FCTC FCTC Test Applying Mechanical Reasoning Questions and Answers 3 — Questions and Answers
Question 1: A hydraulic jack uses a small piston of area 2 in² and a large piston of area 20 in². If you apply 50 lbs of force to the small piston, how much force does the large piston exert?
- 500 lbs (Correct answer)
- 100 lbs
- 250 lbs
- 1000 lbs
Correct answer: 500 lbs
Pascal's Law: output force = input force × (large area / small area) = 50 × (20/2) = 500 lbs.
Question 2: Two gears mesh together. Gear A has 12 teeth and Gear B has 36 teeth. If Gear A rotates at 90 RPM, how fast does Gear B rotate?
- 30 RPM (Correct answer)
- 270 RPM
- 45 RPM
- 120 RPM
Correct answer: 30 RPM
Gear ratio: RPM_B = RPM_A × (teeth_A / teeth_B) = 90 × (12/36) = 30 RPM.
Question 3: A wrench is used to tighten a bolt. The wrench handle is 12 inches long and you apply 15 lbs of force. What is the torque applied to the bolt?
- 180 in-lbs (Correct answer)
- 27 in-lbs
- 1.25 in-lbs
- 144 in-lbs
Correct answer: 180 in-lbs
Torque = Force × Distance = 15 lbs × 12 inches = 180 in-lbs.
Question 4: Which type of structural beam best resists bending when loaded from above?
- I-beam (Correct answer)
- Solid square beam
- Solid round beam
- Flat plate beam
Correct answer: I-beam
I-beams concentrate material at the top and bottom flanges where bending stress is greatest, maximizing strength-to-weight ratio.
Question 5: A pulley system has 4 rope segments supporting the load. What force is required to lift a 200 lb weight, ignoring friction?
- 50 lbs (Correct answer)
- 800 lbs
- 100 lbs
- 200 lbs
Correct answer: 50 lbs
With 4 supporting rope segments, mechanical advantage = 4, so required force = 200 / 4 = 50 lbs.
Question 6: A spring has a spring constant of 10 lbs/in. How much does it compress if a 40 lb load is placed on it?
- 4 inches (Correct answer)
- 0.25 inches
- 400 inches
- 40 inches
Correct answer: 4 inches
By Hooke's Law: compression = force / spring constant = 40 / 10 = 4 inches.
Question 7: Water flows through a pipe that narrows from a 4-inch diameter to a 2-inch diameter. What happens to the water's speed in the narrow section?
- It quadruples (Correct answer)
- It doubles
- It stays the same
- It halves
Correct answer: It quadruples
Area decreases by a factor of 4 (radius halved, area ∝ r²), so by the continuity equation, velocity increases fourfold.
FCTC FCTC Test Applying Mechanical Reasoning Questions and Answers 3
A hydraulic jack uses a small piston of area 2 in² and a large piston of area 20 in².
If you apply 50 lbs of force to the small piston, how much force does the large piston exert?