Solve Quarry Crane Problem: Find Rope 2 Tension

[yandao87]

Homework Statement

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. 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 tither. Both poles have length 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.

http://img3.imageshack.us/img3/4794/97030.jpg

Find tension in rope 2.

Homework Equations

The Attempt at a Solution

i tried to find torque about point O, but i couldn't resolve the angles. i know that the moment about O caused by tension in rope two should be equal to moment about O caused by the weight mg.

 

[LowlyPion]

i tried to find torque about point O, but i couldn't resolve the angles. i know that the moment about O caused by tension in rope two should be equal to moment about O caused by the weight mg.

I'd resolve the angles. With the 2 poles the same length, recognize that you have an isosceles triangle and that the other angle at the top will also be θ.

That means you can resolve the bottom angle and hence the angle that the pole holding the m*g is making with the horizontal.

 

[yandao87]

yes I've solved it. thank you. i need to use triangle geometry.