
STATICS  EXAMPLE



Example


The pulley system for an elevator is shown in the figure on the left. This mechanical system consists of 5 pulleys and 2 electric motors. The maximum allowable weight for the elevator is 5 kip.
a. What is the minimum required force for each motor?
b. If one of the electromotors is removed and instead the cable is directly attached to the wall, what will be the minimum required force for the remaining single motor? 




Solution



a. As with all statics problem, a freebody diagram will assist in solving the problem. In this example, all forces acting on the elevator cabin is first analyzed. The 5000 lb weight is divided evenly between the cables due to symmetry. Consequently the force of each cable will be
P = 5000 / 2 = 2,500 lb






Next, assume the cable force in each motor is F. The diagram on the left shows the pulley system with the external forces and with the elevator forces. 





The freebody diagram for pulley number 2 is shown on the left. Note that the freebody diagram for the pulley number 4 would be similar. Summing the forces in the vertical direction gives,
ΣF_{y} = 0
0 = 2 T_{2}  2,500 lb
T_{2 }= 1,250 lb
Since the cable is continuous,
T_{2} = F = 1,250 lb 





b. If one of the electromotors is removed, then the cable is directly attached to the wall. The freebody diagram and the solution procedure would be the same. In this case the reaction force at the wall is equal to 1,250 lb. Therefore removing one of the motors will not affect the final answer. Also, by removing one of the electromotors, both cost and energy will be saved for the consumer and manufacturer.

