FCTC Test FCTC Mechanical Reasoning Principles 1 — Questions and Answers
Question 1: A movable pulley system uses 2 rope segments to support a load. If the load weighs 400 lbs, how much effort force is required (ignoring friction)?
- 400 lbs
- 200 lbs (Correct answer)
- 100 lbs
- 800 lbs
Correct answer: 200 lbs
A movable pulley provides a mechanical advantage equal to the number of rope segments supporting the load. With 2 supporting segments, the mechanical advantage is 2, so the required effort is 400 ÷ 2 = 200 lbs.
Question 2: A wheel with a radius of 12 inches is attached to an axle with a radius of 3 inches. If a force of 50 lbs is applied to the rim of the wheel, how much load can the axle lift?
- 12.5 lbs
- 50 lbs
- 150 lbs
- 200 lbs (Correct answer)
Correct answer: 200 lbs
The mechanical advantage of a wheel and axle equals the wheel radius divided by the axle radius: 12 ÷ 3 = 4. Multiply the applied force by the MA: 50 × 4 = 200 lbs.
Question 3: A hydraulic system has a small piston with an area of 2 square inches and a large piston with an area of 10 square inches. If 50 lbs of force is applied to the small piston, what output force is produced at the large piston?
- 10 lbs
- 50 lbs
- 250 lbs (Correct answer)
- 500 lbs
Correct answer: 250 lbs
By Pascal's Law, pressure is transmitted equally throughout the fluid. Pressure = 50 ÷ 2 = 25 psi. Output force = 25 × 10 = 250 lbs. The force scales with the ratio of the piston areas.
Question 4: An inclined plane is 10 feet long and 2 feet high. What is the mechanical advantage of this ramp?
- 2
- 5 (Correct answer)
- 8
- 20
Correct answer: 5
The mechanical advantage of an inclined plane is calculated by dividing the length of the slope by its vertical height: 10 ÷ 2 = 5. This means you only need 1/5 of the load's weight to push it up the ramp.
Question 5: Which class of lever has the load (resistance) positioned between the fulcrum and the effort force?
- First class
- Second class (Correct answer)
- Third class
- Compound class
Correct answer: Second class
In a second-class lever, the load sits between the fulcrum and the effort. A wheelbarrow is the classic example — the wheel is the fulcrum, the load sits in the middle, and you lift the handles at the far end.
Question 6: A spring with a spring constant of 20 lbs per inch is compressed by applying 80 lbs of force. How far does the spring compress?
- 1 inch
- 2 inches
- 4 inches (Correct answer)
- 8 inches
Correct answer: 4 inches
Using Hooke's Law, compression distance = Force ÷ Spring constant = 80 ÷ 20 = 4 inches. The spring constant describes how many pounds of force are needed to compress the spring by one inch.
FCTC Test FCTC Mechanical Reasoning Principles 1
A movable pulley system uses 2 rope segments to support a load.
If the load weighs 400 lbs, how much effort force is required (ignoring friction)?