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Chapter 12: (Static) Equilibrium and
Elasticity
Reading assignment: Chapter 13.1-13.3
Homework : (due Wednesday, Oct. 26, 2005):
Problems:
4, 10, 24, 31, 35, 42
• Objects in static equilibrium don’t move.
• Of special interest to civil and mechanical engineers and architects.
• We’ll also learn about elastic (reversible) deformations.
• Plastic deformations are irreversible (like play dough)
Conditions for static equilibrium
Objects in static
equilibrium don’t
______ or _______.
Conditions for static equilibrium
(For ____________ objects)
1. The net force acting on the
particle must be _________.

F 0
2. The net torque about any axis
acting on the particle must be
______.

  0
3. The _______ and _______
speeds must be zero.
Conditions for static equilibrium
(For extended objects)
Is this object in
static equilibrium?
A force couple is acting on an object. A
___________ ___________ is a pair of
forces of equal magnitude and opposite
direction along parallel lines of action
It matters at which point the
force is applied!!
If equal and opposite forces are applied at _________________
points  object is not in equilibrium, since there is a net torque.
If equal and opposite forces are applied at the same ___________
or along the same _______________  object is in equilibrium
Conditions for static equilibrium
(For extended objects)
1. The net force acting on the
particle must be zero.

F 0
2. The net torque about any axis
acting on the particle must be
zero.

  0
3. The angular and linear speeds
must be zero.
We restrict ourselves to
forces in the x-y plane.
Thus:
 F __  0
 F __  0
 __ 0
How do we treat the
_____________ force?
Center of gravity
Consider an extended object.
- The gravitational force ___ always acts on the center of gravity!
- The center of gravity is equal to the center of _______(Ch. 9.2).
Examples of rigid objects in static
equilibrium
We will only consider objects that are _______________
and in a ________________________ gravitational field.
Balanced rock
For this system to be in static equilibrium, the center of gravity must
be directly over the support point.
Why??
Problem-solving hints:
Objects in static equilibrium
1. Draw a _____ __________ diagram.
-
Show and label all the _______ forces acting on the object.
-
Indicate ____________ the forces are applied.
2. Establish a convenient ______________ system for forces.
Then apply condition 1: Net force must equal _________.
3. Establish a convenient ____________ system for torque. Then
apply condition 2: Net torque must equal ______________.
Black board example 12.1
A uniform 40.0 N board supports a father (800 N) and daughter (350 N)
as shown. The support is under the center of gravity of the board
and the father is 1.00 m from the center.
(a) Determine the magnitude of the upward force n exerted on the
board by the support.
(b) Determine where the child should sit to balance the system.
Black board example 12.2
HW 9
A diver of weight 580 N stands
at the end of a 4.5 m diving
board of negligible mass
(see Fig). The board is
attached to two pedestals
1.5 m apart.
(a) Draw a free body diagram.
(b) What are the magnitude and direction of the force on the board
from left pedestal?
(c) What are the magnitude and direction of the force on the board
from right pedestal?
(d) Which pedestal is being stretched and which is compressed?
Elastic properties of solids
We will consider three types of deformations and define an
elastic modulus for each.
1. Change in length. _______________ MODULUS
measures the resistance of a solid to a change in its
length.
2. Shearing. ______________ MODULUS measures the
resistance to shearing.
3. Change in volume. _______________ MODULUS
measures the resistance to changes in volume.
Elastic properties of solids
Definitions of stress and strain.
Stress: _________ per unit cross sectional area.
Strain: Measure of the degree of ___________.
Elastic properties of solids
Tension or
compression
Young’s modulus:
tensile _____
F/A
Y

tensile ______ L / Li
Stress-strain curve
Elastic properties of solids
Shear modulus:
shear _______ F / A
S

shear _______ x / h
Elastic properties of solids
Hydraulic _____________
or stress
Bulk modulus:
volume ______
F/A
P
B


volume ______ V / Vi V / Vi
P… pressure
Black board example 12.4
A 200 kg load is hung on a wire with a length
of 4.00 m, a cross-sectional area of 2.00·10-5
m and a Youngs modulus of 8.00·1010 N/m2.
What is its increase in length (Assume elastic
deformation)?