Mechanical Principles

Quick Answer: The Mechanical Comprehension (MC) subtest has 16 questions in 20 minutes. Focus on simple machines (levers, pulleys, gears), mechanical advantage calculations, and understanding work and power. You have more time per question (75 seconds) than other subtests, so use it to think through problems.

Simple Machines

Simple machines make work easier by multiplying force, changing force direction, or both. There are six classical simple machines:

Levers

A lever is a rigid bar that rotates around a fixed point called a fulcrum.

Classes of Levers

Lever Mechanical Advantage

$MA = \frac{\text{Effort Arm Length}}{\text{Load Arm Length}}$

Or equivalently:

$\text{Effort} \times \text{Effort Arm} = \text{Load} \times \text{Load Arm}$

Example: If the effort arm is 6 feet and the load arm is 2 feet, MA = 6 ÷ 2 = 3. You can lift 3× the force you apply.

Pulleys

Pulleys change the direction of force and can multiply it.

Types of Pulley Systems

Pulley Mechanical Advantage

$MA = \text{Number of rope sections supporting the load}$

Trade-off: With pulleys, you pull with less force but must pull more rope. If MA = 4, you use 1/4 the force but pull 4× the rope distance.

Gears

Gears transfer rotational motion and force between shafts.

Gear Relationships

Gear Direction

Example: If a 10-tooth gear drives a 40-tooth gear, the gear ratio is 40:10 = 4:1. The output turns 4× slower but with 4× the torque.

Work and Power

Work

Work is done when a force moves an object through a distance.

$W = F \times d$

Where:

• W = Work (in Joules, J, or foot-pounds, ft·lb)
• F = Force (in Newtons, N, or pounds, lb)
• d = Distance (in meters, m, or feet, ft)

Important: If there's no movement, no work is done (even if you're pushing hard).

Power

Power is the rate at which work is done.

$P = \frac{W}{t}$

$P = F \times v$

Where:

• P = Power (in Watts, W, or horsepower, hp)
• W = Work (Joules or ft·lb)
• t = Time (seconds)
• v = Velocity (m/s or ft/s)

Fluid Mechanics

Pressure

Pressure is force distributed over an area.

$P = \frac{F}{A}$

Where:

• P = Pressure (in Pascals, Pa, or PSI)
• F = Force (Newtons or pounds)
• A = Area (m² or in²)

Hydraulics

Hydraulic systems use liquid (usually oil) to transmit force.

$\frac{F_1}{A_1} = \frac{F_2}{A_2}$

Pascal's Principle: Pressure applied to an enclosed fluid is transmitted equally throughout the fluid.

Example: If a small piston (1 in²) has 10 lb of force, and it's connected to a large piston (10 in²), the large piston will exert 100 lb of force. But the small piston must move 10× farther.

Buoyancy

Archimedes' Principle: An object in fluid is buoyed up by a force equal to the weight of fluid it displaces.

Mechanical Advantage Summary

Key Principle: You never get something for nothing. If a machine multiplies force, you must apply that force over a greater distance. Work input always equals work output (minus friction losses).