Forces in 2D Chapter 5

5.1 Vectors Both magnitude (size) and direction Magnitude always positive Can’t have a negative speed But can have a negative direction

Representing Vector Quantities Graphical representation Arrow Length represents magnitude Arrow 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 ruler Use a protractor Determine a scale To graphically add vectors they need to be drawn head to tail

Algebraic Addition of Vectors Draw a diagram Use Pythagorean Theorem Only when there is a right triangle Use the Law of Cosines or Law of Sines Make 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 F h vertical component F v

Sample Problem A plane travels on a heading of 40.0 o for a distance of 3.00 x 10 2 km. How far north and how far east does the plane travel?

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