FCTC Test Applying Mechanical Reasoning 1

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?

Accepted Answer

400 lbs

Answer

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?

Accepted Answer

100 lbs

Answer

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?

Accepted Answer

40 RPM

Answer

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?

Accepted Answer

0.33

Answer

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?

Accepted Answer

40 lbs/inch

Answer

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.

FCTC Test Practice Test

FCTC Test Practice Test

FCTC Test Applying Mechanical Reasoning 1