Law of sine/cosines to find resultant force

In summary, Casey is using the Law of Sines/Cosines to find the resultant force R and its direction. Their teacher suggested decomposing the given forces into x and y components, but Casey is struggling to see how it helps. They also mention using the parallelogram law and the relationship between y components. Casey realizes that when adding vectors graphically, the vectors must be aligned tail to tip, and that the x components of A and B are in opposite directions, so one must be taken as negative. This helps them solve the problem.
  • #1
Saladsamurai
3,020
7

Homework Statement


So I am using Law of sine/cosines to find resultant force R and its direction.

th_Photo3.jpg


My teacher gave me a hint to decompose the 600 and 800 into x and y components...but I have done this and cannot see what it helps me to derive? Anyone else see it?

Casey

Also, I have drawn parellogram law
 
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  • #2
I just don't see the relationship here. It looks like the y components might add up to the y component of R...but I am not sure how to prove it or if that can even help me here.
 
  • #3
I'm going postal as we speak...I just thought you should know.
 
  • #5
stewartcs said:

So if A+B=R then [itex]A_x+B_x=R_x[/itex] and [itex]A_y+B_y=R_y[/itex] and [tex]R=\sqrt{(R_x^2+R_y^2)}[/tex]

Is this what I just read?! If so I did this earlier and got the wrong answer...but most likly because of a stupid mistake.

Is this correct though?
 
  • #6
When you add vectors graphically, which way must the be aligned? Tail to Tip. Otherwise, you will have a sign problem and add when you should subtract.

So,

Rx = Ax + Bx, but A (the 600 N vector) is tail to tail with the B vector, so what does this tell you?
 
  • #7
stewartcs said:
When you add vectors graphically, which way must the be aligned? Tail to Tip. Otherwise, you will have a sign problem and add when you should subtract.

So,

Rx = Ax + Bx, but A (the 600 N vector) is tail to tail with the B vector, so what does this tell you?

So, since the x components are in opposite directions, I need to take one as negative...thanks stewartcs! I knew I was overlooking the obvious!

Casey
 

1. What is the Law of Sines and how is it used to find the resultant force?

The Law of Sines is a mathematical formula that relates the lengths of the sides of a triangle to the sine of its angles. It can be used to find the resultant force by solving for the unknown side or angle in a triangle formed by two known forces and the resultant force.

2. How does the Law of Cosines differ from the Law of Sines in finding the resultant force?

The Law of Cosines is another mathematical formula that relates the lengths of the sides of a triangle to the cosine of its angles. It differs from the Law of Sines in that it can be used to find the unknown side or angle in a triangle formed by three known sides or two known sides and an included angle.

3. What information is needed to use the Law of Sines or Cosines to find the resultant force?

To use the Law of Sines or Cosines to find the resultant force, you will need to know at least two side lengths or one side length and its corresponding angle in the triangle formed by the two known forces and the resultant force.

4. Can the Law of Sines and Cosines be used to find the resultant force in non-right triangles?

Yes, the Law of Sines and Cosines can be used to find the resultant force in any triangle, not just right triangles. This is because they are general formulas that apply to all triangles, regardless of their angles.

5. Are there any limitations to using the Law of Sines and Cosines to find the resultant force?

One limitation of using the Law of Sines and Cosines to find the resultant force is that they assume the forces act in a two-dimensional plane. If the forces are acting in three dimensions, a different formula, such as the Law of Vectors, must be used to find the resultant force.

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