Rope BCA passes through a pulley at point C and supports a crate at point A. Rop

Question

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 Phi = 55.0degree with the floor and rope segment CD creates an angle theta with the horizontal. If both ropes BCA and CD can support a maximum tensile force Tmax = 875 N, what is the maximum weight Wmax of the crate that the system can support? What is the angle Phi required for equilibrium? Express your answers numerically in newtons and degrees to three significant figures separated by a comma.

Explanation / Answer

tension in cd be T1
tension in bca be T2
balancing forces in vertical directiob
T1sin=T2+T2sin -(1)

balacing forces in horizontal direction

T1cos=T2cos-(2)

T2=Wmax-(3)

from (1) and (2) we get:(1+sin)/sin=cos/cos

solving we get =72.5 degrees

from (3):T1=T2*1.907

T1>T2

so T1 can reach its maximum value T1=875N

T2=T1/1.907=458.84 N=Wmax

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