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Tension in both wires?

If you hang a pot-plant with mass of 8kg from two lengths of wire attached to a horizontal beam 100cm apart. The wire on the left has a length of 50cm and the wire on the right has a length of 75cm.What is the tension in both wires?

Answer:

The tension in both wires.? If you hang a pot-plant with mass of 8kg from two lengths of wire attached to a horizontal beam 100cm apart. The wire on the left has a length of 50cm and the wire on the right has a length of 75cm. What is the tension in both wires? In the triangle ABC, AB(c) = 100 cm, BC (a) = 50 cm and AC (b) = 75 cm 2s = a+b+c = 225 cm s = 112.5 s-a = 112.5 - 50 = 62.5 s-b = 112.5 - 75 = 37.5 s-c = 112.5 - 100 = 12.5 tan A/2 = √ {(s-b)*(s-c) / [s*(s-a)] = √ {37.5*12.5) / [112.5*62.5] A = 28.95? tan B/2 = √ {(s-c)*(s-a) / [s*(s-b)] = √ {12.5*62.5) / [112.5*37.5] B = 46.57? C = 180-28.95-46.57 =104.48? --------------------------------------... 46.57? is the angle between horizontal and 50 cm wire. 28.95 is he angle between horizontal and 100 cm P is the tension in the 50 cm wire and Q is the tension in the 75 cm wire Equating the horizontal components of the tensions P cos 46.57? = Q cos 28.95 ? P = Q cos 28.95 ?/ cos 46.57? P = 1.27 Q-------------------1 Equating the sum of the vertical components of the tensions to the weight of the pot P sin 46.57? + Q sin 28.95 = 8*9.8 N 0.73P + 0.48 Q = 78.4N 0.73(1.27 Q) + 0.48 Q = 78.4N Q = 55.72 N and P = 70.76 N ============================= Or use Lamis theorm Angle between P and Q = 104.48? Angle between P and the pot = 90 + 46.57? Angle between Q and the pot = 90 + 28.95 By Lamis theorm P/ cos 46.57? = 78.4/ sin 104.48? P = 55.67 N and Q = (78.4/ sin 104.48? ) cos28.95 = 70.85N ====================================

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