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

















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.

2

5. Calculating the position vector of the center of the force system.



 

 

 















m

m

kN

kNm

a

r

a

r

OO

i

i

i

6

,

6

,

4

2

12

,

12

,

8

2

2

2

,

6

,

0

2

2

,

4

,

0

1

0

,

1

,

2

4

2

,

0

,

0

3

2





































6. Answer
At the center of the parallel system

the system is reduced to the resultant force



m

O

6

,

6

,

4













kN

S

W

2

,

0

,

2







.