Forces and Pulleys

Mechanics

Science describing rest/motion of bodies under forces

Rigid body mechanics

Divided into statics and dynamics

Statics

Objects at rest or constant velocity; Newton’s 1st & 3rd laws

Dynamics

Objects with acceleration; Newton’s 2nd law

Newton’s First Law

Body remains at rest or constant velocity if resultant force = 0

Newton’s Second Law

Acceleration proportional to resultant force; F = ma

Newton’s Third Law

Forces between two objects equal in magnitude, opposite in direction

Coordinate system

Defined relative to Cartesian axes

Right-handed system

Right hand rule: fingers x→y, thumb points positive z

Scalar quantity

Described by magnitude + units only (time, mass, temperature)

Vector quantity

Has magnitude + units + direction (force, velocity, acceleration)

Parallelogram law

Two forces replaced by resultant along diagonal of parallelogram

Triangle law (tip-to-tail)

Resultant found by connecting tail of one to tip of other

Rectangular components

Resolve force into x and y components

SOH

Sine = Opposite / Hypotenuse

CAH

Cosine = Adjacent / Hypotenuse

TOA

Tangent = Opposite / Adjacent

Unit vector

Defines direction of a vector with magnitude 1

Equilibrium of a particle

Resultant of all forces = 0; ΣF = 0

Free body diagram

Diagram showing all forces acting on a particle/object

Pulley

Provides mechanical or directional advantage

Frictionless pulley

Tension same on both sides under equilibrium

Directional advantage

Pull down to lift up; load still equals weight

Mechanical advantage (single movable pulley)

Load supported by 2 rope arms; effort = half load

Pulley tension rule

Tension equal in each rope segment supporting load