Couple of a Triangle Question

In summary, Homework Equations state that the net couple moment on the triangle is 1140 Nm. To find this, the equation of moments is used and the moments are calculated for F1, F2, and F3. The origin is assumed to be at the point where the three moments intersect. This results in the equation: 1140=45520d.
  • #1
tbarker5
10
0

Homework Statement



In the figure F1= 27.9KN, F2= 39.8KN, F3= 61.8KN
What distance d is required for the net couple moment on the triangle to be 1140 counterclockwise?
Express your answer to three significant figures and include the appropriate units.
link to image http://imgur.com/cBnLJ

Homework Equations



I'm thinking the only really relevant equation is Mc=rXf or Mc=|r||F|sin(theta)

The Attempt at a Solution



So I wrote each moment in terms of d using trig. I got:
Mf1= 27900d Nm
Mf2= 19900d Nm
Mf3= 61800cos(30)d Nm
Then I set the sum of the three moments (with direction taken into respect) equal to 1140 Nm.
1140 = 11900d + 61800cos(30)d - 27900d
d~= 0.03038 m or 3.04*10^-2 m.

Unfortunately this was wrong and I have no clue where I went wrong. Any help would be greatly appreciated.
 
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  • #2
1140 = 11900d + 61800cos(30)d - 27900d

Where did 11900 come from? I know F2-F1=11900 but can't see how you got F2*D-F1*D from the drawing if indeed that's how you got to 11900.

Can you tell us which point you choose as origin, which direction you assumed as +ve and write the equation in terms of F1, F2 and F3 rather than substituting the values.

for example your equation above appears to be...

Total = (F2 - F1)d + F3Cos(30)d - F1d

Is that right?
 
  • #3
CWatters said:
Where did 11900 come from? I know F2-F1=11900 but can't see how you got F2*D-F1*D from the drawing if indeed that's how you got to 11900.

Can you tell us which point you choose as origin, which direction you assumed as +ve and write the equation in terms of F1, F2 and F3 rather than substituting the values.

for example your equation above appears to be...

Total = (F2 - F1)d + F3Cos(30)d - F1d

Is that right?

I didn't choose any point as an origin. The question asked about the couple on the entire triangle. And sorry here's my work for the equations:

It says that the total moment couple has to be 1140 counterclockwise, so I assumed counterclockwise as the positive direction for all the moments.
Then this is the part I wasn't too sure of. I figured that F2 and F3 would cause counter clockwise rotation while F1 would cause clockwise rotation.
Therefore 1140=MF2+MF3-MF1
subbing in: 1140=19900d+61800cos(30)d-27900d
1140=45520d
d=0.025m
WOW. I think I made an arithmetic error. just got it with 0.025m. I feel like an idiot. Thanks for the help though man
 

1. What is a "couple of a triangle" question?

A "couple of a triangle" question refers to a mathematical problem or puzzle that involves finding the relationship or characteristics of a couple of points in a triangle.

2. How do you solve a "couple of a triangle" question?

The solution to a "couple of a triangle" question usually involves using concepts from geometry and trigonometry, such as the Pythagorean theorem, sine and cosine functions, and angle measurements.

3. Can you give an example of a "couple of a triangle" question?

One example of a "couple of a triangle" question is finding the length of one side of a right triangle, given the lengths of the other two sides and the measure of one angle.

4. What skills are required to solve a "couple of a triangle" question?

Solving a "couple of a triangle" question requires a strong understanding of geometric concepts, trigonometric functions, and the ability to apply them in a problem-solving context. It also requires critical thinking and analytical skills.

5. Why are "couple of a triangle" questions important in science?

"Couple of a triangle" questions are important in science because they help us understand and analyze the relationships between different points or objects in a given system. They also require the use of mathematical and analytical skills, which are essential in many areas of scientific research.

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