A bag of cement of weight 300 N hangsfrom three wires as suggested in the figure

Question

A bag of cement of weight 300 N hangsfrom three wires as suggested in the figure(http://www.webassign.net/pse/p5-24.gif). Two of the wiresmake angles 1 = 55.0° and2 = 22.0° with thehorizontal. Assuming the system is in equilibrium, find thetensions in the wires.
T1 = 1 N T2 = 2 N T3 = 3 N

T1 = 1 N T2 = 2 N T3 = 3 N

Explanation / Answer

From Free body diagram we can write             T2 Cos2 - T1Cos1 = 0             T2 Sin2 + T1 Sin1 - T3= 0 Tension T3 = Mg = W =300N            ........1           ==> 0.374T2 + 0.8191 T1 = 300     ...........2 and                  0.9271T2 - 0.5735 T1 = 0                    ==> T2 = 0.6186T1         ......3     Substituting 3 in 1 we get               0.374 * 0.6186 T1 + 0.8191 T1 =300               1.050 T1 = 300 N                ==> T1 = 285.5 N       .....4 Substituting 4 in 3 we get                         T2 = 176.66 N Therefore           T1 = 285.5N           T2 = 176.66N           T3 = 300N

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