Making proper free body diagrams is the absolute key to solving statics problems!
If you can’t make a perfect free body diagram (yes, perfect!) then it doesn’t matter how well you do the rest of the elements of solving the problem. You’re not going to get the problem solved correctly without a proper free body diagram.
So it seems that the engineering analysis of problems of static equilibrium depends of whether or not you can draw a picture. In a word ... yep!
Free body diagrams show either single or multiple elements of a mechanical system drawn isolated from anything else in the system. That’s why they’re called “free” ... if the parts were still connected to the rest of the system they wouldn’t exactly be free of it, would they?
Free body diagrams show all the forces associated with the system, including applied loads and weights. But most importantly, the free body diagram shows the forces that come from the interaction between the part(s) being sketched and those that “used to be” in contact.
This is probably the most important
rule of thumb there is in statics: when drawing free body diagrams
you MUST have unknown forces where points of contact occur between the
body being sketched and those items not included in the sketch.
There will not be forces on elements of a mechanical device that are still
connected together. The skill comes in knowing how to draw these
forces. It’s just as important to understand that these “reaction”
forces cannot occur anywhere other than where the contact occurred.
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Remember, if there was no body attached or in contact where you are drawing a force, there isn’t supposed to be a force there! Don’t forget forces ... and don’t add forces that don’t exist! |
Finally, a free body diagram includes all body forces (such as weight) unless they are specifically neglected. For the purpose of solving statics problems, unless you’re told about weight or a body’s mass, you may neglect it. All forces MUST be given unique names!
And that’s pretty much it! When you’re beginning your “learning curve” on drawing perfect free body diagrams, follow the steps below to assure you’re doing it right. Before we apply these concepts to the following example, always keep these assumptions in mind:
1. If the contact surface is “smooth” that means there’s no friction and the reaction force will always be drawn normal to a tangent line at the point of contact. If that point of contact is on a plane surface, the reaction force will ALWAYS be perpendicular to that surface:
2. A flexible body that has little or no stiffness (belts, ropes, chains, etc.) only exerts a pull on another object along the axis line of the flexible body.
Here's an example problem. For this problem, sketch the free body diagram of the cylinder:
Step 1) Sketch the body of interest, isolated from all other bodies in the mechanical system. Here, you would sketch the cylinder, with absolutely nothing in contact with it.
FYI - Don’t miniaturize your sketches! Make them large enough so that you can draw forces on them with clear labels, good dimensions, and other notation that we’ll see being used as we go along. This can really make a difference later on when the problems get much more complex and potentially confusing.
Step 2) Mentally trace a boundary around the object, placing appropriate forces where objects “used to be” in contact. The boundary is just a trick to help you make sure you don't miss anything!
IMPORTANT - Most of the time we don’t know the direction of the force. That’s not a problem at all ... just assign an arbitrary direction. When you find the solution to the unknown forces using the equations of equilibrium you’ll find out whether your assumed direction was right or not. If the answer is positive then your assumption about direction was correct. If the answer is negative, then that’s telling you that your assumed direction was incorrect and the force is going in the opposite direction!
3. Always choose coordinate axes and show them on your free body diagram. Also include pertinent dimensions on the free body diagram too.
The final free body diagram of the cylinder looks like this:
Notice, in this free body diagram:
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Masses are not forces! One of the oldest tricks
in the statics book is to specify the mass of a body instead of its weight.
Only weight (newtons or pounds) is a force. Students are usually
all too eager to include the mass as a force in their free body diagrams!
When you encounter a mass you must convert it to a weight by multiplying
by the appropriate acceleration due to gravity:
SI System: kg (of mass) x 9.81 m/sec2 = newtons
of force
If you see this in a problem, convert it right away before doing anything else. That will keep you from forgetting to do it later, when you’re preoccupied by the rest of the solution! |
Here’s another example. Let's assume the weight
of object A is 10 lb and the weight of object B is 8 lbs :
FYI - One of the underlying assumptions of statics is that if an entire system is in equilibrium, then every individual part of it will be in equilibrium as well. You'll see this applied many times throughout the course!
In this figure, the free body diagram of ring B will look like this:
And the free body diagram of ring C will look like this:
Notice that: