The University of British Columbia
Faculty of Applied Science, School of Engineering
APSC 180 Assignment 1
Instructions: Read each question carefully and answer in full. To receive full marks, you must show all of
your work and use appropriate significant digits. State any assumptions used, and where appropriate, draw
all relevant free body diagrams (FBDs).
Due Date: Tuesday, May 27th at 11:59PM via Canvas
Question 1
Determine the magnitudes of the two components of F along members AB and AC, where F = 350 lb.
A
45
350 is
75
Ac
-100
↳
>
=
AB
Sin 60
AC
=
2561D
AB
=
3141b
Figure 1 Figure for Question 1.
Question 2
The two forces F1 and F2 have a resultant force of FR = {-100k} lb. Determine the magnitude and coordinate
direction angles of F2.
F
F
+
Fz
100k
-
=
60 Los 30 Cos 50 i + 60 Sin30 Cos50;
=
---
---
60 Sin50k
F
-
S
-
,
"
↓
=
Fzi
Fij
F2
33
-
=
=
=
-
-
-
.
4i
F, j
=
.
3
%
45 9k
i
.
33 4 ;
Figure 2 Figure for Question 2.
.
Fj
Fx
+ 19
-
=
-
-
100k
42
32
54
19 3)
+ 19
.
=
.
+
.
et
54 1k
.
5a.
~
-
=
B
=
1870
U
=
1448
1
=
Cos
Cos
(a)
1
=
59 8
.
Cost
The University of British Columbia
Faculty of Applied Science, School of Engineering
Question 3
Determine the magnitude and coordinate direction angles of the resultant of the two forces acting at point
A.
A
=
(0
B A
-
A
0,
(5 ,
=
F(A
(5
=
-
.
=
-
.
324 4i
-
&F
129 8
.
.
,
,
,
=
; + 194 7k
cost
.
j + 194
648 8i + 0j
=
43 , 0 0 E = (5 0 3)
=
,
140
=
324 4i + 129 8
-
(5-4 3) D
C =
-x400
(
=
4 , 3)
3)
2 ,
,
,
,
=
FBA
B
01
(5 2 3)
=
-
c
,
7k
389
+
.
.
⑳
3k548Figure 3 Figure for Question 3.
82 + 389 3 =
.
.
.
%
°
~
757N
149 B 90 U 590
Question 4
Determine the magnitude of the components of F = 600 N acting along and perpendicular to segment DE
of the pipe assembly.
=
=
B
(0 0 0)
=
B
E
-
E
,
,
(
=
-
4
5 , -2)
,
2)
5,
-
,
(4
=
=
O
&
-
4i
-
5j + 2k
Yes
5
UED
"
0
.
743i
0
-
.
56
,
+ 0
.
37k
+2
0 56
,
=
HEB
=
&
.
:
600
=
-
445 72
-
.
Fu
=
-
334
.
445 7x0
.
⑨
2) + 222 8k
.
+
334 3x 1
-
.
+
222
.
8x0
Figure 4 Figure for Question 4.
498N
Question 5
334N
334
2002
The spring has a stiffness of k = 800 N/m and an unstretched length of 200 mm. Determine the force in
cables BC and BD when the spring is held in the position shown.
=
-
F=
240
L
kx
Bi
45
·
37
800 X0 3 =
.
.
tan" )
4
tan"
4
!
Bu
0 5-0
24ON
(*)
.
=
450
=
36 90
.
2
=.
3
.
3
[Fx
=
-
240
+
BDCOS 36
& Fy
=
BCCos45 +
.
9
BCSin45-BDSin36 S
.
* matrix
FBD
=
17 IN
Figure 5 Figure for Question 5.
2
FBc
=
145N
The University of British Columbia
Faculty of Applied Science, School of Engineering
Question 6
If each cord can sustain a maximum tension of 50 N before it fails, determine the greatest weight of the
flowerpot the cords can support.
o
-
①
DA
FAD
ADSin30i-ADCos30SinGoj + ADCos 30
=
FAC
AC)-Sin30i-Cos30Sin6oj
=
FAB
0
=)
+ Cos30Cos 60k )
AB (Sin45j + c0S45k)
=
Ad
cos so k
-
.
5i
0 5;
.
ABO
GFx
.
ADO 75
-
.
1(0
-
707j
+
.
j
75j
.
+
10
.
③
·
0
=
*
=
-
AD0 75
.
=
AB0 701- A co 75 =
+
ABO
[Fz
433k
.
AD = AC
SFy
.
ABO TOT #
.
①
AD0 433k
+
ADO 5 - ACO S
=
Figure 6 Figure for Question 6.
.
.
707
.
=
AD0 433 +
.
AC
0
AB1
.
5
AB0 707 +
170 433
.
.
F
.Sh-
10
~07x50
=
=
F
A
Also
AB
=
2
.
366x23
.
57
=
=
23.
56N
]
3