Tower cranes are used at major construction sites to raise loads up to 120 tons. A tower crane consists of a central tower with two arms holding a fixed and a mobile counterweight. The operator moves the mobile counterweight to balance the load.
Suppose the arms have a mass of 100 tons , the lengths of the short and long arms are 56 m and 84 m, and that the center of mass is in the middle at 14 m to the right of the center of the tower. The fixed and mobile counterweights weigh 100 tons and 120 tons and ). The normal force and the weight of the tower do not generate any torque. Let be the weight of the load.
Then the position of the mobile can be calculated from
The example is taken from H. C. Ohanian and J. T. Markert, Physics for Engineers and Scientists, Volume 1, 3rd ed., W. W. Norton & Co Inc (np), 2007.