# Finding the Unknown Mass; Given Tension & Normal Force

The figure below shows an object of unknown mass m, held by a massless string on a frictionless inclined surface. The angle θ is also uknown. If a tension of magnitude T = 5.8 N and a normal force of magnitude N = 9.7 N act on the object, what is the mass m?

http://img161.imageshack.us/img161/4345/q3qs7.gif [Broken]

I can't seem to find an equation in my textbook that I could manipulate in order to find the unknown mass, using the givens. Any help would be much appreciated, thanks.

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Welcome to the forums.

I haven't gotten very far with the working, because I'm stuck on finding a formula. But I looked at:

1. To find its tension:

T = mg sinθ
5.8 N = [?kg] x 9.8 x [sinθ?]

I can't manipulate this formula because I'm missing both the mass and the angle.

2. To find its force:

N = mg cosθ
9.7 N = [?kg] x 9.8 x [cosθ?]

Also missing both mass and angle.

Is there any way to find one of the unknowns? At first I thought that the angle is irrelevant, and we can solve for the mass just using the tension and the normal force. But then I found that every other formula requires information about the mass or the angle.

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Alright so I found out that I can take the two formulas, put them both equal to 0, and then allow them to equal eachother in order to solve for the mass.

0 = mg sinθ - T

0 = mg cosθ - N

mg cosθ - N = mg sinθ - T

m (9.8) cosθ - 9.7 = m (9.8) sinθ - 5.8

The 9.8 can be cancelled out, and we can rearrange the equation so that:

m cosθ - m sinθ = - 5.8 + 9.7

m cosθ - m sinθ = 3.9

Where can I go from here? I'm assuming trig identities, but I haven't used them for so long...

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OR would I be able to use m = T/g to find the mass, since this problem goes by Newton's first law because there is no acceleration taking place...

Hello! You are missing one key piece of information from the question. You are going to need to use the ratio N/T (or T/N, whichever you fancy) to obtain something along the lines of: N/T = 9.7N / 5.8N = ...something.

So we now have another equation to use to solve this question: N = (T)(something...) From here you will be able to substitute into those lovely equations you have already setup.

Bear in mind the trig identity sinθ/cosθ = tanθ, but this is the only one you will need to know to solve this question... at least in my case :P.

Hope this helps!