Forces in 2DChapter 5

5.1 Vectors

Both magnitude (size) and direction

Magnitude always positiveCan’t have a negative speedBut can have a negative direction

Representing Vector Quantities

Graphical representationArrow

Length represents magnitudeArrow point in correct direction

The Resultant Vector

No matter how you get to work from your home the displacement is the same

Resultant vector is the single vector that will replace all the other vectors (equal to the sum of two or more vectors)

Graphical Addition of Vectors

Use a rulerUse a protractorDetermine a scaleTo graphically add vectors they

need to be drawn head to tail

Algebraic Addition of Vectors

Draw a diagramUse Pythagorean Theorem

Only when there is a right triangleUse the Law of Cosines or Law of

SinesMake sure your calculator is in

degrees

Components of Vectors

Sine equals the opposite side divided by the hypotenuse

Cosine equals the adjacent side divided by the hypotenuse

Tangent equals the opposite side divided by the adjacent side

Make sure your calculator is in degrees

works only with 90 degree triangles

hypotenuse is always opposite the 90 degree angle

Adding Perpendicular Vectors

Use Pythagorean theorem to calculate the resultant

use trig to calculate the angle

Components Of Vectors

Start with a single vector (usually the resultant)

what two perpendicular vectors would add up to the single vector

those two vectors are the component vectors

Vector Resolution

The process of finding the magnitude of a component in a given direction

horizontal component Fh

vertical component Fv

Sample Problem

A plane travels on a heading of 40.0o for a distance of 3.00 x 102 km. How far north and how far east does the plane travel?

Sample Problem

Find the sum of 23 N 25o, 48 N 108o, and 37 N 297o