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CE 201 - Statics
Lecture 7
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EQUILIBRIUM OF A PARTICLE
CONDITION FOR THE EQUILIBRIUM OF A PARTICLE
A particle is in EQUILIBRIUM if:1.it is at rest, OR2.it is moving with constant velocity
The term "EQUILIBRIUM" is often used to describe a particle at rest. For a particle to be in EQUILIBRIUM, Newton's First Law of Motion must be satisfied.
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Newton's First Law of Motion
"IF THE RESULTANT FORCE ACTING ON A PARTICLE IS ZERO, THEN THE PARTICLE IS IN EQUILIBRIUM".
F = 0
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Newton's Second Law of Motion
F = m × aApplying the condition for equilibrium
F = m × athen,
m × a = 0since m ≠ o then, a = 0this means that the particle acceleration is equal to zero, therefore the particle is moving at constant velocity.
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THE FREE-BODY DIAGRAM
To apply the equilibrium equation ( F = 0), all known and unknown forces must be included in the equation.
The equilibrium equation will best be applied when a free-body diagram of the particle is drawn.
What is a free-body diagram?
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Example
Suppose that we have a ball supported on a surface with force F is applied.
How can we draw a free-body diagram of the ball?
1.Isolate the ball from all surroundings
2.Indicate all known and unknown forces acting on the ball.
F = 50 N
30
F = 50 N
30
W
R
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In this case, we have the following forces acting on the particle:F = 50 NBall weight, W = ?Surface reaction, R = ?
F = 50 N
30
F = 50 N
30
W
R
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Example
Draw a free-body diagram of the following system:
Tips•Label known forces: should be labeled with their magnitude and direction•Label unknown forces: should be labeled using letters•Assume +ve magnitude of unknown forces. If magnitude of an unknown force was obtained –ve, then the direction of the force is opposite to the direction assumed.•Apply equilibrium equation
F
F
W
R1
R2
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Connections
Two types of connections will be discussed:
1. Springs
2. Cables and Pulleys
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Springs
If a spring is subjected to a force, the length of the spring will change in direct proportion to the force acting on it (if it is a linear elastic spring).
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Example
In this case, the following equation can be used:
F = k sF = acting forcek = spring constant or stiffnesss = deformed distance measured from its unloaded position (elongated or compressed)
If ( s ) is +ve, then ( F ) pulls on the spring, while if ( s ) is –ve, then ( F ) pushes on the spring.
s = L – L0
L0
Ls (-ve)
-F
+F
L0s (+ve)
L
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Cables and Pulleys
• All cables are assumed to have negligible weight and can not be stretched
• Cables can support only tension or pulling forces
T T
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