DAD Lab 1 Vector Addition PDF

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Do at domicile exercise weekly assignment ...

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Letícia Mendes DAD Lab 1: Vector Addition [Do-At-Domicile] Team for synchronous, Individual for those who cannot attend. As an initial exercise, answer the following questions by using the following simulation from PhET: https://phet.colorado.edu/sims/html/vector-addition/latest/vector-addition_en.html

Objectives: Remind everyone of trigonometry and vector addition as well as introduce PhET simulations, and introduce team members. Explore 1D Physics usually starts with 1D kinematics and it is easy to forget that these are actually vectors because everything is in the same direction. This is to help make this clear. Start in the “Explore 1D” and add the following three vectors. Be sure to show the sum. Notice they can be described with unit vectors, polar coordinates, or (x, y) components:  =+15 ^x a b=−7 ^x

c =+3 x^

so |a|=15 θ =0 a x =15 a y =0 so |b|=7 θ=180 bx =−7 b y =0 so |c|=3θ=0 c x =3 c y =0

Use the Screenshot feature from PhET and insert your work just below.

Because we live in a multi-dimensional world, we need to be able to handle another direction. Typically, we choose perpendicular directions unless there is a compelling reason not to. Since there is no compelling reason at the moment, let’s do a similar thing for the y- direction. Add the three vectors below and take a screenshot. Notice that to make the distinction between y and x vectors, PhET is now calling the vectors d, e, f. Notice that the magnitudes are always positive. d=+10 ^y so |d|=10θ=90 d x =0 d y =10 e =−12 ^y so |e|=−12θ =−90 =+ 270 e x =0 e y =−12 f =−5 y^ so |f |=5 θ=−90 f =0 f =−5 x

y

Explore 2D Adding a second dimension to vectors allows the study of many more problems (such as projectiles and planetary motion), but also requires trigonometry to fully appreciate what is happening. The relations between the various representations of a 2D vector are  A = A x ^x + A y ^y so Ay Ax Components: A x =A cos θ A y = A sin θ

Polar:

−1 2 | A |=A= √ A x2 + A y θ=tan

Add these two vectors (polar representation is given): |a|=10 θ =53.1° |b|=10.8 θ=21.8° and What is the sum vector? |s|=20.0 θ=36.9 ° Now do this by adding components. x-components a cos θ a sin θ 6.0 10.0 b cos θ b sin θ Sum for x Sum for y s cos θ s sin θ 16.0

y-components 8.0 4.0 12.0

Do you see this is a special triangle? It is one of the Pythagorean Triples because the sides are in the ratio of (3:4:5). Notice that for (3:4:5) triangles what the angles are: θ = 36.9

90-θ = 53.1...