19 -
Force Vectors
Easy
1
.
Fxy =
Fcoszoo
45 93
240
fy f (05450 B 52
,
=
+ y
= 45 ,
93N -
D =
arcos =
,
75
=x =
Exy Sin 450 = 45 , 93N -
D a = 52 240
,
O , 866
Fz = Fsingoo -
j = arcos = 300 = 120
%
75
↳
.
2
O =
arctan
- = 36
,
90
Fxy = F(0450
Fy = F 10536 90
x ,
=
28 , 27 N
&
↑
Fx ExySin 36
°
(0 =
9 =
-
21 23N D
, ,
F2 =
Fsin45
°
=
35 , 36N
-
F =
( -
21 ,
2 + 28 , 35 + 35
, 44N
3
.
↑
Fa
Fx = 80010450
·
y
Fx Ex y c0s30
°
= =
489 , 9N
Fy =
Fx y Sin 300 = 282 8 ,
N
F2 = 8005 in 450 =
-565 , 7 N
= =
9489 92 ,
+ 282 , 85 -
565, 73N
Fx = o
Fy =
.
500 N Fr : +
50
S
+
300
=
[489 92 ,
+ 682 . 85 -
265 , 7N
4 .
2 = ? m a = 42 + 2" =
4 , 47m
2 = 82 -
a = 6 , 63m
8m
a
4M
2M
.
5
= =
( - bi +
9j + 3 GkN - D
F =
11 ,
22mN
Fo =
( -
15 +
25 253m -
- D v = 3m
(For) ((6-1t(2 (
0 arccos ( -2.3)
+
!
:
=
accos = 57
,Medium
1
450N
2 :
450 cosix + cos" B + cos28 = 1
°
B 60
10528 600 das
:
U
=
: = =
-
120
j 8 =
?
& E < = -159
,
11 +
-
275 ,
6+
6
318 ,
2
E (4242 =
+
3005 -
3003N
Good
Fi (264 92 =
,
+ 575
,
65 + 18 , 23N =
F = 633 9 i ,
(hola)
& =
bgcos 65, 30 I BR :
R =
" 1)
Wi = ...
2 .
Bernal Ez Zodat Fr =
(95)nN :
guN
Fu =
12 uN
,
F2 =
10 UN
F =
(02 + 1200530 -
12sinsoGaN =
90 + 10 , 45 -
GGUN
&- + 10 G-9 2
>
Fu 10 05 9
-
= + =
,
+
O + 3 ,
S ! F ahh
=
9,2 +
Fzx = 0 :
23
=
bgcos(at) 10 4
,
+
Fzy = 9 (= ) = E (9 25 =
,
- 1
, 45 + 2 ,
73N
= 16 , 60
-
2 1 , + fzz = 0 Faz = 2 1
,
UN
98 , 40
= Fz = 9 ,
6 u
Bz =
0 =
77 48 ,
3
.4 , 5 niet gemaant
End
1
.
Fr =? Fi = 600N ,
Fc = 490N
-B =
1 + 22 + 2
2 = 3m
,
( ( = -
2i -
1j + 2n )m
rc
>
=
22 + 3
,
52 + 22 = 4 , 5m
,
=
) -
22 +
2j + 3, 54m
(ris(3)
-
Fis =
Fi .
= 6000 .
( E 5j &1) N -
+
=
( -
4005 -
2005 400m)N +
F 490( + 5 25)
= +
4,5
( 217 82 217 8j 381 1
=
-
, + ,
+
,
Fr =
+ 617 , 8 + 47 ,
832 (781 1)2+
,
= 996 05N ,
.
2
3m Fr enuel negative y-component
W = 1 54N
,
(3 -a)
( -2 di + (0 6)y +
E E z Fy Ef
-
B f =f
-
= = - -
+ = = -
+
2m ( -
2) + ( 6)2 + 32 -
>
-
ic
-
>
=
E Gj En -
+ = Fc =
F-Efj Ef +
Fr = -
Fij en w (1 5) uN =
,
= + 3 + w( -
frj =
( - E f Ef) ( Ef Ef)j + +
- -
+ (Ef E + -
1
, 5)
& I
0 =
-
Efz Ef +
Fi = 2,4 uN
Ef-f
2)
-
-
-R
=
0 =
3fB 77 + -
1
,
5
, 4
.
Fii =
( -
22 +
6j - zn 3m = 3
TAB = 7m
4m
== =
( -
42 +
6j +
154m = 3
(a) = 7 , 3m
I I
0 bgc0s0 36 3 9
bgcos(0
= +
34
-
82)
= =
,
,
7 .
7,3
3M
3m
1 -
Equilibrium of P
a article
Easy
1
.
M "Fr Y : Fusin81 ,
9
°
+ RSin450 -
m .
g
= 0 7) 0
,
99 Fu + 0 , 71R =
49 , 05
R - Fucos81
°
-Ros45
°
0 14 Fu
o
X :
,
9 = 0
,
-0 , 71R =
O
0 ,5 M
& & Fu
0 99x 0 71y 49 , 85
,
+ , =
43 4 =
(8
,
3)
0
, 14x -
0
, 71y = 0 56 = R
,
O
- Ses 43 4 ,
Fr = k .
1l(= ) Al =
200
= 0 , 217
-
10 =
0
.
5 -
0
,
217 = 0
,
283m
2
.
Ov W
I
Fr
·
E
E
300
Y
F = m, . 9 =
40 .
9 , 81 =
392 , 4N
Katrol
F2 = m .
g mg
0, 5 ·
(392 , 4)
E :
( + 4) Y :
Fasin30 °
-m .
g = o s m = =
Long
9
, 81
3
.
- Fr Est
15 %
·
Ts &
T
·
10
MB9 W
mc9
B : x :
T
+ FCoS15 = 0
C : X : Ecoso -
T = 0
Y : FSim15° =
98 ,
1 Y :
ESiR8-15 .
9 , 81 = 0
S )
()
T = 366 , 1 N F2 = 394 3N
,
=
=
F =
379 03N ,
O =
by + an (0 4) ,
= 21 , 80
36
(E2
F
SO (
=
Ecosp = 366 , 1
(=
3
Sing =
147 , 2
V .
Sin = 147 , e
Medium "tanO
1
.
7
M
2 T(OS53 10 =
5 .
9 81
, ,
T ⑧
T
0
, 2
49 , 05
I
T = = 40 88N
,
2553 200 25
8
210353 , 1
mg
,
,
,
2
.
g i
200 Y :
Tn COS200 + T2 (0530" =
50000
°
- TeSin20
°
X :
TzSin30 = O
S
&
, 94T1 +
0 0
. 87T2 =
50000
T ,552
0 -
0. 34T1 = 0
V
S
22 , 2 UN
Tz = 22222 ,
22N =
T1 = 32 , 6uN
,3
.
M
Fabloso
°
mg X : -98 1(0575 ,
-
98 1105450 = 0
,
⑳
10
() FABCoSO = 94 , 7 N
mg I 75
Y 98 1 Sin FabSinO
°
:
98 , 1Sin45 = o
M
-
-
- ,
AB
& (=) FABSinO = 15 , 4
0 =
by+ an(0 268) =
150
,
-10ng
FAB =
98 N
4 .
3
- Y :
Tsind = 196 2
,
X = arctan
1962 = 63
X : TcoSd =
100 B
- 1
4)
°
A 100N
1 ,5
x =
2 tan 63
.
= 3 93m
,
S
C b = 3 , 93 1 5 = 2 , 43m
196
-
2 N X ,
,
V
63 %.
& S
2
5 .
-3 4 55 S -F-FB5- f
>
25) 6
-
=
-
1
,
- -
s M = ) T =
.
5 = =
-
>
Fc (0 2865x5 4297(5 8577>33
)
(ai
-
6m = rc 7 =
r
35
=
c
= -
-
=
,
-
0, -
0
,
>
-
r /02 =
+ 2 55 63m,
-
=>
ry = 65 ,
=
fi =
(0 385fDj 923fp) + 0
,
-
0,
If = 0
=> Fi + + Fy = + = 0
S /:
-
0
,
231 F + 0
. 2867 = 0
-
0
,
308 FB -
0
, 429fc + 0. 3857 = 0
-
0
. 923 F3 -
0. 8577) -
0
, 92373 + 800 = 0 Fx =
427 , 1N
6.
Fab =
FCB
E" Fac Faj 667fa]
-
0
. 333 +
, 667
0 + 0
,
, 333
0 F 2 >
+ 0
, 667f(j + 0
. 667f)
=i =
G0 -
9 , 65 4) -
=)
(x = 10 4 =
, E = o2 Fyj
- 0
,
923 -
0
, 385m)
w =
(02 + 0j) 1962) -
En F F + + + w = 0
! (2
-
. 333
0 Fa + 0
, 333F ,
= 0
0
, 6677a + 0, 66777 -
0, 923fD = 0
0
, 667 FA +
0, 6677) -
0
,
385 -
1962 = 0 FD =
3647N
7 .
D 0
,5
!
① &
X Y: 3 .
1000 LOSX = 981
-
2 T = 1000N ·
A (=>x = 70 , 90
&
0.
5/ + an(70 90
-
981N -
z =
= 0 , 173m
· W ,
A
, End
1 .
~
Fa
4
↳1 T5 D: Y :
Fesimb0 °
-
9 , 81m = 0 () Fe = 19 , 62 m
-
-......
· S X:
FE(OS30 °
T = 0 Es T = 16 , 99m
45
-
Fi 450
Fe C : Y :
fa-Ebsin45 = 0 Es Fa = 0 , 884
fig
TD
& ⑳
( 308 X : -
fa -
FB(0545 + T =
0 () fi =
13 ,7m = fa = 12 , 1m
m
I
⑫62m-D 19 , Grooste ! -
D 400N = 19 62m
,
T 16 , 99m () m 20 ,
= =
3849
fi =
13 , 7m
FA = 12 , 1m
2 en 3 niet gemaant
2a -
Moment en Koppel 2D
Easy
1
.
F =
500N
,
Fu =
300N
,
Fz =
GOON
Mo =
600 (1m) -
500 (3m + 2 , 5 cos45) + 300(2 5 , sin 45)
= 1, 26 hN
.
2
520N. 6m = 2880 N
Mo
:
.
.
m
3
.
3 ↓ = rY
- = TX
-
Mp =
1 .
520(2 + 6) -
: .
520(4(0330) :
3147 Ni
4
.
tegenwijzerzin
& Ma =
(G -
100 .
9, 81)(2 , 5m + 0, 25m) + (250 . 9, 81)(0 ,
5 - 0
,
25)
=
= 2082 5 Nm fo
,
= 2082 58 ,
Force Vectors
Easy
1
.
Fxy =
Fcoszoo
45 93
240
fy f (05450 B 52
,
=
+ y
= 45 ,
93N -
D =
arcos =
,
75
=x =
Exy Sin 450 = 45 , 93N -
D a = 52 240
,
O , 866
Fz = Fsingoo -
j = arcos = 300 = 120
%
75
↳
.
2
O =
arctan
- = 36
,
90
Fxy = F(0450
Fy = F 10536 90
x ,
=
28 , 27 N
&
↑
Fx ExySin 36
°
(0 =
9 =
-
21 23N D
, ,
F2 =
Fsin45
°
=
35 , 36N
-
F =
( -
21 ,
2 + 28 , 35 + 35
, 44N
3
.
↑
Fa
Fx = 80010450
·
y
Fx Ex y c0s30
°
= =
489 , 9N
Fy =
Fx y Sin 300 = 282 8 ,
N
F2 = 8005 in 450 =
-565 , 7 N
= =
9489 92 ,
+ 282 , 85 -
565, 73N
Fx = o
Fy =
.
500 N Fr : +
50
S
+
300
=
[489 92 ,
+ 682 . 85 -
265 , 7N
4 .
2 = ? m a = 42 + 2" =
4 , 47m
2 = 82 -
a = 6 , 63m
8m
a
4M
2M
.
5
= =
( - bi +
9j + 3 GkN - D
F =
11 ,
22mN
Fo =
( -
15 +
25 253m -
- D v = 3m
(For) ((6-1t(2 (
0 arccos ( -2.3)
+
!
:
=
accos = 57
,Medium
1
450N
2 :
450 cosix + cos" B + cos28 = 1
°
B 60
10528 600 das
:
U
=
: = =
-
120
j 8 =
?
& E < = -159
,
11 +
-
275 ,
6+
6
318 ,
2
E (4242 =
+
3005 -
3003N
Good
Fi (264 92 =
,
+ 575
,
65 + 18 , 23N =
F = 633 9 i ,
(hola)
& =
bgcos 65, 30 I BR :
R =
" 1)
Wi = ...
2 .
Bernal Ez Zodat Fr =
(95)nN :
guN
Fu =
12 uN
,
F2 =
10 UN
F =
(02 + 1200530 -
12sinsoGaN =
90 + 10 , 45 -
GGUN
&- + 10 G-9 2
>
Fu 10 05 9
-
= + =
,
+
O + 3 ,
S ! F ahh
=
9,2 +
Fzx = 0 :
23
=
bgcos(at) 10 4
,
+
Fzy = 9 (= ) = E (9 25 =
,
- 1
, 45 + 2 ,
73N
= 16 , 60
-
2 1 , + fzz = 0 Faz = 2 1
,
UN
98 , 40
= Fz = 9 ,
6 u
Bz =
0 =
77 48 ,
3
.4 , 5 niet gemaant
End
1
.
Fr =? Fi = 600N ,
Fc = 490N
-B =
1 + 22 + 2
2 = 3m
,
( ( = -
2i -
1j + 2n )m
rc
>
=
22 + 3
,
52 + 22 = 4 , 5m
,
=
) -
22 +
2j + 3, 54m
(ris(3)
-
Fis =
Fi .
= 6000 .
( E 5j &1) N -
+
=
( -
4005 -
2005 400m)N +
F 490( + 5 25)
= +
4,5
( 217 82 217 8j 381 1
=
-
, + ,
+
,
Fr =
+ 617 , 8 + 47 ,
832 (781 1)2+
,
= 996 05N ,
.
2
3m Fr enuel negative y-component
W = 1 54N
,
(3 -a)
( -2 di + (0 6)y +
E E z Fy Ef
-
B f =f
-
= = - -
+ = = -
+
2m ( -
2) + ( 6)2 + 32 -
>
-
ic
-
>
=
E Gj En -
+ = Fc =
F-Efj Ef +
Fr = -
Fij en w (1 5) uN =
,
= + 3 + w( -
frj =
( - E f Ef) ( Ef Ef)j + +
- -
+ (Ef E + -
1
, 5)
& I
0 =
-
Efz Ef +
Fi = 2,4 uN
Ef-f
2)
-
-
-R
=
0 =
3fB 77 + -
1
,
5
, 4
.
Fii =
( -
22 +
6j - zn 3m = 3
TAB = 7m
4m
== =
( -
42 +
6j +
154m = 3
(a) = 7 , 3m
I I
0 bgc0s0 36 3 9
bgcos(0
= +
34
-
82)
= =
,
,
7 .
7,3
3M
3m
1 -
Equilibrium of P
a article
Easy
1
.
M "Fr Y : Fusin81 ,
9
°
+ RSin450 -
m .
g
= 0 7) 0
,
99 Fu + 0 , 71R =
49 , 05
R - Fucos81
°
-Ros45
°
0 14 Fu
o
X :
,
9 = 0
,
-0 , 71R =
O
0 ,5 M
& & Fu
0 99x 0 71y 49 , 85
,
+ , =
43 4 =
(8
,
3)
0
, 14x -
0
, 71y = 0 56 = R
,
O
- Ses 43 4 ,
Fr = k .
1l(= ) Al =
200
= 0 , 217
-
10 =
0
.
5 -
0
,
217 = 0
,
283m
2
.
Ov W
I
Fr
·
E
E
300
Y
F = m, . 9 =
40 .
9 , 81 =
392 , 4N
Katrol
F2 = m .
g mg
0, 5 ·
(392 , 4)
E :
( + 4) Y :
Fasin30 °
-m .
g = o s m = =
Long
9
, 81
3
.
- Fr Est
15 %
·
Ts &
T
·
10
MB9 W
mc9
B : x :
T
+ FCoS15 = 0
C : X : Ecoso -
T = 0
Y : FSim15° =
98 ,
1 Y :
ESiR8-15 .
9 , 81 = 0
S )
()
T = 366 , 1 N F2 = 394 3N
,
=
=
F =
379 03N ,
O =
by + an (0 4) ,
= 21 , 80
36
(E2
F
SO (
=
Ecosp = 366 , 1
(=
3
Sing =
147 , 2
V .
Sin = 147 , e
Medium "tanO
1
.
7
M
2 T(OS53 10 =
5 .
9 81
, ,
T ⑧
T
0
, 2
49 , 05
I
T = = 40 88N
,
2553 200 25
8
210353 , 1
mg
,
,
,
2
.
g i
200 Y :
Tn COS200 + T2 (0530" =
50000
°
- TeSin20
°
X :
TzSin30 = O
S
&
, 94T1 +
0 0
. 87T2 =
50000
T ,552
0 -
0. 34T1 = 0
V
S
22 , 2 UN
Tz = 22222 ,
22N =
T1 = 32 , 6uN
,3
.
M
Fabloso
°
mg X : -98 1(0575 ,
-
98 1105450 = 0
,
⑳
10
() FABCoSO = 94 , 7 N
mg I 75
Y 98 1 Sin FabSinO
°
:
98 , 1Sin45 = o
M
-
-
- ,
AB
& (=) FABSinO = 15 , 4
0 =
by+ an(0 268) =
150
,
-10ng
FAB =
98 N
4 .
3
- Y :
Tsind = 196 2
,
X = arctan
1962 = 63
X : TcoSd =
100 B
- 1
4)
°
A 100N
1 ,5
x =
2 tan 63
.
= 3 93m
,
S
C b = 3 , 93 1 5 = 2 , 43m
196
-
2 N X ,
,
V
63 %.
& S
2
5 .
-3 4 55 S -F-FB5- f
>
25) 6
-
=
-
1
,
- -
s M = ) T =
.
5 = =
-
>
Fc (0 2865x5 4297(5 8577>33
)
(ai
-
6m = rc 7 =
r
35
=
c
= -
-
=
,
-
0, -
0
,
>
-
r /02 =
+ 2 55 63m,
-
=>
ry = 65 ,
=
fi =
(0 385fDj 923fp) + 0
,
-
0,
If = 0
=> Fi + + Fy = + = 0
S /:
-
0
,
231 F + 0
. 2867 = 0
-
0
,
308 FB -
0
, 429fc + 0. 3857 = 0
-
0
. 923 F3 -
0. 8577) -
0
, 92373 + 800 = 0 Fx =
427 , 1N
6.
Fab =
FCB
E" Fac Faj 667fa]
-
0
. 333 +
, 667
0 + 0
,
, 333
0 F 2 >
+ 0
, 667f(j + 0
. 667f)
=i =
G0 -
9 , 65 4) -
=)
(x = 10 4 =
, E = o2 Fyj
- 0
,
923 -
0
, 385m)
w =
(02 + 0j) 1962) -
En F F + + + w = 0
! (2
-
. 333
0 Fa + 0
, 333F ,
= 0
0
, 6677a + 0, 66777 -
0, 923fD = 0
0
, 667 FA +
0, 6677) -
0
,
385 -
1962 = 0 FD =
3647N
7 .
D 0
,5
!
① &
X Y: 3 .
1000 LOSX = 981
-
2 T = 1000N ·
A (=>x = 70 , 90
&
0.
5/ + an(70 90
-
981N -
z =
= 0 , 173m
· W ,
A
, End
1 .
~
Fa
4
↳1 T5 D: Y :
Fesimb0 °
-
9 , 81m = 0 () Fe = 19 , 62 m
-
-......
· S X:
FE(OS30 °
T = 0 Es T = 16 , 99m
45
-
Fi 450
Fe C : Y :
fa-Ebsin45 = 0 Es Fa = 0 , 884
fig
TD
& ⑳
( 308 X : -
fa -
FB(0545 + T =
0 () fi =
13 ,7m = fa = 12 , 1m
m
I
⑫62m-D 19 , Grooste ! -
D 400N = 19 62m
,
T 16 , 99m () m 20 ,
= =
3849
fi =
13 , 7m
FA = 12 , 1m
2 en 3 niet gemaant
2a -
Moment en Koppel 2D
Easy
1
.
F =
500N
,
Fu =
300N
,
Fz =
GOON
Mo =
600 (1m) -
500 (3m + 2 , 5 cos45) + 300(2 5 , sin 45)
= 1, 26 hN
.
2
520N. 6m = 2880 N
Mo
:
.
.
m
3
.
3 ↓ = rY
- = TX
-
Mp =
1 .
520(2 + 6) -
: .
520(4(0330) :
3147 Ni
4
.
tegenwijzerzin
& Ma =
(G -
100 .
9, 81)(2 , 5m + 0, 25m) + (250 . 9, 81)(0 ,
5 - 0
,
25)
=
= 2082 5 Nm fo
,
= 2082 58 ,
