A mass of 50 kg hangs from a rope that passes over a frictionless pulley and is pulled horizontally. Neglecting the mass of the rope and pulley, the tension in the rope throughout its length is:

For a frictionless pulley with a single rope: tension T is the same throughout the rope. The hanging mass requires T = W = mg = 50 x 9.81 = 490.5 N. The horizontal pull must also be 490.5 N (same rope, frictionless pulley). The pulley support force = vector sum of the two rope tensions (490.5 N each at 90 deg = 490.5 x sqrt(2) = 693 N at 45 deg).

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