Class Today
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• Particle Equilibrium
– Conditions for Equilibrium
– Summing Forces
– Free Body Diagrams
– Springs
– Cables and Pulleys
• Example Problems
• Group Work Time
From resultants to equilibrium
• Vectors
– Defined: What do they tell us?
– Components: How do we express them?
– Resultants: How do we manipulate them?
• So …
– What is equilibrium?
– Why do I care about equilibrium?
– How do I solve equilibrium problems?
What: Conditions for Equilibrium
• RECALL: When writing a vector in
Cartesian vector format, we resolve into
components (typically directed along the x,
y, z axes).
• RECALL: Equilibrium means that a system
is either
– At rest
– Moving at a constant velocity
What: Conditions for Equilibrium
• If the whole system is
in equilibrium, then
each part of the
system must
independently satisfy
the conditions of
equilibrium
• The sum of all
external forces acting
on the system is equal
to ZERO.
How: Summing Forces
IF the sum of all forces acting on a
system is zero (or Σ F = 0) THEN …
• Σ Fx = 0
• Σ Fy = 0
• Σ Fz = 0
(or any other direction
for that matter)
How many unknowns can a system have in 2D? 3D?
How: Free Body Diagrams
• A sketch showing the
system being evaluated
“free” from its
supports.
• ALL forces are shown
acting on the system (in
this case a particle)
• Show forces in the
assumed direction of
action.
How: Free Body Diagrams
• A sketch showing the
system being evaluated
“free” from its
supports.
• ALL forces are shown
acting on the system (in
this case a particle)
• Show forces in the
assumed direction of
action.
Springs
For problems involving springs we
need to add an equation
F = k Δs
k = stiffness of spring (constant)
Δs = distance that spring deforms
compression / shortens ( − )
expansion / lengthens ( + )
Image copyright 2013, Pearson Education, publishing as Prentice Hall
Cables and Pulleys
The tension force in
a continuous cable
passing over a
frictionless pulley
must have a
constant magnitude
Image copyright 2013, Pearson Education, publishing as Prentice Hall
Example Free Body Diagram
Image copyright 2013, Pearson Education, publishing as Prentice Hall
General Approach to
Equilibrium Problems
1. Establish a coordinate axis system.
2. Sketch force vectors (both known and
unknown) and label the given diagram.
3. DRAW A FREE BODY DIAGRAM!
4. Apply the equations of equilibrium.
5. Solve.