Derive the formula for \ m F_3 in terms of the experimentally measured quantitie

Question

Derive the formula for m F_3 in terms of the experimentally measured quantities m m_1, m m_2, m heta_1, and m heta_2.
[Answer: m F_3 = m_1 g cos heta_1 + m_2 g cos heta_2.]  
Make sure you understand how this formula was derived.  
QUESTION:
If the mass of both weights is 200 gm, the first mass is located 20 m ^{circ} north of east, the second mass is located 20 m ^{circ} south of east, and the transducer sensitivity is 0.5 volts/Newton, how large a voltage do you expect to measure?  Assume the transducer has been properly zeroed so that V = 0 when m F_3 = 0.   

Explanation / Answer

Due to symmetry the y components cancel and the x components F3 = 2*m*g*cos(20) =
= 2*.200kg*9.8m/s^2*cos(20) = 3.68N

SO the transducer should read 3.68N*0.5V/N = 1.84V

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