INSTRUCTIONAL MEDIA THE MOVEMENT WITH VEKTOR ANALYZE COMPILED BY TUTI RESRI YANTI RSA1C312017 LECTURER Drs.M.HIDAYAT,M.Pd.
Nov 15, 2014
INSTRUCTIONAL MEDIA
THE MOVEMENT WITH VEKTOR ANALYZE
COMPILED BYTUTI RESRI
YANTIRSA1C312017
LECTURER Drs.M.HIDAYAT,M.Pd.
THE MOVEMENT WITH VEKTOR ANALYZE
UNIT VECTOR
CIRCULAR MOTION
THE PARABOLIC MOTION
THE MOVEMENT WITH VEKTOR ANALYZE
Competition standart. Analysist of natural indication and regularity in scope mechanics point object.
BASIC COMPETENCE1.1 Analyze straight motion,
circular motion and using the parabolic motion vector.
RECTILINEAR MOTION ANALYSIS
DEFINITIONSMEANING OF MOTION
An object is said to move when they change the position of other objects that serve as a reference point.
Body is said stationary (not moving)position when the object was not changed to other property used as a reference point.
MOTION STRAIGHT. object-motion trajectory straight-called rectilinear motion. -straight motion of an object in everyday life generally irregular.
A. UNIT VECTOR
Y
Ayj
α x Ax i
Unit vector is a vector whose magnitude one, without force, its direction along the coordinate axes. For the Cartesian coordinate system, the unit vectors along the x-axis direction, y, and z.The components of a vector to the x and y axes, respectivelyAx = A cos α and Ay = A sin α.
ACCELERATION
POSITION VECTOR VELOCITY
1. position vector
The position of a car (A) of the reference point (O) can be expressed by a position vector (position vector), ie OA or r.r = x i+y j -> two-dimensionalLarge (long) position vector expressed
r = x i y j z k -> three dimensional
A
r = x i + y j
y j
x iO
Displacement experienced by the point A in the time interval t.r = r2 – r1
r = x i + y jLarge displacement can be written
Direction of movement of point A
As a function of time, the component vector
22 )()(r yx
x
y
tan
jir )()()( tytxt
2. VELOCITYSpeed : displacement of the object in a certain time interval.Average speed: position change interval divided
t
r
v
tx
x
vty
y
v
tz
z
v
The average speed equation
Large average speed
Directions average speed
kjiv zyx vvv
222zyx vvv v
x
y
v
vtan
INSTANTANEOUS VELOCITY : Velocity of object any given moment
The instantaneous velocity equation
The instantaneous velocity
Instantaneous velocity direction
dt
d
tv
rr
lim
dt
dxvx
dt
dyvy dt
dzvz
kjivdt
dz
dt
dy
dt
dx kjiv zyx vvv
222zyx vvv v
x
y
v
vtan
determine position of velocity function
On the z axis can be obtined in the same way
dt
dxvx dxdtvx
t
x
x
x
dtvdx00
t
x dtvxx0
0
t
x dtvxx0
0
t
y
y
y
dtvdy00
t
y dtvyy0
0
t
y dtvyy0
0
accalerationAcceleration: change of velocity per unit timea. Average acceleration: a change of pace once in a while
t
v
a
t
va xx
t
va yy
t
va zz
Average acceleration aquation :
The average acceleration :
Average acceleration direction
kjia zyx aaa
222zyx aaa a
x
y
a
atan
acceleration
b. instantaneous acceleration Instantaneous acceleration (a) is defined
as the average acceleration for the time interval approaches zero. Systematically, instantaneous acceleration is formulated as follows:
However, v = dr / dt to obtain
c. Determine velocity from acceleration function
On the z axis can be obtined in the same way
dt
dva xx
xx dvdta
t
x
v
v
x dtadv00
t
xxx dtavv0
0
t
xxx dtavv0
0
t
y
v
v
y dtadv00
t
yyy dtavv0
0
t
yyy dtavv0
0
acceleration
Parabolic motion
Blend motion trajectory uniform rectilinear motion in the horizontal direction (x-axis) with a uniformly accelerated motion in the vertical direction (y-axis) is called parabolic parabolic motion.
B
C
D
Evx=vo cos
vy=
vo s
in
Parabolic motion
At y axisAcceleration equation
GLBB velocity equation
Transfer equation
• At x axisVelocity equation
GLB transfer equation:cosox vv
tvx o cos
cos
xt
tavv oyy tgvv oy sin
2
2
1sin tgtvy o
2bxaxy
Parabolic motionWhen the bullet reaches its highest point, bullet velocity component in the vertical direction is zero or Vy = 0. thus at the highest point applies
so the time it takes a bullet to the highest point
substitution equation y in the equation of uniformly accelerated motion and bullet time required to produce the highest point of maximum height
with varying elevation angles will be obtained by varying the maximum height anyway. The maximum height is obtained if the elevation angle α = 90 °.Achieved the maximum horizontal distance defined by
C. ANALYZE OF CIRCULAR MOTION
CIRCULAR MOTION: motion trajectory of a circle.
x =
r s
in
r
vv
v
v
• ANGLE position
• angular velocityAverage angular velocity
Instantaneous angular velocity
the position of angle can determine too :
cosrx sinry
22 yxr x
ytan
12
12
ttt
dt
d
t
lim
t
dtt0
0 )(
• Angular acceleration
instantaneous angular acceleration
angular velocitu can determine too :
12
12
ttt
2
2
dt
d
dt
d
dt
d
t
dtt0
0 )(
CIRCULAR MOTION
Circular motion acceleration
Initial position
Acceleration of the object which always leads to the centre of the circle said centripetal acceleration.
t 0(t)
ar
va atau
2
o
v
v
v
CIRCULAR MOTION
In addition to centripetal acceleration, the change uniform circular motion there is also a tangential acceleration
Total acceleration possessed by objects that undergo uniform circular motion
rat
va TT
atau
sTtotal aaa
22sTtotal aaa
CIRCULAR MOTION
example
1. Kedudukan awal seekor kucing terletak pada r1 = 5i + 6j. Kemudian kucing bergerak sehingga kedudukannya berpindah ke posisi r2 = 5i + 2j. Perpindahan yang dialami kucing adalah....
A 4
B 5
C
D
E
7
9
25
SalahBenar!