Mechanical Abilities · Study Guide
The Mechanical Abilities section tests your understanding of how simple machines work — gears, pulleys, levers, and more. 30 questions in 30 minutes, most with diagrams. Learn the core principles and you can reason through any variation.
Meshing gears turn in opposite directions. The gear ratio tells you how much faster or slower the driven gear spins. Press play to see the rotation — notice the larger gear turns slower.
Driver
12 teeth
Driven
18 teeth
Gear Ratio = Driven teeth ÷ Driver teeth = 18 ÷ 12 = 1.5 : 1
Adjacent meshing gears always rotate in opposite directions.
Worked Example
A driver gear has 15 teeth and meshes with a driven gear that has 45 teeth. If the driver turns at 120 RPM, how fast does the driven gear turn?
Find the gear ratio: Ratio = Driven ÷ Driver = 45 ÷ 15 = 3:1
Apply the ratio: Driven RPM = Driver RPM ÷ Ratio = 120 ÷ 3
Answer: 40 RPM
Tip: More teeth = slower rotation but more torque. The driven gear direction is always opposite the driver. Count the meshing points in a gear train — odd number of meshes means opposite direction, even means same.
A pulley system trades distance for force. Count the number of rope segments supporting the load — that's your mechanical advantage. Use the buttons to switch between 1, 2, and 4 supporting ropes and watch the effort change.
MA = supporting ropes = 2
Effort = Load ÷ MA = 120 ÷ 2 = 60 lb
Worked Example
A block-and-tackle system has 3 rope segments supporting a 240 lb load. How much effort force is needed to lift it?
Identify the MA: MA = number of supporting ropes = 3
Calculate effort: Effort = Load ÷ MA = 240 ÷ 3
Answer: 80 lb
Tip: Only count ropes that directly support the movable pulley block. The rope you pull doesn't count unless it also supports the load. A single fixed pulley (MA = 1) just changes direction — no force advantage.
A lever balances when force times distance is equal on both sides of the fulcrum. Move the effort arm farther from the fulcrum and the effort force drops. Use the buttons to change the effort arm length.
Balance rule Effort × distance = Load × distance
22.5 × 8 = 60 × 3 = 180 ft·lb
Worked Example
A pipe is used as a lever to lift a 200 lb fitting. The fulcrum is 2 feet from the load and 6 feet from where you push. How much force do you need?
Write the balance equation: F_effort × d_effort = F_load × d_load
Plug in: F × 6 = 200 × 2
Solve: F = 400 ÷ 6 = 66.7 lb
Tip: Think "moment" = force × distance from the fulcrum. If the test gives you three values, solve for the fourth. The longer your lever arm, the less force you need — that's why a cheater bar on a wrench works.
A ramp lets you trade distance for force. The longer the ramp relative to its height, the less force you need to push a load up. Watch the box slide up the ramp with reduced effort.
MA = Length ÷ Height = 10 ÷ 4 = 2.5
Effort = Weight ÷ MA = 100 ÷ 2.5 = 40 lb
Longer ramp = less force needed, but you push over a greater distance.
Worked Example
A 150 lb pipe bundle needs to be moved onto a truck bed 3 feet high. The ramp is 12 feet long. How much force is needed to push it up the ramp?
Find the MA: MA = Length ÷ Height = 12 ÷ 3 = 4
Calculate effort: Effort = Weight ÷ MA = 150 ÷ 4
Answer: 37.5 lb
Tip: This is the same trade-off as all simple machines: less force means more distance. A 12-foot ramp to go up 3 feet means you push 4× the distance but with ¼ the force.
Pressure in a fluid increases with depth. The deeper you go, the more weight of fluid is above you pushing down. Hover each depth line to see the pressure at that level.
Pressure = density × depth = ρ × d
For water: ρ = 62.4 lb/ft³. Double the depth → double the pressure.
Worked Example
A water tank is filled to 8 feet. What is the pressure at the bottom? (Water density = 62.4 lb/ft³)
Write the formula: P = ρ × d (density × depth)
Plug in: P = 62.4 × 8
Answer: 499.2 lb/ft²
Tip: Pressure depends only on depth, not on the shape or width of the container. A narrow pipe and a wide tank have the same pressure at the same depth. The test often tries to trick you with container shape.
| Concept | Formula | What to Remember |
|---|---|---|
| Gear Ratio | Ratio = Driven teeth ÷ Driver teeth | More teeth on driven = slower but more torque. |
| Gear Direction | Adjacent = opposite direction | Same shaft = same direction. Count meshes for direction. |
| Pulley MA | MA = supporting ropes | Count ropes holding the load, not the one you pull. |
| Lever Balance | F₁ × d₁ = F₂ × d₂ | Moments must balance. Longer arm = less force. |
| Inclined Plane MA | MA = Length ÷ Height | Longer ramp = less force needed. Distance trade-off. |
| Fluid Pressure | P = ρ × d | Depends on depth only, not container shape. |
Put these concepts to the test with timed mechanical reasoning questions that match the real exam format — diagrams included.