Transcript Equilibrium

Equilibrium
Zero Net Force


Most objects we encounter are not accelerating.
These objects are following the law of inertia.
• The net force is zero
• The object is in equilibrium

The net force is due to the sum of forces acting on
the object.
• The forces are vectors


Fnet   F  0
Static Equilibrium

The law of inertia applies to objects at rest and at
constant velocity.

An object at rest with no net force is in static
equilibrium.
Equilibrium in One Dimension

Two weights are hung
supported by strings.
• On the lower block the two
forces balance: FT2 = m2g
• On the upper block there
are three: FT1 = m1g + FT2
• FT1 = (m1 + m2)g
3 forces on the upper block
FT1
m1
m1g
FT2
FT2

The upper string has more
tension than the lower string.
m2
m2g
2 forces on the lower block
At Rest
-mg
-mg

mg
mg
2mg
-mg
-mg
-mg
mg
Failure to maintain equilibrium results in net force and
acceleration.
•
•
•
•
Hyatt Regency Kansas City, 1981
Designed to have a single pole from the ceiling to the lower deck
Two pins instead of one on the upper deck
Twice the force on the top pin caused collapse
Equilibrium in Two Dimensions

Normal forces
FN2
FN1
m


The forces in each
component must be zero.
Use a tilted set of
coordinates to find
components of gravity.
• FN1 = mg sin
• FN2 = mg cos
Gravity force
Fg = mg
Constant Velocity

Constant velocity means no
acceleration.
• Zero net force here, as well
• Motion can be at equilibrium


v0
Dynamic equilibrium applies
in states of constant, nonzero velocity.
All the forces add to zero net
force.
FN
Ffr
Fx
Fg
Fy
Matching Components

Vertical component
• FN = Fg + Fy
v0

Horizontal component
• Fx = Ffr

Applied force

F  Fxiˆ  Fy ˆj

F  F fr iˆ  ( FN  Fg ) ˆj
FN
Ffr
Fx
Fg
Fy
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