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Material Type: Assignment; Class: Basic Mechanics I (Statics); Subject: CE-Civil Engineering; University: Purdue University - Main Campus; Term: Fall 2007;
Typology: Assignments
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Vector Mechanics for Engineers: Statics and Dynamics , 8/e, Ferdinand P. Beer, E. Russell Johnston, Jr.,
Elliot R. Eisenberg, William E. Clausen, David Mazurek, Phillip J. Cornwell
Vector Mechanics for Engineers: Statics and Dynamics , 8/e, Ferdinand P. Beer, E. Russell Johnston, Jr.,
Elliot R. Eisenberg, William E. Clausen, David Mazurek, Phillip J. Cornwell
A steel plate is acted upon by two couples as shown. Determine ( a ) the
moment of the couple formed by the two 40-N forces. ( b ) the value of
if the resultant of the two couples is 8 N m counterclockwise and
d 820 mm, ( c ) the perpendicular distance between the two 24-N
forces if the resultant of the two couples is zero.
( a ) Have
1 1 1
M d F
Where
1 1
d 0.6 m and F 40 N
1
M 0.6 m 40 N
or
1
M 24.0 N m
( b ) Have
Total 1 2
M M M
8 N m 24.0 N m 0.820 m cos 24 N
cos 0.
or 35.6
( c ) Have
1 2
M M 0
2
24 N m d 24 N 0
or
2
d 1.000 m
Vector Mechanics for Engineers: Statics and Dynamics , 8/e, Ferdinand P. Beer, E. Russell Johnston, Jr.,
Elliot R. Eisenberg, William E. Clausen, David Mazurek, Phillip J. Cornwell
Have
1 2
M M M
Where
DE D
1
0.7 m k 80 N j
56.0 N m i
And
GF B
2
Now
2 2 2
0.300 m 0.540 m 0.350 m
BF
d
0.710 m
Then
B BF B
0.300 m 0.540 m 0.350 m
0.710 m
i j k
30 N i 54 N j 35 N k
2
0.54 m 30 N 54 N 35 N
M j i j k
18.90 N m i 16.20 N m k
Finally
56.0 N m 18.90 N m 16.20 N m
M i i k
74.9 N m i 16.20 N m k
and
2 2
M 74.9 N m 16.20 N m
76.632 N m or M 76.6 N m
cos cos cos
x y z
or 12.20 90.0 77.
x y z
Vector Mechanics for Engineers: Statics and Dynamics , 8/e, Ferdinand P. Beer, E. Russell Johnston, Jr.,
Elliot R. Eisenberg, William E. Clausen, David Mazurek, Phillip J. Cornwell
As four holes are punched simultaneously in a piece of aluminum sheet
metal, the punches exert on the piece the forces shown. Knowing that the
forces are perpendicular to the surfaces of the piece, determine ( a ) the
resultant of the applied forces when 45 and the point of
intersection of the line of action of that resultant with a line drawn
through points A and B , ( b ) the value of so that the line of action of
the resultant passes through fold EF.
