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

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 ? = 52.0? with the floor and rope segment CD creates an angle ? with the horizontal. If both ropes BCA and CD can support a maximum tensile force Tmax = 145lb , what is the maximum weight Wmaxof the crate that the system can support? What is the angle ? required for equilibrium?

Express your answers numerically in pounds and degrees to three significant figures separated by a comma.

Explanation / Answer

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

2.T(AC) + T(BC)Cos? = T(CD)Sin?

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

Then from 1,2,3 W(Max) = T(CD)[Sin?-Cos?Tan?] which implies W(Max)? T(Max)[Sin?-Cos?Tan?]

Use the values to compute W(Max).

Related Questions

Navigate

• Browse (All)
• Browse R
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.