20.1104 Intro. to Engng Analysis
Test #1, Sept. 22, 1995
Name ______________________________
1. For each of the problems below, draw the indicated free body diagram(s). Don’t solve the
problems.
a. (20 points) The man in the figure is slowly pulling a drum over a circular hill. The drum
weighs 60 N, and the hill is smooth. In the given equilibrium position, find the tension in the
rope (which does not vary along the rope if the hill is smooth). Draw a free body diagram of
the drum.
Free Body Diagram:
y
x
z
FH
45
TR
o

= 8.1o
x
y
x
WD=60N
NOTE: Theta must also be drawn in on the figure given for the problem.
b. (20 points) Determine the weight of the cart A if the system shown is in equilibrium. Draw a
free body diagram of the loop at D and the loop at E.
FBD for loop at D:
FBD for loop at E:
y
xz
y
xz
TC
4
12
TDE
D
8
15
TA
Problem 2 (60 points total)
3
TF
5
x
x
12
5
E
TDE
WB=280 lb
20.1104 Intro. to Engng Analysis
Test #1, Sept. 22, 1995
Name ______________________________
Referring to the following sketch of a 100 lb bucket supported by three cables, please answer the
following questions.
(a) (10 points) Using rectangular component form, write expressions for three position vectors:
from D to B, from D to A, and from D to C.

rDB  (0i  15
. j  0k) ft

rDA  (3i  15
. j  3k) ft

rDC  ( 15
. i  1 j  3k) ft
(b) (10 points) Find unit vectors parallel to each of the position vectors in part (a) above.
e DB

rDB
    j
rDB
3i  15
. j  3k 3i  15
. j  3k

 0.667i  0.333 j  0.667 k
4.5
9  2.25  9
15
. i  1 j  3k 15
. i  1 j  3k


 0.428i  0.285 j  0.857 k
35
.
2.25  1  9
e DA 
e DC
(c) (15 points) Use vectors to compute the rectangular scalar component of position vector DA
(rDA) along the direction of position vector DC (rDC).
20.1104 Intro. to Engng Analysis
Test #1, Sept. 22, 1995
Name ______________________________


 
rDA  rDC  rDA rDC cos


rDA  rDC 


rDA cos  desired component along rDC  
 rDA  e DC
rDC


rDAx rDCx  rDAy rDCy  rDAz rDCz
35
. ft

.    15
. 1  33 ft 2
3 15
35
. ft
 0.857 ft
(d) (25 points) Given that the bucket and its contents weigh 100 lb, set up and solve for the
tension in each cable. Please show your full set up of the problem on the test paper for full
credit. A correct numerical answer by Maple or other appropriate method will be worth 5
bonus points.
Free Body Diagram :
(.667, -.333, .667)
TDA
TDC
z
x
z
TDB
(0, -1, 0)
x
Vectors:
TDB

TDA

TDC

W
Theory:
(-.428, .285, .857)
y
x
(0, 0, -1)
W= 100 lb
 TDB e DB  TDB j


0.428i  0.285 j  0.857k
 TDA e DA  TDA 0.667i  0.333 j  0.667 k
 TDC e DC  TDC
 100k
20.1104 Intro. to Engng Analysis
Test #1, Sept. 22, 1995




 
F

0
T
+
T
+
T
+
W
=0

DB
DA
DC
 Fx  0: 0.667T  0.428T  0
 Fy  0: 0.333T  0.285T  T  0
. T  100  0
 Fz  0: 0.667T  0857
DA
DA
DA
DC
DC
DB
DC
Solution:
See Maple File (not available for R4).
Name ______________________________