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4) A 500 mm diameter pulley is driven at 400 rev/min by a belt 100 mm wide by 20 mm thick with a safe working stress of 400 kN/m². The tension in the tight side of the belt is 2.5 times the tension in the slack side and the coefficient of friction between contact surfaces is 0.35.

Calculate EACH of the following:

(a) The power input at 85% efficiency; (10)

(b) The angle of lap in degrees using the relationship: (6)

where:

F₁/F₂ = e^μθ

F₁= force in the tight side of the belt.

F₂= force in the slack side of the belt.

μ = the coefficient of friction.

θ = the angle of lap in radian.