Moments & couples 2D (for now)

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In summary, the conversation is discussing a homework problem involving determining the equivalent forces-couple system at point O and finding the resultant force and point of action. The participants discuss how to solve the problem using vectors and breaking them down into components. They also mention the importance of showing their work and seeking further assistance if needed. The conversation ends with a question about solving a different homework problem involving moments and forces applied to a body in the XY-plane.
  • #1
random101
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Moments & couples 2D (for now) (cant move on :( )

Hey guys and girls, I am new to this forum but been looking at it for a while, its a great read and always a challenge here or there, but for now i was hoping to get a little help

:)

Homework Statement



The direction of the two thrust vectors of an experimental aircraft can be independently changed from the conventional forward direction within limits. For the thrust configuration shown, determine the equivalent forces-couple system at point O. then replace this force-couple system by a single force and specify the point on the x-axis through which the line of action of this resultant passes. These results are vital to assessing the design performance.


Homework Equations



http://206.229.17.58/dl/1364f79aea6cc95c449481aa34b672e5/46de37d0/image/4903phy.JPG


any help would be really really helpful cheers!
 
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  • #2
of the middle of the plane is Point O giving me a moment i can rotate on

lol now i can get somewhere :)
 
  • #3
I hope you are getting it, because as you say, the diagram is not too clear.
 
  • #4
yeah i have got a much better diagram now

should find Mx but yeah I am really not too sure how to go about it
 
  • #5
please help :(
 
  • #6
As noted, your image wasn't too clear, and now I don't see it at all. It appears though that you should find the resultant of the 2 thrust force vectors (magnitude and direction), and the torque of those 2 vectors about point O (break the lower thrust vector into components for simplicity in calculating its torque), then place that resultant force and couple at O. To find the equivalent force through the x axis, I'd divide the couple by the y component of the resultant force.
 
  • #7
http://38.119.88.15/dl/733f4285bc921a9884d963ee84c66e48/46defcb0/image/2760phy.JPG

yeah that's what i have been attempting, ill give it another good shot when i get home :)

thanks :)
 
  • #8
im not to sure what i can do with that angle of thrust

at 15degrees
 
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  • #9
attachment.php?attachmentid=10820&stc=1&d=1189047829.jpg
 

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  • #10
mm i think i have gone down the wrong road with this question should i be looking at it as a torsional question? that might make life easier
 
  • #11
bump?
 
  • #12
Nice pic. As I mentioned earlier, the resultant force is the sum of the 2 thrust vectors, and the resultant moment about O (couple, or torque, if you wish), is the sum of the moments of those vectors about O. Try breaking each vector into its x and y components. The upper force has an x component only. The lower one has an x component of Tcos15 and a y component of T sin 15. Sum torques of those componnents about O, watch plus and minus signs. Show your work so that we may be of further assistance. Your result will be a function of T, which is not given.
 
  • #13
is the answer 2.69T

Mo = 0: T3+tsin15x10 - Tcos15x3
 
  • #14
random101 said:
is the answer 2.69T

Mo = 0: T3+tsin15x10 - Tcos15x3

EDIT: Oops sorry! You're right. I was wrong. I'm still confused by the Mo=0.
 
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  • #15
random101 said:
is the answer 2.69T

Mo = 0: T3+tsin15x10 - Tcos15x3
Your picture seems to come and go quicker than the Chesire Cat. I think as I view it that you have 2 thrust vectors T, spaced 6 meters apart vertically, 3 m each from the x axis. One is horizontal, the other 15 degrees up from the horizontal. I don't see how yu can arrive at 2.69T as a resultant ...even if they were both horizontal, they'd add up to 2T, so surely the resultant must be less. You are just going to have to show your work if you need more help. Your moment looks good, but don't set it equal to zero, it is what it is. Then you still have to determine at what point on the x-axis the resultant falls.
 
  • #16
how could i solve this question?

Three forces acting in the XY-plane are applied to a body.
F1= i + 3j applied at (2,5)
F2= 3i - 3j applied at (0,11)
F3= i + 12j applied at (5,-4)

(a) Show that the moments of F1 and F1 about the point P(3,8) are both zero.

(b) Find the moment of F3 about P

(c) Write down the moment of F about P
 

1. What are moments and couples in 2D?

Moments and couples in 2D refer to the forces and torques that act on an object in two-dimensional space. Moments are rotational forces that cause an object to rotate around an axis, while couples are two equal and opposite forces that act on an object at different points, causing it to rotate.

2. How are moments and couples calculated?

Moments and couples can be calculated using the equation M = F x d, where M is the moment, F is the force acting on the object, and d is the perpendicular distance from the point of rotation to the line of action of the force. For couples, the magnitude of the torque can be found by multiplying one of the forces by the distance between the two forces.

3. What is the difference between a moment and a couple?

The main difference between a moment and a couple is that a moment is a single force acting on an object, while a couple is two equal and opposite forces acting on an object at different points. Moments tend to cause an object to rotate around a fixed axis, while couples cause an object to rotate without changing its position.

4. How do moments and couples affect equilibrium?

Moments and couples play a crucial role in maintaining equilibrium in an object. In order for an object to be in equilibrium, the sum of all the moments acting on it must be zero. This means that the clockwise moments must balance out the counterclockwise moments. Similarly, the sum of all the forces acting on the object must also be zero.

5. What are some real-life examples of moments and couples in 2D?

Moments and couples can be found in many everyday situations. For example, when opening a door, the force applied to the doorknob creates a moment that causes the door to rotate around its hinges. Another example is a seesaw, where two equal and opposite forces act on either side of the pivot point, creating a couple that allows the seesaw to rotate.

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