Transcript Equilibrium of a Particle

Equilibrium
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A particle (mass, but a size that can be neglected) is in
equilibrium provided it is at rest if originally at rest or has
constant velocity if originally in motion
Typically the term “static equilibrium” refers to an object at
rest
To maintain equilibrium, the resultant force acting on a
particle must be equal to zero, ∑ F = 0 (the ∑ F is the vector
sum of all forces acting on the particle)
The equilibrium equation, ∑ F = 0, can be used to determine
unknown forces acting on an object in equilibrium
Free-body diagrams
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A sketch showing the particle isolated or “free” from its
surroundings where all the forces acting on the particle are
shown
Drawing a free-body diagram involves the following steps
– Draw a sketch of the particle isolated from its surroundings
– Draw vectors representing all of the forces acting on the isolated
particle
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Active forces – tend to set the particle in motion
Reactive forces – result from constraints or supports and tend to
prevent motion
– Label the known forces with their magnitudes/directions and use
letters to represent the unknown forces
– Choose a coordinate system
Springs
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For a linear elastic spring, the length of the spring will change
in direct proportion to the force acting on it
The “elasticity” of a spring is characterized by its spring
constant or stiffness, k
The magnitude of the force exerted on a linearly elastic spring
as it is deformed a distance “s” from its unloaded position is:
F = ks = k(ℓ – ℓo)
k = spring constant or stiffness
s = (ℓ – ℓo) = difference in spring’s deformed length from its
undeformed length
Cables/cords and pulleys
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The force in a cable/cord is in tension and the line of action of
that force is collinear with the cable/rope
The tension in a cable/cord is the same on both sides of a
pulley
Coplanar force systems
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System of forces is 2-D or coplanar
Orienting a coordinate system such that forces lie in the x-y
plane, ∑ F = (∑ Fx) i + (∑ Fy) j = 0
Since a vector is zero if and only if its components are zero,
∑ Fx = 0, ∑ Fy = 0
EXAMPLES (pg 98 – 104)
Three-dimensional force systems
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System of forces is 3-D
Equilibrium, ∑ F = (∑ Fx) i + (∑ Fy) j + (∑ Fz) k = 0
Since a vector is zero if and only if its components are zero,
∑ Fx = 0, ∑ Fy = 0, ∑ Fz = 0
EXAMPLES (pg 112 – 116)