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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