Question

A bag of cement weighing 325 N hangs in equilibrium from three wires. Two of the wires make make angles u1 60.0 degrees and u2 40.0 degrees with the horizontal. Assuming the system is in equilibrium; find the tensions T 1 , T 2 , and T 3 in the wires

Answer 1

$T_3=325(N)$

$T_1\cos60°=T_2\cos40°\to T_2=T_1\cos60°/\cos40°$

$T_1\sin60°+T_2\sin40°=T_3$

$T_1\sin60°+T_1\cos60°\sin40°/\cos40°=T_3$

$T_1=\frac{T_3}{\sin60°+\cos60°\sin40°/\cos40°}=$

$=\frac{325}{\sin60°+\cos60°\sin40°/\cos40°}=253(N)$

$T_2=T_1\cos60°/\cos40°=$

$=253\cdot\cos60°/\cos40°=165(N)$