Transcript Vectors Chapter 6 - School District of La Crosse

Vectors Chapter 6
KONICHEK
JUST DOING SOME ANGLING
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:
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.
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.
Vector addition
Mathematical method of
vector addition
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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
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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
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˚
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 xcomponent is named Fx. This would be read 'F sub
x'. So, in the above math we should remove 'xcomponent' 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