Free Body Diagrams

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It is easy to make a mistake drawing a freebody diagram. It is the preliminary analysis of the statics problem and the basis for writing down your balancing equations. Take care to get the diagram correct and if your results are not making sense, review the diagram to be sure it is not misleading you.

A force system
A free body diagram of the force system

Notice that while the force on the rope is correctly propagated as the same on both sides of the pulley the forces as provided are not possible. After the force on the left is decomposed into an X and Y Cartesian component to add to the other forces, they do not balance. This weight must be swinging to the left as shown until there is a restoring force to the right. The Weight straight down is not balanced by the vertical component of the rope on the right. So the weight must be sinking. This diagram is not in static equilibrium so it cannot be analyzed for useful information using static methods which assume the system shown by the free body diagram is in static equilibrium (motionless).

Example problem:[edit | edit source]

Given that the shown rope tension is incorrect, find the correct tension in the rope for the Weight and Pulley Configuration shown.


Not enough information given. The bottom pulley will have to move sideways to establish equal angles in the two legs of the line wrapping the bottom pulley. The tension to define equilibrium will depend on these angles, which must be given, or, alternatively, the diameters of the pulleys and the distance between them must be given.