Statics- Resultant couple moment

In summary, the problem involves finding the magnitude and coordinate direction angles of the resultant couple moment given three forces with their respective magnitudes. The solution involves using the equations M=Fd, M=r x F, and MR=Ʃ(r x F). The difficulty lies in finding the moment for the fourth force, which has both x and y components and is parallel to the xy plane. Once this is determined, the correct answer is (MC)R=71.9 Nm.
  • #1
rico22
51
0

Homework Statement


If F_1 = 100N , F_2 = 120N and F_3 = 80N , determine the magnitude and coordinate direction angles of the resultant couple moment.

Homework Equations


M=Fd
M=r x F
MR=Ʃ(r x F)


The Attempt at a Solution


I found the couple moment for each force:
M1=F1d=100(0.2) or (-20j using right hand rule)
M2=F2d=120(0.2) or +24i
M3=F3d=80(0.2) or -16k
M4=this is what I am having problems with...not sure how to get the moment for F4... if do 150(.3)(cos30)=38.97 i get the wrong resultant.

The correct answer should be (MC)R=71.9 Nm...
Any help would be greatly appreciated.
 

Attachments

  • Hibbler_ch4_p95.jpg
    Hibbler_ch4_p95.jpg
    8.9 KB · Views: 944
Physics news on Phys.org
  • #2
hi rico22! :smile:
rico22 said:
The correct answer should be (MC)R=71.9 Nm...

i don't get 71.9 unless i use .33 instead of .3 :redface:
 
  • #3
Note that the F4 couple is not in the x-direction. It is parallel to the xy plane but it has both x and y components which you will need to work out.
 
  • Like
Likes 1 person
  • #4
TSny said:
Note that the F4 couple is not in the x-direction.

ooh, i didn't notice that! :redface:

i read the axis of that pipe, and the short line above the positive x-axis, as one continuous straight line! :rolleyes:

yes, now i get 71.9 … thanks, Tsny :smile:​
 
  • #5
thanks for the replies guys...
 

1. What is a resultant couple moment in statics?

A resultant couple moment is a measure of the rotational force acting on a body caused by two equal and opposite forces that are parallel to each other but do not share the same line of action. It is also known as a torque or moment of a couple.

2. How is a resultant couple moment calculated?

A resultant couple moment is calculated by multiplying one of the forces by the perpendicular distance between the force and the point of rotation. This distance is known as the moment arm. The resultant couple moment is measured in units of force multiplied by distance, such as Newton-meters (Nm) or pound-feet (lb-ft).

3. What is the significance of a resultant couple moment in statics?

A resultant couple moment is important in statics because it can cause a body to rotate around a fixed point. It is also used to analyze the stability and equilibrium of structures, as well as in the design of mechanical systems and machines.

4. How does a resultant couple moment differ from a single force?

A resultant couple moment is different from a single force because it is a combination of two forces acting in opposite directions, while a single force acts in only one direction. Additionally, a resultant couple moment causes rotational motion, while a single force causes linear motion.

5. Can a resultant couple moment be balanced or canceled out?

No, a resultant couple moment cannot be balanced or canceled out. This is because it is a rotational force and does not have a specific direction that can be counteracted by another force. However, it can be counteracted by an equal and opposite resultant couple moment.

Similar threads

Determining the magnitude of the resultant couple
    • Introductory Physics Homework Help
Replies
2
Views
3K
Engineering Hand tool boundary conditions - Forces determination
    • Engineering and Comp Sci Homework Help
Replies
3
Views
904
What are the coordinate direction angles for the resultant couple moment?
    • Introductory Physics Homework Help
Replies
4
Views
7K

Hot Threads

Recent Insights

Back
Top