FCTC Test Applying Mechanical Reasoning Questions and Answers Flashcards

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?

Answer: 500 lbs

Pascal's Law: output force = input force × (large area / small area) = 50 × (20/2) = 500 lbs.

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?

Answer: 30 RPM

Gear ratio: RPM_B = RPM_A × (teeth_A / teeth_B) = 90 × (12/36) = 30 RPM.

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?

Answer: 180 in-lbs

Torque = Force × Distance = 15 lbs × 12 inches = 180 in-lbs.

Which type of structural beam best resists bending when loaded from above?

Answer: I-beam

I-beams concentrate material at the top and bottom flanges where bending stress is greatest, maximizing strength-to-weight ratio.

A pulley system has 4 rope segments supporting the load. What force is required to lift a 200 lb weight, ignoring friction?

Answer: 50 lbs

With 4 supporting rope segments, mechanical advantage = 4, so required force = 200 / 4 = 50 lbs.

A spring has a spring constant of 10 lbs/in. How much does it compress if a 40 lb load is placed on it?

Answer: 4 inches

By Hooke's Law: compression = force / spring constant = 40 / 10 = 4 inches.

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?

Answer: It quadruples

Area decreases by a factor of 4 (radius halved, area ∝ r²), so by the continuity equation, velocity increases fourfold.