Machines: Problem Solving II

Machines are complex structures consisting of movable, pin-connected multi-force members that work together to transmit forces. Consider a lifting tong carrying a 100 kg load. It comprises movable sections DAF and CBG linked together with member AB.

Assuming the structure is symmetrical at point E, the force acting on member AB can be calculated.

First, a free-body diagram indicating the forces acting at point E is considered. The weight of the load that equals the mass times the acceleration due to gravity is calculated as 981 N. The cable's tension force balances the load's weight and acts vertically upwards. ED and EC are two-force members. As a result, the forces F_ED and F_EC are directed towards joints D and C, respectively.

Next, the forces F_ED and F_EC are resolved into horizontal and vertical components. The structure's geometry can calculate the angle between the member ED and the horizontal force component as 30.96 degrees.

The force equilibrium conditions can be applied to joint E.

Applying the force equilibrium condition along the horizontal direction ensures that F_ED equals F_EC. Similarly, the vertical force equilibrium condition yields the force along the member ED as 953.46 N.

Now, a free-body diagram for section DAF is considered. The moment equilibrium condition can be applied to joint F.

The result gives the force along member AB as 2423.76 N.

Understanding the forces acting on each member in this lifting tong system is essential for ensuring safe operation and designing efficient lifting mechanisms. By analyzing the forces and applying equilibrium conditions, engineers can optimize the structure and ensure it can safely carry loads under various conditions.