1 1 N 2 7 N 3 9 N 4 4 N example As the angle between two concurrent forces

# 1 1 n 2 7 n 3 9 n 4 4 n example as the angle between

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1. 1 N 2. 7 N 3. 9 N 4. 4 N
example As the angle between two concurrent forces decreases, the magnitude of the force required to produce equilibrium 1. decreases 2. increases 3. remains the same
10/9 do now Write all you know all about vector Definition: Examples (3): Representation: Ways to add vectors Head to tail: (sketch) Parallelogram method: (sketch)
objectives Homework questions? How to add vectors mathematically? Homework: castle learning No post session today Homework quiz is on Friday
Apply the Pythagorean theorem and tangent function to calculate the magnitude and direction of a resultant vector The procedure is restricted to the addition of two vectors that make right angles to each other . Add vectors mathematically
Using tangent function to determine a Vector's Direction θ opp. Hyp. adj . opp. adj . tanθ = opp. adj . θ = tan -1 ( )
example Example: Eric leaves the base camp and hikes 11 km, north and then hikes 11 km east. Determine Eric's resulting displacement.
Note: The measure of an angle as determined through use of SOH CAH TOA is not always the direction of the vector. R 2 = (5.0km) 2 + (10km) 2 R = 11 km Or at 26 degrees south of west
example An archaeologist climbs the Great Pyramid in Giza, Egypt. If the pyramid’s height is 136 m and its width is 2.30 x 10 2 m, what is the magnitude and the direction of the archaeologist’s displacement while climbing from the bottom of the pyramid to the top?
Equilibrant The equilibrant vectors of A and B is the opposite of the resultant of vectors A and B. Example: A B A B R Equilibrant A B R Equilibrant Head to tail Parallelogram
Vector Components In situations in which vectors are directed at angles to the customary coordinate axes, a useful mathematical trick will be employed to transform the vector into two parts with each part being directed along the coordinate axes.
Any vector directed in two dimensions can be thought of as having an influence in two different directions. Each part of a two-dimensional vector is known as a component . The components of a vector depict the influence of that vector in a given direction. The combined influence of the two components is equivalent to the influence of the single two-dimensional vector. The single two-dimensional vector could be replaced by the two components.
Vectors can be broken into COMPONENTS X-Y system of components A X = A cos θ A Y = A sin θ Example v i = 5.0 m/s at 30° v ix = 5.0 m/s (cos 30°) = 4.33 m/s v iy = 5.0 m/s (sin 30°) = 2.5 m/s Any vector can be broken into unlimited sets of components
EXAMPLE Calculate the x and y components of the following vectors. a. A = 7 meters at 14° b. B = 15 meters per second at 115° c. C = 17.5 meters per second2 at 276°
Adding with Components Vectors can be added together by adding their COMPONENTS Results are used to find RESULTANT MAGNITUDE RESULTANT DIRECTION Adding Vectors Algebraically
Example Add vectors D and F by following the steps below.

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• Fall '15
• Von Mosser
• Physics, pH, Velocity, m/s