8/13/2019 MTE119 - Solution Quiz 2
1/2
Mechatronics Engineering
NAME &ID DATEMTE119STATICS
UIZ 2
PAGE
You have 15 minutesto complete this quiz. Only simple scientific
calculators are allowed.
A cable extends from pointCto
pointE. It exerts a 50 lb force T
on the plate at Cthat is directedalong the line from CtoE.
a. Express T in terms ofCartesian components
b. What are the direction cosinesof the force T
c. What are the coordinatedirection angles of the force
T
Solution:
a) T
in terms of Cartesian components(6 Points)
Strategy:
Find the unit vector CEe
in the direction of the force and multiply its magnitude.
Coordinates of point C:
( ) ( )4, 4 sin20, 4cos20 ft 4, 1.37, 3.76 ft =
Coordinates of pointE:
( )0, 2, 6 ft.
Position vectorCEr
:
( ) ( ) ( )
( ) ( )( ) ( )
0 4 2 1.37 6 3.76
4 3.37 2.24
CE E C E C E C r x x i y y j z z k
i j k
i j k
= + +
= + +
= + +
Magnitude of CEr
:
( ) ( ) ( )2 2 2
2 2 2 4 3.37 2.24
5.69
CE E C E C E C r x x y y z z= + +
= + +
=
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8/13/2019 MTE119 - Solution Quiz 2
2/2
Mechatronics Engineering
NAME &ID DATEMTE119STATICS
UIZ 2
PAGE
Unit vector in the direction of the force CE
e :
( ) ( ) ( )
( ) ( ) ( )
( ) ( )( ) ( )
2 2 2
2 2 2
0 4 2 1.37 6 3.76
4 3.37 2.24
0.703 0.592 0.39
E C E C E CCECE
CEE C E C E C
x x i y y j z z kre
r x x y y z z
i j k
i j k
+ +
= =
+ +
+ +
=
+ +
= + +
The tension T
in Cartesian form:
50 CET e=
35.2 29.6 19.7 lbT i j k = + +
ANS
b) Direction cosines of the force T
(2 Points)
Strategy:
From the solution of part a
0.703 0.592 0.39CE
e i j k = + +
The unit vector can also be expressed in terms of the direction
cosines as,
cos cos cos .CEe i j k = + +
Therefore, the direction cosines are
cos 0.703
cos 0.592
cos 0.39.
=
=
=
ANS
c) Coordinate direction angles of the force T
(2 Points)
Strategy:
The coordinate direction angles , and are measured from the
positive coordinate
axes.
Therefore,
134.7
53.7
67
o
o
o
=
=
=
ANS
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