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So my question is

Rope BCA passes through a pulley at point C and supports a crate at point A. Rope segment CD supports the pulley and is attached to an eye anchor embedded in a wall. Rope segment BC creates an angle of ϕ = 62.0∘ with the floor and rope segment CD creates an angle θ with the horizontal. If both ropes BCA and CD can support a maximum tensile force Tmax = 700N , what is the maximum weight Wmax of the crate that the system can support? What is the angle θ required for equilibrium?


My first thoughts were to make the sum of all forces acting along each axis = 0 as it is in equilibrium.

(X axis) TCD cos θ - TBC cos 62 = 0 (We know TCD = 700)

Therefore 700 cos θ = TCB cose 62

(Y axis) 700 sin θ = TCA + TCB sin 62 = 0

But I have no idea where to go from here.

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Assuming the pulley is massless, use Newton's First Law to establish the conditions for equilibrium. 1.T(BC)Cosɸ = T(CD)Cosθ

2.T(AC) + T(BC)Cosɸ = T(CD)Sinθ

Also, considering the equilibrium of the mass, 3.T(AC) = W(Max)

Then from 1,2,3 W(Max) = T(CD)[Sinθ-CosθTanɸ] which implies W(Max)≤ T(Max)[Sinθ-CosθTanɸ]

Use the values to compute W(Max).

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