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8.7 Free body diagram (application)

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Solving problems is an essential part of the understanding process.

Questions and their answers are presented here in the module text format as if it were an extension of the treatment of the topic. The idea is to provide a verbose explanation, detailing the application of theory. Solution presented is, therefore, treated as the part of the understanding process – not merely a Q/A session. The emphasis is to enforce ideas and concepts, which can not be completely absorbed unless they are put to real time situation.

Representative problems and their solutions

We discuss problems, which highlight certain aspects of the study leading to the Free body diagram (FBD). The questions are categorized in terms of the characterizing features of the subject matter :

  • Vertically Staked blocks
  • Block, string and pulley
  • Block, spring and incline
  • Hinged rod
  • Rod and spherical shell

Vertically staked blocks

Problem : Draw free body diagram of three blocks placed one over other as shown in the figure.

Vertically staked blocks

Three blocks of different masses are placed one over other on a horizontal surface.

Solution : We start drawing FBD of the topmost block as we do no need to consider normal force due to an overlying body as the case with other blocks.

Forces on the blocks

The forces on the individual elements of the system are shown.

The forces on the block “C” are :

  • W C = m C g = its weight, acting downward
  • N B = normal reaction on “C” due to the upper surface of block B, acting upward

The forces on the block “B” are :

  • W B = m B g = its weight, acting downward
  • N B = normal reaction on “B” due to the lower surface of block C, acting downward
  • N A = normal reaction on “B” due to the upper surface of block A, acting upward

The forces on the block “A” are :

  • W A = m A g = its weight, acting downward
  • N A = normal reaction on “A” due to the lower surface of block B, acting downward
  • N O = normal reaction on “A” due to horizontal surface, acting upward

The FBD of the blocks as points with external forces are shown here. Note that motion is not involved. Hence, no information about acceleration is given in the drawing.

Free body diagram

The elements are shown as point with forces.

We have deliberately not shown the coordinate system which may be selected, keeping in mind the inputs available. In this instant case, however, a vertical axis is clearly the only choice.

Got questions? Get instant answers now!

Block, string and pulley

Problem : Three blocks are connected with the help of two “mass-less” strings and a “mass-less” pulley as shown in the figure. If there is no friction involved and strings are taught, then draw free body diagram of each of the blocks.

Three blocks connected with two strings

Three blocks are connected through two "mass-less" strings and one "mass-less" pulley.

Solution : Since there are two separate strings. Tensions in two strings are different. We see here that block -1 has no attachment to its left. Hence, it would involve minimum numbers of forces. Thus, we start from block -1.

Forces on the blocks

The forces on the individual elements of the system are shown.

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Source:  OpenStax, Physics for k-12. OpenStax CNX. Sep 07, 2009 Download for free at http://cnx.org/content/col10322/1.175
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