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Homework Statement
https://ibb.co/g6iKDQ
Calculate the magnitude of the force on cables 1 and 2 in the figure below if θ_1 = 55° and θ_2 = 35°.
(Round your answers to two decimal places.)
Homework Equations
Is my method incorrect or did I go wrong somewhere in my calculations??
The Attempt at a Solution
So what I did was I used the equation for F_1 + F_2 + F_g = 0.
F_1 = f_1 * <cos(125˚), sin(125˚)>
F_2 = f_2 * <cos(35˚), sin(35˚)>
F_g = 9.8 * (50) = 490<0, -1>
Then set F_1 + F_2 + F_g = <0, 0>
Moving to the system of equations
f_1*cos(125˚) + f_2*cos(35˚) = 0
f_1*sin(125˚) + f_2*sin(35˚) - 490 = 0
Solved for f_2 on first equation
f_2 = -f_1(cos(125˚)/cos(35˚))
plugged it into the 2nd equation
f_1*sin(125˚) + (-f_1(cos(125˚)/cos(35˚))sin(35˚) - 490 = 0
Solved for f_1 and got 502.46 rounded
and for f_2 I got 351.82.
After that, I plugged it into the F_1 and F_2 equations by
F_1 = 502.46<cos(125˚), sin(125˚)>
F_2 = 351.82<cos(35˚), sin(35˚)>
F_1 = <-288.2, 411.59>
F_2 = <288.2, 201.8>
Then got the magnitude with
Sqrt(288.2^2 + 411.59^2) = 502.46
Sqrt(288.2^2 + 201.8^2) = 351.83
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