1. The top view of a revolving entrance door is shown. Two persons simultaneously
approach the door and exert force of equal magnitudes as shown. If the resulting
moment about the door pivot axis at O is 25 N.m, determine the force magnitude F.
2. Express and identify the resultant of the two forces and one couple
shown acting on the shaft angled in the x-z plane.
300 N
18 cm
400 N.m
300 N
3. Determine the distance d between points A and B so that the resultant
couple moment has a magnitude of CR= 20 Nm.
CR= 20 Nm
𝑟𝐵/𝐴
 

C1  rC / A  F1







C1  0.25i  d cos 30 j  d sin 30k   50i 
𝑟𝐶/𝐴



C1  50d cos 30k  25dj

 


 



C2  rB / A  F2 
C2   d cos 30 j  d sin 30k  35k


C2  35d cos 30i


 


Resultant Couple: C R  C1  C2  50d cos 30k  25dj  35d cos 30i
CR 
50d cos 302  25d 2  35d cos 302
d  0.342 m
 20
4. Three couples are formed by the three pairs of equal and opposite
forces. Determine the resultant CR of the three couples.

C1






 
C1  r1  F1  0.2 j   100k  20i

C3

 
C 2  r2  F2




C 2   0.3 j   120 cos 45i  120 sin 45 j 


C 2  25.46k

C2

C3
20o
80 N
C3
80 N
20o
30o
20o
z
y
C 3  80  0.18 cos 20   13.53 N  m



C 3  13.53  cos 30k  sin 30 j



C 3  6.765 j  11.71k






CR   C  20i  6.765 j  37.17k

5. Determine the couple acting on surface ABC in vector form.
z
C (0, 0, 4)
𝑪
y
O
A (3, 0, 0)
x
B (3, 6, 0)
6. Three couples are formed by the three pairs of equal and opposite forces.
Determine the resultant of the three couples.