, KINEMATICS
*
VICTOR Physical quantity that has both magnitude and direction SINA.IE Physical quantity that has magnitude only
RESULTANT ✓ [ ([ _
The single vector which has the sane effect as the
original vectors acting together .
•
As the
angle between the vector increases the magnitude of the resultant decreases .
•
Maximum resultant :
when two or more vectors act in the same direction C@ 0
'
to each other)
•
Minimum resultant when two vectors act in the
opposite direction C@ other)
'
: or more 180 to each
COMPONENTS Of VICTORS
0 a 0
Sin h cos h tan a
When a vector ( v ) acts at an
angle (O) to the horizontal it can be resolved into rectangular components
i. e. horizontal csc) and vertical (y) components
-7 ,
- - - - - -
n
'
ch i
Vy = Vsinct ✓
: Horizontal component cvx) Vertical component (Vg )
10
•
> coso = = % since = ¥ : =
a
✓✗ = Vcoscl Vx=VcosO
Vy
=
Using
HEAD 1-01-1111 METHOD
7 ^
Fi = SOON
^
① ②
vi. ✓ f- 2
Fi Fi
✓ ! I
Draw the tail of f- 2 at the head of f- i. The resultant is A
! 'o
. _ _
"
the vector draw from the starting point to the head of f- 2 .
A. .
-6¥ .
A ! - - -- - -
s.net
f- 2=200 N
J
fret = (Soo)
'
+ Czooi tan 0=2%0 " fret =
538,52N on a bearing of 51,8°
°
=
29000
=
538,52N 0=21,8 ( bearing is measured clockwise from north]
RESULTANT OF MULTIPLE FORCES
f- 4=304 7
f-4 (A) = ON
' '
Fi = ISON F, ( Horizontal) = 150 Cos 10 =
147,72N f-2 ( horizontal ) =
50 Cos 30 = 4313N F> ( H ) = -20N
1- 3=2ON
"
-1 ? fi (vertical ) = 1505in 10 -25N F > (v ) -54 Cut 30N
'
f- 2Cvertical ) -50 Sink
=
ON
'
g- - - - - -
=
26,05N = = =
'
30
v -52 = 150N
Sum of Horizontal components : sum of vertical components :
f- I + f- 2+1-3 =
147,72+43,3-20 =
171,02 right f- It f- 2-1 f- 4=26,05-25+30 =
31,05N upwards
" sun or
" vertical
"
"
Resultant / Fret Direction of resultant : ÷ .
Fret =
173,82N on a
bearing
= = , , ,◦sN
µ
.
g.
31,0512
• °
2 Fret =
( 171,0212-1 ( =
173,82N tan 0 =
2
=
10,29 of 10,29
Sum of Horizontal
= 171,02 N
?⃝
*
VICTOR Physical quantity that has both magnitude and direction SINA.IE Physical quantity that has magnitude only
RESULTANT ✓ [ ([ _
The single vector which has the sane effect as the
original vectors acting together .
•
As the
angle between the vector increases the magnitude of the resultant decreases .
•
Maximum resultant :
when two or more vectors act in the same direction C@ 0
'
to each other)
•
Minimum resultant when two vectors act in the
opposite direction C@ other)
'
: or more 180 to each
COMPONENTS Of VICTORS
0 a 0
Sin h cos h tan a
When a vector ( v ) acts at an
angle (O) to the horizontal it can be resolved into rectangular components
i. e. horizontal csc) and vertical (y) components
-7 ,
- - - - - -
n
'
ch i
Vy = Vsinct ✓
: Horizontal component cvx) Vertical component (Vg )
10
•
> coso = = % since = ¥ : =
a
✓✗ = Vcoscl Vx=VcosO
Vy
=
Using
HEAD 1-01-1111 METHOD
7 ^
Fi = SOON
^
① ②
vi. ✓ f- 2
Fi Fi
✓ ! I
Draw the tail of f- 2 at the head of f- i. The resultant is A
! 'o
. _ _
"
the vector draw from the starting point to the head of f- 2 .
A. .
-6¥ .
A ! - - -- - -
s.net
f- 2=200 N
J
fret = (Soo)
'
+ Czooi tan 0=2%0 " fret =
538,52N on a bearing of 51,8°
°
=
29000
=
538,52N 0=21,8 ( bearing is measured clockwise from north]
RESULTANT OF MULTIPLE FORCES
f- 4=304 7
f-4 (A) = ON
' '
Fi = ISON F, ( Horizontal) = 150 Cos 10 =
147,72N f-2 ( horizontal ) =
50 Cos 30 = 4313N F> ( H ) = -20N
1- 3=2ON
"
-1 ? fi (vertical ) = 1505in 10 -25N F > (v ) -54 Cut 30N
'
f- 2Cvertical ) -50 Sink
=
ON
'
g- - - - - -
=
26,05N = = =
'
30
v -52 = 150N
Sum of Horizontal components : sum of vertical components :
f- I + f- 2+1-3 =
147,72+43,3-20 =
171,02 right f- It f- 2-1 f- 4=26,05-25+30 =
31,05N upwards
" sun or
" vertical
"
"
Resultant / Fret Direction of resultant : ÷ .
Fret =
173,82N on a
bearing
= = , , ,◦sN
µ
.
g.
31,0512
• °
2 Fret =
( 171,0212-1 ( =
173,82N tan 0 =
2
=
10,29 of 10,29
Sum of Horizontal
= 171,02 N
?⃝
