Three balanced forces pull on a ring that is centered over a force table. Two forces F1 and F2 are due to weights hanging from pulleys. A frictionless pulley changes the direction of a force without altering its magnitude. The third force F3 is applied by a string that passes over a pulley and pulls on the force transducer. The equivalent vector diagram for this configuration is shown in Figure 5.2.
Derive the expected value of θ2 in terms of m1, m2, and θ1.
FIG. 5.1 twitpic com/10mgby
FIG 5.2 twitpic com/10mgdb
The answer is θ2 = arcsin (m1sinθ1/m2)
Could you explain how the answer was derived with what equations and laws and how to apply them to the figures? I don't have a good grasp on interpreting the figures.
I know that F=ma=mg and Fg=Fsinθ was used, but I don't know how.
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Ok I actually understand part of it now, but why is sin (θ1) used instead of cos? Wouldn't using cos give the horizontal component of F2?
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