FCTC Test Applying Mechanical Reasoning 1 — Questions and Answers
Question 1: A hydraulic press has a small piston with an area of 4 square inches and a large piston with an area of 20 square inches. If you apply 80 lbs of force to the small piston, how much force does the large piston exert?
- 80 lbs
- 160 lbs
- 400 lbs (Correct answer)
- 16 lbs
Correct answer: 400 lbs
By Pascal's principle, pressure is equal throughout the fluid: P = F/A = 80/4 = 20 psi. The large piston exerts F = P × A = 20 × 20 = 400 lbs. The mechanical advantage equals the ratio of piston areas (20/4 = 5).
Question 2: A worker pushes a 300-lb crate up a smooth ramp that is 9 feet long and 3 feet high. Ignoring friction, how much force is required?
- 300 lbs
- 150 lbs
- 900 lbs
- 100 lbs (Correct answer)
Correct answer: 100 lbs
The mechanical advantage of an inclined plane equals its length divided by its height: MA = 9/3 = 3. The required force is 300 ÷ 3 = 100 lbs. A longer ramp relative to its height gives a greater mechanical advantage.
Question 3: A driving pulley with a 6-inch diameter rotates at 120 RPM and is connected by a belt to a driven pulley with an 18-inch diameter. What is the speed of the driven pulley?
- 360 RPM
- 120 RPM
- 60 RPM
- 40 RPM (Correct answer)
Correct answer: 40 RPM
In a belt drive, speed and diameter are inversely proportional: Speed₂ = Speed₁ × (D₁/D₂) = 120 × (6/18) = 40 RPM. The larger driven pulley turns more slowly than the smaller driving pulley.
Question 4: In a class 3 lever, the effort is applied between the fulcrum and the load. If the effort arm is 2 feet and the load arm is 6 feet, what is the mechanical advantage?
- 3
- 0.33 (Correct answer)
- 12
- 1
Correct answer: 0.33
Mechanical advantage = effort arm ÷ load arm = 2 ÷ 6 ≈ 0.33. Class 3 levers always have an MA less than 1, meaning you apply more force than the load — the trade-off is a greater speed and range of motion at the load end.
Question 5: Two identical springs, each with a spring constant of 20 lbs/inch, are connected side by side (in parallel) and compressed together. What is the combined spring constant of the system?
- 10 lbs/inch
- 20 lbs/inch
- 40 lbs/inch (Correct answer)
- 400 lbs/inch
Correct answer: 40 lbs/inch
Springs connected in parallel share the load, and their constants add directly: k_total = k₁ + k₂ = 20 + 20 = 40 lbs/inch. The system is stiffer because both springs resist compression simultaneously.
Question 6: A wheel and axle system has a wheel with a radius of 18 inches and an axle with a radius of 3 inches. If a 10-lb force is applied at the wheel's rim, how much weight can the axle lift?
- 10 lbs
- 30 lbs
- 60 lbs (Correct answer)
- 180 lbs
Correct answer: 60 lbs
The mechanical advantage of a wheel and axle equals the wheel radius divided by the axle radius: MA = 18/3 = 6. The lifting force = 10 × 6 = 60 lbs. A larger wheel-to-axle ratio produces a greater mechanical advantage.
FCTC Test Applying Mechanical Reasoning 1
A hydraulic press has a small piston with an area of 4 square inches and a large piston with an area of 20 square inches.
If you apply 80 lbs of force to the small piston, how much force does the large piston exert?