Connected bodies on rough Frictional surface Solving using Newton laws of motion

Connected bodies acceleration and tension between them in the string can be calculated using Newton laws of motion. If one body is on rough horizontal surface, frictional force also has to be taken into consideration. We need to solve this basing on free body diagram and using equations of motion.

Let us consider two bodies of two different masses connected over a light weighted pulley with the help of light strings. As the pulley is friction less, the same tension in the lower string is passed to the string on horizontal surface.

Assuming the force in the downward direction dominates, the system is tend to move in the downward direction and the lower body moves in the downward direction and the upper body on the horizontal rough surface is tend to move from left to right in the system.

We shall apply Newton laws of motion for each body of the system and we shall consider all the forces acting on the body to study its

motion and never the force applied by the body. Using this concept we can draw free body diagram for each body as shown here in the video. While drawing free body diagram we will consider only forces acting on the body.

The forces along the direction of motion shall be treated as positive and forces acting against the motion shall be treated as negative while we are writing equation of motion.

As the weight of the hanging body acts in the downward direction,it creates a tightness in the wire and it generates tension in the wire. The same tension is passed to the connected part of the string via friction less pulley.

For the body on the rough horizontal surface, the tension pulls it from left to right and hence frictional force is generated between the rough horizontal surface against the relative motion. We can write equation of motion to this body also as shown.

Solving this two equations of motion, we can get the values of acceleration of the system and tension in the string as shown below.