Vectors Bellwork ( Clickers ) Some Notes Stations ( Take Notes!! ) Open Notes/Book Quiz on Thur ( 09/13/12 )

What’s On Quiz – 6 Qs Conceptual Questions on Vectors – Conceptual Clickers / Stations Finding resultants/angles of vectors (free-response) – Graphical and Analytical – AP will have 3 of these ( Honors only 2 )

If each component of a vector is doubled, what happens to the angle of that vector? a) it doubles b) it increases, but by less than double c) it does not change d) it is reduced by half e) it decreases, but not as much as half Question 3.2a Vector Components I

If each component of a vector is doubled, what happens to the angle of that vector? a) it doubles b) it increases, but by less than double c) it does not change d) it is reduced by half e) it decreases, but not as much as half The magnitude of the vector clearly doubles if each of its components is doubled. But the angle of the vector is given by tan  = 2y/2x, which is the same as tan  = y/x (the original angle). Follow-up: if you double one component and not the other, how would the angle change? Question 3.2a Vector Components I

A certain vector has x and y components that are equal in magnitude. Which of the following is a possible angle for this vector in a standard x-y coordinate system? a) 30° b) 180° c) 90° d) 60° e) 45° Question 3.2b Vector Components II

A certain vector has x and y components that are equal in magnitude. Which of the following is a possible angle for this vector in a standard x-y coordinate system? a) 30° b) 180° c) 90° d) 60° e) 45° The angle of the vector is given by tan  = y/x. Thus, tan  = 1 in this case if x and y are equal, which means that the angle must be 45°. Question 3.2b Vector Components II

The Components of a Vector **Notice arrow above and bold font / Angle goes counterclockwise!! Can resolve vector into perpendicular components using a two- dimensional coordinate system:

The Components of a Vector Length, angle, and components can be calculated from each other using trigonometry:

The Components of a Vector Signs of vector components:

Adding and Subtracting Vectors Adding vectors graphically: Place the tail of the second at the head of the first. The sum points from the tail of the first to the head of the last.

Finding Vector Resultants Graphical method is approximate – Limited by accuracy of graph, measurements, etc. Using components ( analytical ) is more accurate

Outdoor Lab Example Building Light-pole Tree Components Resultant ( Sum )

Adding and Subtracting Vectors Adding Vectors Using Components: 1. Find the components of each vector to be added. 2. Add the x- and y-components separately. 3. Find the resultant vector.

Adding and Subtracting Vectors

Subtracting Vectors: The negative of a vector is a vector of the same magnitude pointing in the opposite direction. Here,.

Examples A x = (5.00 m)*cos 60.0 o A y = (5.00 m)*sin 60.0 o B x = (4.00 m )*cos 20.0 o B y = (4.00 m )*sin 20.0 o Add x and y components separately C x is 6.26 m and C y is 5.70 m

Adding and Subtracting Vectors

Examples – Take a Step Further

Examples – Take a Step Further

Stations – Take Notes!! #1 – Basic conceptual / 1D Kinematics review – Average speed ( distance / time ) – Average velocity ( displacement / time or: #2 – Basic Resolution of Vector into Components #3 – Vector Addition ( starts empty ) #4 – PhET Vector Addition Simulation #5 – Playing with Force Table at front of room

Question 3.3Vector Addition Question 3.3 Vector Addition You are adding vectors of length 20 and 40 units. What is the only possible resultant magnitude that you can obtain out of the following choices? a) 0 b) 18 c) 37 d) 64 e) 100

Question 3.3Vector Addition Question 3.3 Vector Addition You are adding vectors of length 20 and 40 units. What is the only possible resultant magnitude that you can obtain out of the following choices? a) 0 b) 18 c) 37 d) 64 e) 100 minimum opposite20 unitsmaximum aligned60 units The minimum resultant occurs when the vectors are opposite, giving 20 units. The maximum resultant occurs when the vectors are aligned, giving 60 units. Anything in between is also possible for angles between 0° and 180°.