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
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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
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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)
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objectives Homework questions? How to add vectors mathematically? Homework: castle learning No post session today Homework quiz is on Friday
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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
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Using tangent function to determine a Vector's Direction θ opp. Hyp. adj . opp. adj . tanθ = opp. adj . θ = tan -1 ( )
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example Example: Eric leaves the base camp and hikes 11 km, north and then hikes 11 km east. Determine Eric's resulting displacement.
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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
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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?
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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
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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.
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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.
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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
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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°
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Adding with Components Vectors can be added together by adding their COMPONENTS Results are used to find RESULTANT MAGNITUDE RESULTANT DIRECTION Adding Vectors Algebraically
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Example Add vectors D and F by following the steps below.
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  • Fall '15
  • Von Mosser
  • Physics, pH, Velocity, m/s

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