Transcript Technical Physics 1

Technical Physics 1
Vectors
Vector Addition
• Scalar Quantities - measurement which are
magnitude only
• Vector Quantities - measurements which
include the magnitude and direction
• Methods of vector addition
Measuring with ruler and protractor
– Graphical
• polygon method
• parallelogram method
– Analytical (Trigonometry)
• component method
Measuring with ruler and
protractor
• With these types you will
determine the magnitude and
direction of a vector by using a
ruler and a protractor. You must be
very accurate and you must have a
scale for length.
Graphical Methods
Parallelogram Method
R
F2
F1
Polygon Method
R
F2
F1
Parallelogram Method
Use a protractor and ruler to draw aF21line
starting
parallel
from
to the
F21 passing
origin
through the tip of F12
F1
R
F2
The resultant is drawn from the origin to the intersection of
these two lines. Use a protractor and ruler to measure the
angle and length.
Polygon Method
Use a protractor and ruler to draw F21 starting from the tip
origin
of F1
Be careful to use horizontal and vertical reference lines.
F2
F1
R
The resultant is drawn from the origin to the tip of F2 Use a
protractor and ruler to measure the angle and length.
Trig functions
• sine
sin  =
opposite
hypotenuse
cos  =
adjacent
hypotenuse
• cosine
• tangent
tan  =
opposite
adjacent
• Pythagorean Theorem
c 2 = a2 + b 2

opposite
adjacent
Component Method
Take each force and separate
it into x and y components
x = Fcos
y = Fsin
y1

x1

x2
y2
Component Method
Use
resulting
Addthe
together
the xy
x values
and y values to
R
determine the
resultant and angle
y1
F1
F2
y2

x2
x1
Component Method
R
y1
Ry
y2

Rx x2
x1
Component Method
Force
X -component Y - component
F1
F1cos
F1sin
F2
F2cos
Rx
F2sin
Ry
Resultant
R =  Rx2 + Ry2
 = invtan (Ry/Rx)
Other analytical methods
• law of sines, law of cosines
F1 = F2
= R
sin 1
sin 2
sin R
F2
R
F1
2
1
R
F12 + F22 - 2 F1 F2 cos R = R2