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Answer to Question #134148 in Physics for Samanta
Question #134148
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
Expert's answer
"T_3=325(N)"
"T_1\\cos60\u00b0=T_2\\cos40\u00b0\\to T_2=T_1\\cos60\u00b0\/\\cos40\u00b0"
"T_1\\sin60\u00b0+T_2\\sin40\u00b0=T_3"
"T_1\\sin60\u00b0+T_1\\cos60\u00b0\\sin40\u00b0\/\\cos40\u00b0=T_3"
"T_1=\\frac{T_3}{\\sin60\u00b0+\\cos60\u00b0\\sin40\u00b0\/\\cos40\u00b0}="
"=\\frac{325}{\\sin60\u00b0+\\cos60\u00b0\\sin40\u00b0\/\\cos40\u00b0}=253(N)"
"T_2=T_1\\cos60\u00b0\/\\cos40\u00b0="
"=253\\cdot\\cos60\u00b0\/\\cos40\u00b0=165(N)"
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