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Vector Addition and Terminology

Learn about vector addition and terminology, including graphical and mathematical methods, concurrent vectors, and vector components.

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Vector Addition and Terminology

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  1. Vectors Chapter 6 KONICHEK

  2. JUST DOING SOME ANGLING

  3. TERMINOLGY • I.Vector vrs Scalar A.has magnitude and direction B. Scalar- measures only magnitude or direction( speed) • II.Resultant vector B."sum" of several vectors; the effect of the resultant vector is always greater than the effect of its individual components. • III.Concurrent vectors A.act on the same point at the same time • IVEquilibrant vector A.a vector that produces equilibrium; it is equal in magnitude and opposite in direction to the resultant vector Graphical method of vector addition:

  4. HOW VECTOR DIAGRAMS WORK • V.Graphical method of vector addition: • A.Vectors are represented graphically by using arrows. • 1.The length of the arrow represents the vector’s magnitude • 2.the direction the arrow points represents the direction of the vector. • 3.Vectors are drawn graphically using a scale.

  5. B.Vectors are added graphically by placing them "tips to tails." • 1.The tail of the second vector is touches the tip of the first vector, etc. • 2.The resultant vector is drawn graphically by placing the tail of the resultant at the tail of the first vector and the tip of the resultant at the tip of the last vector. • 3.It is drawn from where you started to where you ended. • 4.The resultant vector’s magnitude can be determined graphically by measuring its length and converting its length using the scale chosen. • 5.Its direction is the direction that it points. • 6.There are two parts that describe the resultant vector graphically—its magnitude and its compass direction.

  6. Vector addition b a a c e r b c

  7. Mathematical method of vector addition • I.One dimension: A.Vectors that act in a line linearly are assigned positive and negative signs to indicate their direction. Positive signs are assigned to vectors acting right, up, east, or north. Negative signs are assigned to vectors acting left, down, west, or south. B.Using their signs, vectors are added algebraically to determine the magnitude and sign (direction) of the resultant

  8. II.Two dimensions: • A.The resultant vector is found mathematically. We will use the component method of vector addition. A resultant vector can be considered to be the vector sum of its resultant x-component and its resultant y-component, separated by 90°. This can also be done using graphing calculators. • B.The magnitude of the resultant vector can be determined using the Pythagorean theorem • 1.c2 = a2 + b2 (you remember this!!!) • The direction of the resultant vector can be expressed as an angle between 0° and 90°, and use the appropriate trig function • a) sin =o/h, cos a/h , tan o/a ( this might be new) • 1. right triangle trigonometry using SO/H-CA/H-TO/A

  9. Practice- sometimes drawing a picture helps visualizing( advised) • a boat is traveling at 7m/s across a river. The current is 1.5m/s. find the vector of the boat. • Mag= 72 + 1.52 = 7.2m/s • Direction is: Tan-1 = 1.5/7= 12.1˚

  10. VECTOR COMPONENTS • Let's find the size of the x-component; that is, let's find the size of the adjacent side. • We know the hypotenuse, (316 Newtons), and we know the angle, (35 degrees). We want to find the length of the adjacent side, (x-component). What trigonometry function relates the hypotenuse, an acute angle and its adjacent side in a right triangle? The cosine function does. The math looks this way: • Now, since the original vector is named F, its x-component is named Fx. This would be read 'F sub x'. So, in the above math we should remove 'x-component' and replace that term with Fx, as in: • We can solve for Fx by doing a little algebra and looking up the cosine of thirty-five degrees: • 35˚= F/316N

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