Vectors

A vector is a quantity that has both magnitude and direction. The length of the arrow is proportional to the magnitude of the vector. 30° 20 m/s

Scalar Quantities (magnitude only) Vector Quantities (magnitude and direction) Speed Length Time Energy Volume Temperature Velocity Displacement Acceleration Force Momentum Electric Field And a whole lot more!

How to specify direction “30 degrees above the horizontal” “45 degrees below the horizontal” 30° 45°

How else to specify direction “30 degrees East of North” “60 degrees South of West” 30° 60°

20° West of North 45° South of East 70° North of East 10° South of West

Vector Addition: Graphical Method Add vectors tip to tail When adding vectors, we can move them but not change their magnitude/direction.

Vector Addition with Multiple Vectors

Add the following vectors: A. 3 cm West and 4 cm South B. 5 cm at 45° North of East and 3 cm North

Vector Treasure Hunt!

Resultants and Components Components: show how much of the vector is in the x-direction and how much is in the y-direction. Resultant: A vector that is the sum of two or more vectors. Resultant vector x component y component

Calculating Components bsinθ b θ acosθ bcosθ a θ asinθ

Vector Treasure Hunt: Component Form + _ + _

x-components y-components

x-components y-components

Step x-component y-component d -56.3 m -32.5 m a -40 m 0 m e +19.4 m +72.4 m c -28.3 m +28.3 m b -30 m

x-components y-components

Vectors Can Be Added in Any Order

Is there an easier way to do this? Wait a second… Is there an easier way to do this?

Adding Vectors Mathematically Step x-component y-component A -30 m 0 m B -40 m C -28.3 m 28.3 m D -41 m -28.7 m E -32.1 m 38.3 m Total Total x-component: y-component:

x-component y-component resultant

There are two ways to add vectors There are two ways to add vectors. In your treasure hunt activity, you used both ways: Graphical Method (Step 1) Mathematical Method(Step 2 and 4) For each method, describe how the process works. Then use the process to add the two vectors below.

Vector Addition: Mathematical Break vectors down into x and y components. Check the sign of each component. Add up all of the x-components to determine the x-component of the resultant vector. Add up all of the y-components to determine the y-component of the resultant vector. Use the Pythagorean Theorem and inverse trig functions to solve for the magnitude and direction of the resultant vector.

Show all of your work in an organized manner. WB Calculate the net force (magnitude and direction) exerted on the object represented by the force diagram. 30° 12 N 60° 8 N Show all of your work in an organized manner.