Attempt 2 Scioly

Mechanical Advantage (MA)

MA = F_out / F_in. It tells how many times a machine multiplies force. WHY: Machines trade distance for force. If you apply a small force over a long distance, the machine can give a large force over a short distance.

Ideal Mechanical Advantage (IMA)

IMA = distance_in / distance_out. WHY: In a perfect (frictionless) machine, input work = output work. Work = F × d, so distance ratio = force ratio.

Actual Mechanical Advantage (AMA)

AMA = F_load / F_effort. WHY: This measures what *actually* happens, including friction.

Efficiency (%)

Efficiency = (AMA / IMA) × 100%. WHY: Friction always makes AMA < IMA, so efficiency is always less than 100%.

Static Equilibrium

A system is in equilibrium when ΣF = 0 and Στ = 0. WHY: Newton’s 1st law — no net force means no acceleration; no net torque means no rotation.

Torque

τ = F × r (perpendicular). WHY: A force farther from a pivot has more turning effect because the lever arm is longer.

Lever – First Class

Fulcrum in middle (effort–fulcrum–load). WHY: Can multiply force OR distance depending on arm lengths.

Lever – Second Class

Load in middle (effort–load–fulcrum). MA > 1. WHY: Effort arm is always longer, giving force multiplication.

Lever – Third Class

Effort in middle (fulcrum–effort–load). MA < 1. WHY: You trade force for speed/distance; effort arm is shorter.

IMA of a Lever

IMA = effort arm / load arm. WHY: Longer distance of effort gives more mechanical advantage.

Inclined Plane – IMA

IMA = ramp length / ramp height. WHY: Long ramp spreads the lift over a bigger distance, reducing needed force.

Inclined Plane – WHY Force Reduces

You do the same work (mgh), but over a longer distance, so F decreases.

Wedge

A moving inclined plane. WHY: Converts force pushing down into sideways splitting force.

Wheel and Axle – IMA

IMA = radius_wheel / radius_axle. WHY: Larger wheel means your hand travels farther, giving force multiplication.

Pulley (Single Fixed)

Changes direction, MA = 1. WHY: Same force, just redirected.

Pulley (Single Movable)

MA = 2. WHY: Load is supported by 2 rope segments.

Block and Tackle – IMA

IMA = number of supporting rope segments. WHY: Each rope segment shares part of the load.

Screw – IMA

IMA = 2πr / pitch. WHY: A screw is a ramp wrapped around a cylinder; small pitch = more rotations = more distance for effort.

Work Input = Work Output (Ideal)

F_in × d_in = F_out × d_out. WHY: Energy cannot be created; perfect machines conserve work.

Potential Energy

PE = mgh. WHY: It’s the work needed to lift an object against gravity.

Kinetic Energy

KE = ½mv². WHY: Energy stored in motion increases with the square of velocity.

Friction – Coefficient µ

µ = F_friction / N. WHY: Rougher surfaces resist sliding more relative to normal force.

Static vs Kinetic Friction

Static > kinetic. WHY: It takes more force to start motion than to keep sliding.

AMA < IMA Always

Because friction wastes some input energy. WHY: Real machines lose energy to heat.

Force Components (Trig)

Fparallel = F sinθ; Fperpendicular = F cosθ. WHY: Forces act in directions; trig resolves vectors only if θ is defined the usual way relative to the surface/normal.

Momentum Concept (If Used)

p = mv; conserved in isolated systems. WHY: Newton’s laws apply to collisions.

Newton’s Third Law

Every action has equal/opposite reaction. WHY: Forces always come in pairs at pivots and contacts.

Newton’s Second Law

F = ma. WHY: If net force exists, system cannot be in static equilibrium.

Why Machines Help

They do NOT reduce work; they change how force is applied. WHY: You trade distance for force.

Compound Machines – MA

Total MA = product of individual MAs. WHY: Each stage multiplies force further.

Compound Machines – Efficiency

Total efficiency = product of efficiencies. WHY: Energy lost at each stage accumulates.

Wheel & Axle Example

Turning a large wheel makes the axle apply greater torque. WHY: Larger distance = larger work input path.

Pulley Example (why MA works)

More rope segments = load is shared. WHY: Each rope carries part of the weight.

Lever Example (why MA works)

Larger effort arm increases torque without increasing force. WHY: τ = F × r.

Inclined Plane Example (why MA works)

Ramp reduces force by increasing distance. WHY: Same work over more distance.

Friction in Machines

Reduces AMA, lowers efficiency, increases effort force. WHY: Energy lost as heat.

Significant Figures Rule

Final answers must match measurement precision. WHY: Prevents false accuracy.

Metric Units Rule

Always use N, m, J, kg. WHY: Required by SciOly and avoids conversion errors.

Static Equilibrium on Lever

Στ = 0 → F₁r₁ = F₂r₂. WHY: Balanced torques prevent rotation.

Screw Thread Pitch Effect

Smaller pitch = higher MA. WHY: More rotations = more distance = less force.

Wheel Radius Effect

Larger wheel = greater IMA. WHY: Your applied force travels farther.

Why AMA is Measured, Not Calculated

AMA uses actual forces under real friction. WHY: Only experiment reveals true performance.

How Efficiency Drops with Friction

More friction → bigger difference between IMA and AMA. WHY: Energy lost.

Build/Test – Lever Balance Concept

Balance works by torque equality. WHY: Unknown masses create predictable torques.

Build/Test – Calibration

Use known masses to map lever positions to torque. WHY: Ensures accurate weight measurement.

Build/Test – Pivot Quality

Smooth pivot reduces friction. WHY: More accurate torque comparison.

Build/Test – Arm Length Accuracy

Small measurement errors cause large torque errors. WHY: Torque depends directly on distance.

Overall Simple Machines Principle

All machines trade distance for force. WHY: Work conservation governs them.