Solving a Vector Problem: Finding x & theta

[rocketboy]

Hey everyone,

My math teacher gave us the following vector problem:

"Three coplanar forces of xN, 10N, and 20N act on a body and maintain it in a state of equilibrium. If the x-N force acts along the horizontal and the 10-N force at an angle of 60 degrees to the horizontal, find the value of x and the direction of the 20-N force, correct to one decimal place."

I drew my diagram, and it doesn't look overly difficult. However I am wondering if there are multiple answers to the question. From the way I have set it up, I can simply choose any value for theta (the angle of the 20N force relative to the horizontal) and then solve for x.

Here is a sketch of what my diagram looks like:

 

[Fermat]

When you resolve the forcecs, you've got to be able to balance all the horizontal forces and all the vertical forces. So, you must ajust your angle to make this look feasible.

How did you set it up - your attachment is not yet available for viewing, but I can imagine what it must look like.

 

[bayan]

I get $$n=13$$ and angle of $$20N$$ to be $$244T$$

 

[rocketboy]

I get $$n=13$$ and angle of $$20N$$ to be $$244T$$

What do you mean 244T?

I set it up so that xN was east, 10N was pointed SW (60 d to horizontal) and 20N was pointing NW, theta d to horizontal. all points are at the same place, acting on the same body, because they have to all cancel out in each of the x and y components to maintain equilibrium.

 

[rocketboy]

When you resolve the forcecs, you've got to be able to balance all the horizontal forces and all the vertical forces. So, you must ajust your angle to make this look feasible.

How did you set it up - your attachment is not yet available for viewing, but I can imagine what it must look like.

The thing is, i can adjust xN to be any force, so no matter what angle the 20N force is (i have both 10N and 20N pushing against xN) i can compensate for it by adjusting x to cancel out the 20N and 10N that are pushing towards xN on their respective angles.

 

[bayan]

http://img83.imageshack.us/img83/569/howto3ms.jpg [Broken] is a howto incase you get stuck

 

[rocketboy]

OMG...I just reviewed my notes and realized that I drew my free-body diagram wrong! I had the heads of the vectors at the body, instead of the tails! My physics teacher would be SO dissapointed! (not to mention my math teacher).

Thank you for your help guys.

 

[Ouabache]

Some of the concepts of this exercise may come in handy for when you want to calculate how far your rockets have traveled (as Homer and Quentin found out).

 

[rocketboy]

Some of the concepts of this exercise may come in handy for when you want to calculate how far your rockets have traveled (as Homer and Quentin found out).

:tongue2: