Static Mechanics Drawing Free Body Diagrams

Chapter 4: Rigid Bodies

4.2 Rigid Trunk Free Body Diagrams

Following what we learned in Department ii.2 on particle Free-Body Diagrams (FBDs), this section will expand on that for rigid bodies. The biggest difference betwixt a particle and rigid body FBD is where the force is applied. In a rigid trunk FBD, you take to exist precise near pointing the head of the force arrow to the location where it applied. For instance. if we wanted to brand a FBD of you and me high-v'ing, you would apply the force from your hand onto my hand, not at my center of mass.

In this section, first nosotros will learn how to practise a FBD for a part, then we look at how to model a organisation of multiple objects.

When modelling a single object using an FBD, you lot are simplifying a circuitous problem into specific forces using arrows and an object floating in space. The floor becomes a normal force arrow and a frictional force arrow. Pushing or pulling on an object becomes an practical force with the pointer pointing to or from (pushing or pulling) the location where the pushing or pulling occurs. Remember the rules from section ii.2 still apply:

• Add coordinate frame (which way is positive x and positive y?)
• Replace surfaces with forces (floor, hand, and objects touching information technology go arrows)
• Point forces in the correct direction (the head of the arrow points to where the forcefulness acts. F_G acts downwardly)
  
• Employ unique (dissimilar) names (be sure to proper noun each force with a dissimilar name).
  

Hither are some tips to keep in mind near each of the forces:

• Gravity acts on every particle in an object. Because we don't want a million piffling arrows on the object, we sum the effect of gravity at the center of mass. This is also because we by and large know the total mass of something and where that occurs on an object (oft at the geometric center), then nosotros concentrate the force of gravity at this eye of mass.
• Normal forces ever act perpendicular to the surface, so if the basis is at an angle, then the normal force acts xc degrees from that bending (perpendicular).
• Frictional forces act parallel to the plane betwixt the 2 surfaces. This makes it a shear force, which we'll look at in Chapter half dozen.
• Friction always opposes motion, a fact that will exist very of import in your dynamics class.
• Spring force is frequently shown equally negative because the force acts in the opposite direction of the motion traveled. In application, y'all set the direction of the frictional force to match if information technology is pushing or pulling.
• Applied forces (and moments), such as distributed loads, motors, pushing on an object, tension, etc.

The steps to brand a FBD are:

1. Draw shape
2. Add together coordinate frame
3. Supercede forces with arrows
4. Label each force uniquely

To model a book being pushed across the table, you would employ the following forces at the following locations (see image below)

• the normal force on the lesser of the book (green arrow)
• the frictional force running along the bottom surface between the book and tabular array (yellowish arrow)
• the gravitational force acting at the center of mass (pink arrow)
• whatsoever practical forcefulness at the point of awarding, such as your hand pushing on the book (blue pointer)

If instead, the book were being pulled by a cord, the image would be the same simply the practical force and frictional strength would change management (because friction always opposes motion).

A gratis body diagram is a tool used to solve applied science mechanics problems. As the name suggests, the purpose of the diagram is to "complimentary" the trunk from all other objects and surfaces around information technology so that it can be studied in isolation. We will as well draw in whatsoever forces or moments acting on the trunk, including those forces and moments exerted by the surrounding bodies and surfaces that nosotros removed.

The diagram below shows a ladder supporting a person and the free torso diagram of that ladder. As y'all can meet, the ladder is separated from all other objects and all forces acting on the ladder are drawn in with fundamental dimensions and angles shown.

The first step in solving virtually mechanics problems volition be to construct a complimentary body diagram. This simplified diagram will allow us to more easily write out the equilibrium equations for statics or strengths of materials problems, or the equations of move for dynamics bug.

To construct the diagram nosotros will use the following process.

1. First depict the torso existence analyzed, separated from all other surrounding bodies and surfaces. Pay close attention to the boundary, identifying what is office of the body, and what is part of the environment.
2. Second, draw in allexternal forces and moments interim directly on the trunk. Do not include any forces or moments that do not directly act on the trunk being analyzed. Practice not include any forces that areinternal to the torso being analyzed. Some common types of forces seen in mechanics issues are:
   • Gravitational Forces: Unless otherwise noted, the mass of an object will result in a gravitational weight force practical to that body. This weight is usually given in pounds in the English arrangement, and is modeled as nine.81 (m) times the mass of the trunk in kilograms for the metric system (resulting in a weight in Newtons). This strength will e'er point down towards the center of the earth and act on the center of mass of the torso.
3. Once the forces are identified and added to the free torso diagram, the last step is to characterization any central dimensions and angles on the diagram.

Source: Engineering Mechanic, Jacob Moore, et al. http://wwhttp://mechanicsmap.psu.edu/websites/1_mechanics_basics/1-6_free_body_diagrams/free_body_diagrams.htmlw.oercommons.org/courses/mechanics-map-open-mechanics-textbook/view

A system free-torso diagram is composed of multiple parts, then you can have multiple 'levels' to consider: the system level with all objects on the same FBD, and a part FBD for each individual part. This is especially helpful if you have a more unknowns than equations when using the equilibrium equations, and so you lot can find more data by splitting the system upward into individual parts.

For the system FBD, you look at the parts combined together and add merely the external forces (gravity, practical, normal, frictional, spring). When you look at each function separately, you now accept to include the interaction between the objects, replacing a part with forces (mostly 2 forces: vertical and horizontal force).

For example, if there are 2 books stacked on top of each other, you now need 3 FBDs:

1. a system level FBD with both books,
2. a part FBD for the lesser book with the top book replaced by arrows (forces)
3. a role FBD for the superlative book with the bottom book replaced by arrows (forces)

To make a system FBD:

1. Depict system FBD using unique consistent labels (ie. a letter or number per office)
   • The system should be floating in infinite with no surface (such as the floor)
   • Include coordinate frame
   • Use only external forces on system FBD (gravity, practical, normal, frictional, bound).
   • Practise Non include internal forces
   • Information technology is especially important to apply unique labels, so the top volume forces are labelled 1, and the bottom book forces are labelled 2 (or T for height and B for bottom, or A and B).
2. Draw a FBD for each office separately & coord frame with equal and opposite arrows for internal system forces

1. • The function should be floating in space with no surfaces or other objects
   • Include a coordinate frame (yes, again! This is to ensure you lot didn't rotate the object).
   • Copy the external forces onto the part FBD from the arrangement FBD with the identical labels and arrow directions
   • Now add internal forces replacing the other object with force arrows (red arrows)
   • When you draw the second part FBD, follow the above bullets for the second object (with label 2 instead of i, copying the system level external force labels). Annotation though that you utilize the same labels for the internal forces from the first part FBD, but the direction is reversed (left becomes right and upwardly becomes down). Following Newton's laws, the objects extert equal and opposite forces on each other, and should cancel out at the system level, so they take the same label (magnitude) and opposite directions.

Some tips:

• Differentiate one object from the other through the labels, using either a letter or number for each part. These same labels go on the system level FBD (except for the internal labels).
• Apply the same labels betwixt the part and organization FBDs for external forces. Don't modify the label – that will make the equations impossible to solve and look like you take more unknowns.
• Use the aforementioned unique labels betwixt the internal forces for the part FBDs, only in the reverse direction.
• If y'all know the location of the center of mass, yous could combine the gravitational forces into ane system level gravitational forcefulness. Y'all could also model the gravitational force into ane force per part interim at the center of mass for each object. This is the better method if yous have to separate the objects to do the calculations.

Here are some examples from: http://mechanicsmap.psu.edu/websites/1_mechanics_basics/one-6_free_body_diagrams/free_body_diagrams.html

Example one: Function FBD

The auto shown below is moving and so slams on the brakes locking up all four wheels. The distance between the two wheels is 8 feet and the center of mass is 3 feet behind and 2.5 feet higher up the point of contact between the front wheel and the ground. Describe a gratis trunk diagram of the car as it comes to a stop.

Source: Engineering Mechanics, Jacob Moore et al., http://mechanicsmap.psu.edu/websites/1_mechanics_basics/1-6_free_body_diagrams/pdf/P3.pdf

Case 2: Part FBD (a beam)

Example 3: System FBD

Two equally sized barrels are being transported in a hand truck as shown below. Draw a free body diagram of each of the 2 barrels.

Source: Applied science Mechanics, Jacob Moore et al., http://mechanicsmap.psu.edu/websites/1_mechanics_basics/one-6_free_body_diagrams/pdf/P2.pdf

External forces in dark-green, pinkish, and yellow. Internal forces between the cart and barrels (C and A/B) in red and between the barrels (A & B) in bluish. Notice the matching labels for internal forces but opposing directions. Detect that the coordinate frame has been rotated consistently in all of the FBDs.

Basically: A part gratuitous-body diagrams (FBDs) requite you a mode to model complicated problem in a simple style with arrows. Systems FBDs allows y'all to combine objects and analyze them separately.

Application: A bat swinging could exist modeled as a part FBD with gravity and multiple practical forces (hands on i end and the brawl on the other). Yous could model the moment the bat and ball are touching using a system FBD.

Looking ahead: You'll use a FBD in every step 2 in nearly every homework problem. These are especially helpful with Equilibrium Equations in the next department.

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Source: https://pressbooks.library.upei.ca/statics/chapter/free-body-diagrams-2/

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