Statics exam 1

Scalar

Physical quantity completely specified by magnitude only (time mass temperature)

Force

Vector because it has both magnitude and direction

Triangle Rule

Place vectors head to tail and draw resultant from first tail to final head

Negative Vector

Has same magnitude as original vector but opposite direction

Resultant Force

Single force equivalent to the combined action of all applied forces

Statics Goal

Determine magnitudes directions and effects of forces acting on bodies

Position Vector

Vector that specifies the location of one point relative to another

Direction of Position Vector

Always points from the starting point to the ending point

Cartesian Vector Form

F = Fx i + Fy j + Fz k

Unit Vector i

Direction of positive x-axis

Unit Vector j

Direction of positive y-axis

Unit Vector k

Direction of positive z-axis

Finding a Force Vector

Multiply force magnitude by its unit vector

Dot Product Purpose

Used to determine angles between vectors and projections of vectors

Dot Product Result

Produces a scalar quantity

Vector Projection

Projection direction is along the unit vector of the reference line

Steps for Position Vector Problems

Find coordinates subtract endpoints create vector calculate magnitude if needed

Steps for Cartesian Force Problems

Find position vector determine unit vector multiply by force magnitude

Reason for Unit Vectors

Describe direction independently from magnitude

Three-Dimensional Force Analysis

Express force as Cartesian vector before performing calculations

Projection Meaning

Amount of one vector acting along a specified direction