Balancing forces in three dimensions

[Birdeye]

I am working on a lab assignment that is having us figure out an unknown force based on various given forces. All the 2-D problems I could do easily. Unfortunately, the last problem has thrown me for a loop as it deals with an actual setup in the lab room with forces in all 3 directions.

Here is the actual text of the question:

The unknown weight is now supported by three strings, each with their own spring balance. This time, using only a meter stick and trigonometry, solve for the value of the unknown weight. Label the known values.

There was also a crude picture supplied with 3 lines going upward from a central point (one line vertical, the other two diagonal and up) each with (what I assume) to be a representation of a spring balance at the top. Where the 3 lines meet there is another line going down to a circle with a ? in it to represent the unknown weight.

The actual set up in the lab matches this: 3 strings hung from 3 different poles with a spring balance at the top of each string; in the middle, hanging from all 3 strings is the unknown weight (although, comparing the sizes to other known weights in the lab, it looks to be 1050g, and so about 10.3 N).

There is a problem though, all the problems we have done before have a) been in 2 dimensions and b) all the strings were hung from the same height. In the lab setup the strings are attached at different heights and the poles they are hung off of are not in a straight line. (The bases of the 3 poles form a right triangle with force 2 at the right corner.)

By looking at the problem I assumed that we were supposed to measure the string lengths, so I did that, but I measured them all from an arbitrary height as if that was the 'ceiling'.

Here are the values I came up with:

F1 = 2.85 N, 42 cm
F2 = 6.2 N, 34 cm
F3 = 3.5 N, 56 cm

The Newton values were obtained by just reading the spring balances (obviously).

Now, usually I don't have as much trouble on problems as I am having on this one, but it has been a decade since my trigonometry class in high school and I don't even know if I gathered enough data from the setup.

So, that's my initial question: Have I collected enough data to solve this problem (within the constraints of what I am allowed to use: just a meter stick and trigonometry).

If I do need more information, what information would that be? The lab manual/assignment we were given neither states nor implies that we need measurements other than the length of the strings, but I may be missing something important.

I just don't want to bash my brain any more trying to figure out what to do if I don't even have enough information to solve the problem yet.

Thanks.

 

[edavey8205]

as long as you have all your angles and then the above lenghts/forces you should be able to do it. do you have a free body diagram of all the strings, angles, lengths, and forces.

 

[Birdeye]

We are not allowed to measure the angles:

The unknown weight is now supported by three strings, each with their own spring balance. This time, using only a meter stick and trigonometry, solve for the value of the unknown weight. Label the known values.

If we were allowed to collect the angles I wouldn't be having any trouble.

After pondering it a bit I think I do need more data, so I'm going to go back to the lab and measure the horizontal and vertical distances from the weight to each of the strings. Perhaps that will help.

As for a free-body diagram, I don't have one yet, other than the crude one on the sheet, because the forces are in 3D and I'm not sure how to draw it. As I said, we have not had ANY 3D problems before this one.