Lesson 6 - Solving problems of statics

Regarding to the specific mechanical system, all loads can be divided into two groups: internal and external. As mentioned in lesson 3, solving of mechanical problem starts from mentally isolating mechanical system from the outer world, and replacing impacts from the surrounding bodies on our system with forces and torques. By "mechanical system" are meant a single body or a group of bodies, which are somehow interacting with the outer world.

Those loads, which results from interaction with external bodies (which are not a part of our system) are external loads. In opposite, loads, which occurs from interaction between the target system parts are internal loads. To make it clear let's take a look on the train:

The third Newton's law says: "The force of action is equal to the force of reaction". If first body impacts the second body with force F, then the second body also impacts the first one with force F', which is of the same magnitude, but opposite directed. The Locomotive is pulling the car forward with force F, so the car is pulling the locomotive backward with the same but opposite force F', making it harder for locomotive to accelerate. Those two forces F and F' are obviously compensating each other.

Now if we solve a case for the locomotive only, we mentally discard the car and replace car's impact with force F'. Thus, relative to the locomotive force F' will be external load. On the other hand, if the target mechanical system is "Locomotive + car", then forces F and F' will be considered as internal loads.

The point is: internal loads can be omitted since they compensate each other. When solving the case we should be concerned on external loads only - they contribute equilibrium equations.

Now we can proceed with solving a problems of statics. The subject of statics is equilibrium state of mechanical system. The goal is to find such a combination of forces and torques, which makes the system to stay in equilibrium state. Usually, external loads are given and reactions should be found. However, the opposite task can also be considered.

The equilibrium equations are used in solving problems of statics. In general they looks as follows: