A nonuniform, horizontal bar of mass m is supported by two massless wires agains

Question

A nonuniform, horizontal bar of mass m is supported by two massless wires against gravity. The left wire makes an angle 1 with the horizontal, and the right wire makes an angle 2. The bar has length L. (Figure 1)

Part A Find the position of the center of mass of the bar, x, measured from the bar's left end. Express the center of mass in terms of L, 1, and 2.

A nonuniform, horizontal bar of mass m is supported by two massless wires against gravity. The left wire makes an angle with the horizontal, and the right wire makes an angle O2 The bar has length L. (Figure Figure 1 of 1 Part A Find the position of the center of mass of the bar, z, measured from the bar's left end Express the center of mass in terms of L pl, and p2 Submit Hints My Answers Give Up Review Part incorrect, Try Again; 6 attempts remaining Provide eedback Continue F

Explanation / Answer

balancing forces in horizontal direction,

TR cos(phi2) - TL cos(phi1) = 0

TR = TL cos(phi1) / cos(phi2) .... (i)

balancing moment about centre of mass point,

( x TL sin(phi1)) - ( ( L - x ) TR sin(phi2)) = 0

putting TR from (i)

x TL sin(phi1) - (L - x) TL sin(phi2) cos(phi1) / cos(phi2) = 0

x sin(phi1) - L tan(phi2) cos(phi1) + x tan(phi2) cos(phi1) = 0

x [ sin(phi1) cos(phi2) + sin(phi2) cos(phi1)] / cos(phi2) = L sin(phi2) cos(phi1) / cos(phi2)

x sin(phi1 + phi2) = L sin(phi2) cos(phi1)

x = L sin(phi2) cos(phi1) / sin(phi1 + phi2)

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