Question

A block of mass 50.0 kg is hung by ropes. The system is in equilibrium. The...

A block of mass 50.0 kg is hung by ropes. The system is in equilibrium. The point O represents the knot, the junction of the three ropes. The magnitude of the tensions in the ropes are T1 (25 degrees) and T2 (30 degrees). By solving for T1 and T2 determine the sum of the magnitudes of the tensions T1 + T2. Answer is 1100 N. Please explain step by step.

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Answer #1

As shown in the figure we will take component of the tension in the x and Y direction
Since the mass is in equilibrium therefore
Net force in X direciton will be zero
T2Cos30 = T1Cos25
T2 = 1.046T1 --------------(1)
Now in the Y direction
T1Sin25+T2Sin30 - (Mg) = 0
T1Sin25 + (1.046T1)Sin30 = 50*10
T1(Sin25 + 1.046Sin30) = 500
T1(0.9456) = 500
T1 = 530
Now ,
T2 = 1.046T1 = 1.046*530= 557
Hence T1 + T2 = 557+530 = 1087 N
which is approximately equal ro 1100 N

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