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The forces on the block – 1 are :
The forces on the block – 2 are :
We note here that “mass-less” string passes over a “mass-less” pulley and no friction is involved. As such, the tensions in the string on either side of the pulley are equal.
The forces on the block – 3 are :
Since strings are taught, it is evident that the acceleration of the blocks and string are same. Also, we note that motion of the blocks on the table is in horizontal direction only. There is no motion in vertical direction. The forces in the vertical direction, therefore, constitute a balanced force system. Thus, for the analysis of motion, the consideration of forces in vertical directions for blocks of masses “ ” and “ ” is redundant and can be simply ignored. Now, taking these two considerations in account, the FBD of the blocks are as shown here :
We should note that the FBD of the blocks show acceleration. Idea here is that we should supplement FBD with as much information as is available. However, we have deliberately not shown the coordinate system which may be selected, keeping in mind the inputs available.
Problem : Draw free body diagrams of two blocks “A” and “B” in the arrangement shown in the figure, where Block “B” is lying on a smooth horizontal plane.
Solution : Drawing FBD is a methodological process. However, its efficient use is intuitive and sometimes experience based.
This problem highlights these aspects of drawing FBD. The figure below gives the sketch of various forces on each of the blocks. Note specially that there are indeed large numbers of forces on block "B".
The FBD of each of the blocks are shown assuming that only translation is involved. The forces are, therefore, shown concurrent at a single point in each case.
If we look closely at the forces on the block "B", then we realize that tension in the string is equal to external force "F". These tensions act on the block "B" through two attached pulleys. Knowing that tension in the string is same everywhere, we could have neglected all the four tensions as far as block "B" is concerned. They form two pairs of equal and opposite forces and, therefore, tensions form a balanced force system for block "B".
We could have further simplified drawing of FBD in the first attempt. We are required to consider only translation in horizontal direction. The forces in vertical direction on block "B", as a matter of fact, may not be required for the force analysis in horizontal direction. We will learn subsequently that we can determine friction in this case by considering vertical normal force only on block "A". Thus, we can simplify drawing FBD a lot, if we have lots of experience in analyzing forces.
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