A quarry crane is used to lift massive rocks from a quarry pit. Consider the sim

Question

A quarry crane is used to lift massive rocks from a quarry pit. Consider the simplified model of such a crane shown in the figure. (Figure 1) The ends of two poles are anchored to the ground at the same point (point O). From this point, one pole rises vertically and the second pole rises at an angle. The vertical pole has its free end connected to the ground via an unstretchable, massless rope labeled rope 1. A second rope, labeled rope 2, connects the free ends of the two poles. The angle between the tilted pole and rope 2 is ?. Both poles have length L and can be considered massless for the purposes of this problem. Hanging from the end of the second pole, via rope 3, is a granite block of mass m.

Throughout this problem use g for the magnitude of the acceleration due to gravity.

Find T1, the tension in rope 1.

Express the tension in terms of some (or all) of the following quantities: m, g, L, ?, and ?.

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Answer involves variable ? . PLEASE READ LEFT

Explanation / Answer

Tension T3 is just the wt = mg

angle between the pole = ( pi - 2 theta)

Toque need to pull the force is at an angle of 2theta = pi/2

applying torue appiled by rope about point O is

T 1 = LMg(2 theta - Pi/2)

T1 = Lmg sin 2 theta

also torque T2 must be equal T1

T2 = LT sin theta

T2   = T1

so

LT sin theta = LMg sin (2 theta )

T = 2mg cos theta ---------<<<<<<<<<<<Answer

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