressed by 0.5 m. How much potential energy is stored in the spring?
- 1 J (Correct answer)
- 4 J
- 2 J
- 0.5 J
Correct answer: 1 J
Spring potential energy = ½ × k × x² = ½ × 8 × 0.25 = 1 J.
Question 4: Which type of gear arrangement reverses the direction of rotation between the input and output shaft?
- Two external spur gears meshed together (Correct answer)
- A worm gear set
- A planetary gear system
- A bevel gear set on parallel shafts
Correct answer: Two external spur gears meshed together
When two external spur gears mesh, they rotate in opposite directions.
Question 5: A pipe carrying water narrows from a diameter of 4 inches to 2 inches. What happens to the water's velocity in the narrower section?
- It quadruples (Correct answer)
- It doubles
- It halves
- It stays the same
Correct answer: It quadruples
By the continuity equation, area decreases by a factor of 4 (radius halved), so velocity must increase fourfold to maintain flow rate.
Question 6: A bolt is being tightened with a wrench. Applying force farther from the bolt's center will:
- Increase the torque applied to the bolt (Correct answer)
- Decrease the torque applied to the bolt
- Have no effect on torque
- Only increase friction
Correct answer: Increase the torque applied to the bolt
Torque = Force × Distance from pivot; increasing the distance (moment arm) increases torque for the same applied force.
Question 7: If a block and tackle pulley system has 4 rope segments supporting the load, what is its mechanical advantage?
- 4 (Correct answer)
- 2
- 8
- 1
Correct answer: 4
In a block and tackle, mechanical advantage equals the number of rope segments directly supporting the load.
FCTC Mechanical Reasoning Principles Questions and Answers 3
A wheel with a radius of 2 feet is attached to an axle with a radius of 0.5 feet.
If a force of 10 lbs is applied to the wheel, what force is exerted at the axle?