## Saturday, March 4, 2017

### Free body diagram and Connected Bodies Video Lesson

Free body diagram is the representation of all the forces acting on a body at a given instant. We shall consider only the forces acting on a body but not the forces applied by the same body. When there are multiple bodies, all of them can be treated as one system if they have same acceleration. When we are solving a system of bodies and we are interested in finding the acceleration and may be tension and contact forces  on a given body. We shall draw free body diagram for each body and we shall further write the equation for the resultant force. We shall consider the force along the direction of motion as positive and vice versa. We are also dealing with contact force in the given video below. Contact force is t he force applied by one body on the other when they are in contact. There will be reaction force also according to Newton's third law of motion.A detailed video lesson is presented below regarding free body diagrams as shown below.

Connected bodies and free body diagram

Here we are discussing about the bodies of different masses connected with the help of string and a force is applied on the system. When force is applied, the string becomes tight and a tension is developed in the wire. We need to identify all the forces acting on each body. We need to be careful and identify only forces acting on the body but not the forces applied by the body. This can be done with the help of free body diagram for each body. Thus we can write equation for resultant force on each body  and we can solve that equations and get the tension in each wire and acceleration of the system as shown in the video lesson below.

Atwood's machine

Two bodies of different masses connected over a smooth pulley with the help of light weighted string could be called as Atwood's machine. We need to find the tension int the wire and the acceleration of the system. We can write free body diagram for each body and equations for resultant force as shown in the video lesson below.

Connected bodies one in vertical mode and other in horizontal position

Let us consider a system of two bodies where one body is hanging vertically from a table and the other body is on a smooth horizontal smooth surface and the two bodies are connected with a light weighted string over a smooth pulley. We need to find the tension in the string and the acceleration of the system. We can draw free body diagram to identify the forces acting on each body and we need to write the equations for resultant force as shown in the video lesson below. We can solve the equations as shown below.

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