Project “The development of the didactic potential of Cracow University of Technology in the range of modern
construction” is co-financed by the European Union within the confines of the European Social Fund
and realized under surveillance of Ministry of Science and Higher Education.
1
Exercise 5_1: For a given system of parallel forces determine the center of the system, and reduce the
system at that point.
Course of action:
1. Choosing the unit vector of the system.
2
2
,
0
,
2
2
2
2
2
,
0
,
2
m
m
BE
BE
e
2. Determining the coefficients
for each vector in the system.
i
a
e
F
F
e
F
F
a
i
i
i
if
if
kN
F
a
kN
F
a
kN
F
a
kN
F
a
2
2
2
2
4
2
3
4
4
3
3
2
2
1
1
kN
a
2
2
i
3. The sum vector of the system can be computed as
kN
kN
e
a
S
i
2
,
0
,
2
2
2
,
0
,
2
2
2
2
4. Determining the position vectors of the points of application of the forces.
m
OD
r
m
OC
r
m
OB
r
m
OA
r
2
,
6
,
0
2
,
4
,
0
0
,
1
,
2
2
,
0
,
0
4
3
2
1
