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Dynamics – Free Body Diagrams
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Unit #3 Dynamics
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Objectives and Learning Targets
1. Define a force and distinguish between contact forces and field forces.
2. Draw and label a free body diagram showing all forces acting on an object.
3. Determine the resultant of two or more vectors graphically and algebraically.
4. Draw scaled force diagram using a ruler and protractor.
5. Resolve a vector into perpendicular components: both graphically and
algebraically.
6. Use vector diagrams to analyze mechanical systems (equilibrium and
nonequilibrium).
Unit #3 Dynamics
Free Body Diagram
• Fortunately, we have a terrific tool for analyzing
the forces acting upon objects. This tool is known
as a free body diagram. Quite simply, a free body
diagram is a representation of a single object, or
system, with vector arrows showing all the
external forces acting on the object. These
diagrams make it very easy to identify exactly
what the net force is on an object, and they’re
also quite simple to create:
Unit #3 Dynamics
Free Body Diagram
1. Isolate the object of interest. Draw the object as a point particle
representing the same mass.
2. Sketch and label each of the external forces acting on the object.
3. Choose a coordinate system, with the direction of motion as one
of the positive coordinate axes.
4. If all forces do not line up with your axes, resolve those forces
into components using trigonometry (note that the formulas below
only work if the angle is measured from the horizontal).
5. Redraw your free body diagram, replacing forces that don’t
overlap the coordinates axes with their components.
Unit #3 Dynamics
Free Body Diagram Example
As an example, picture a glass of soda sitting on the dining
room table. You can represent the glass of soda in the
diagram as a single dot. Then, represent each of the vector
forces acting on the soda by drawing arrows and labeling
them. In this case, you can start by recognizing the force of
gravity on the soda, known more commonly as the soda’s
weight. Although you could label this force as Fgrav, or W,
get in the habit right now of writing the force of gravity on an
object as mg. You can do this because the force of gravity on
an object is equal to the object’s mass times the acceleration
due to gravity, g.
Unit #3 Dynamics
Free Body Diagram Example
Of course, since the soda isn’t accelerating, there
must be another force acting on the soda to balance
out the weight. This force, the force of the table
pushing up on the soda, is known as the normal
force (FN). In physics, the normal force refers to a
force perpendicular to a surface (normal in this case
meaning perpendicular). The force of gravity on the
soda must exactly match the normal force on the
soda, although they are in opposite directions,
therefore there is no net force on the soda. The free
body diagram for this situation could be drawn as
shown at right.
Unit #3 Dynamics
Example Problem #1
Question: Which diagram represents a box in equilibrium?
Answer: (2) all forces are balanced for a net force of zero.
Unit #3 Dynamics
Example Problem #2
Question: If the sum of all the forces acting on a moving
object is zero, the object will
1. slow down and stop
2. change the direction of its motion
3. accelerate uniformly
4. continue moving with constant velocity
Answer: (4) continue moving with constant velocity in
accordance with Newton’s 1st Law of Motion.
Unit #3 Dynamics
Types of Force
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Gravity = FG, W, or mg – always straight down
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Normal = FN – perpendicular surface force
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Friction = Ff – surface force opposite velocity of object
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Air Resistance = FD – opposes velocity
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Spring = Fsp = can be push or pull
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Applied = FA – general push or pull on object
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Tension = FT = pull from a rope, cord or wire
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Buoyant = Fbuoy – displayed fluid (liquid or gas) force
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Magnetic = FB - from moving charged objects
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Electric = FE - from moving charged objects
Unit #3 Dynamics