DEVIL PHYSICS
THE BADDEST CLASS ON CAMPUS
PRE-DP PHYSICS
Chapter 9, Bodies in Equilibrium:
Elasticity and Fracture
 9-1: Statics – The Study of Forces in Equilibrium
 9-2: The Conditions for Equilibrium
 9-3: Solving Statics Problems
 9-4: Applications to Muscles and Joints
 9-5: Stability and Balance
 9-6: Elasticity: Stress and Strain
 9-7: Fracture
 9-8: Spanning a Space: Arches and Domes
Chapter 9, Bodies in Equilibrium:
Elasticity and Fracture
 9-1: Statics – The Study of Forces in
Equilibrium
 9-2: The Conditions for Equilibrium
 9-3: Solving Statics Problems
No New Equations!!!
Chapter 9, Bodies in Equilibrium:
Elasticity and Fracture
 This chapter is devoted to the Future
Engineers of America
 Engineers must ensure the structure is
capable of withstanding all the forces acting
on it
 If your bodies aren’t in equilibrium,
you will have elasticity and/or fracture!
Objectives
 Explain the meaning of the term static




equilibrium
Understand the correlation between
Newton’s Second Law and static equilibrium
Name the first condition for equilibrium
(which is really three conditions)
Name the second condition for equilibrium
Solve problems involving static equilibrium
Static Equilibrium
 Statics – the study of forces in equilibrium
 Equilibrium – Latin for equal forces or
balance
 The study of forces acting on and within
bodies that are in equilibrium
 This, in turn leads to a study of whether or
not the structure is capable of withstanding
the forces without deformation or fracture
Newton’s Second Law
 Sum of the Forces equals mass times
acceleration
 If the forces are in equilibrium, the sum of the
forces equals zero and there is no
acceleration
 Constant velocity
 No motion
 F  ma
F 0
Static Equilibrium
F 0
FN
FN  Fg
Fg
Static Equilibrium
 Now What?
Static Equilibrium
 First Condition for Equilibrium
(which is really three)
F
F
F
x
0
y
0
z
0
Static Equilibrium
 What forces are at work here?
Static Equilibrium
 What forces are at work here?
FT-1
Fg
FT-2
Static Equilibrium
FT-1
Fg
F
y
?
FT-2
F
x
?
Static Equilibrium
FT-1-x
FT-1-y
FT-1
Fg
F
y
0
FT 1 y  Fg
Fg  mg
FT-2
F
x
0
FT 2  FT 1 x
FT 1 x  ?
Static Equilibrium

FT-1-x

FT-1-y
FT-1
Fg
FT-2
 Fy  0
 Fx  0
tan  
FT 1 y  Fg
FT 2  FT 1 x
mg
tan  
FT 1 x
Fg  mg
FT 1 x
FT 1 y
FT 1 x
mg

tan 
Static Equilibrium

FT-1-x

FT-1-y
FT-1
Fg
FT-2
FT 1 y  mg FT 2  FT 1 x
FT 1  ?
FT 1 x
mg

tan 
Static Equilibrium

FT-1-x

FT-1-y
FT-1
Fg
FT-2
FT 1 y  mg FT 2  FT 1 x
FT 1 
FT 1 x
mg

tan 
FT 1 x   FT 1 y 
2
2
Static Equilibrium
 Piece a’ cake, right?
 Well, if you don’t feel a little
torqued by now, you will shortly
Static Equilibrium
F 0
2 FN  Fg T  Fg  B
Fg-B
FN
Fg-T
FN
Static Equilibrium
F 0
FN 1  FN  2  Fg T  Fg  B
 Now What?
FN-1
Fg-T
Fg-B
FN-2
Static Equilibrium
 Second condition of equilibrium


0

Static Equilibrium
F 0
FN 1  FN  2  Fg T  Fg  B
  0
r1 FT  r2 FB  r3 FN  2
r1 FT  r2 FB
 FN  2
r3
FN-1
Fg-T
Fg-B
FN-2
Static
Equilibrium
 What is FT?

Fg-1
FT
Fg-2
FW ???
Static
Equilibrium
FT-x
FT-y

Fg-1
F
x
0
FT  x  FW  x
F
y
0
FT  y  FW  y  Fg 1  Fg 2
FT
Fg-2
FW
Static
Equilibrium
FT-x
FT-y

Fg-1
FT
Fg-2
FW
Note: The wall exerts a force on the beam
that would have to be considered in a ΣF
equation, but we can eliminate it by using Στ
and making the attachment point our
reference point.
FT-y
Fg 2 r1  Fg 1r2  FT  y r3
r3

Fg-1
  0
Fg 2 r1  Fg 1r2

FT-x
Static
Equilibrium
 FT  y
FT
Fg-2
FT-x
Static
Equilibrium
FT-y

Fg-1
  0
FT
Fg-2
Fg 2 r1  Fg 1r2  FT  y r3
Fg 2 r1  Fg 1r2
r3
 FT  y
sin  
FT 
FT  y
FT
FT  y
sin 
Solving Problems with Statics
1. Choose one body at a time and draw free-
body diagram showing all forces acting on it
2. Resolve all forces into their x-y components.
3. Write down equations for ΣFx = 0, ΣFy = 0, Στ
= 0.
Solving Problems with Statics
1. For Στ = 0, choose a reference point for
determining moment arms and ensure all
forces have components perpendicular to the
moment arm. Determine direction of torque
for each force and assign +/- to CW/CCW.
Note: If you choose one of your unknowns as
your reference point, you eliminate it
from the torque equation because its
distance (r) is zero.
Solving Problems with Statics
5. Solve equations for unknowns. Since you
have three equations, you can solve for three
unknowns. Some of these unknowns may be
components of a force. Use trigonometry to
determine a force from its components and
angles.
Note: If any answer comes out to be negative,
it’s okay. It just means the force is acting in a
direction opposite to the one you originally
assigned to it.
Solving Problems with Statics
 Example 9-7
 Figure 9-11
 Example 9-8
 Example 9-9
Σary Review
 Can you explain the meaning of the term static




equilibrium?
Do you understand the correlation between
Newton’s Second Law and static equilibrium?
Can you name the first condition for equilibrium
(which is really three conditions)?
Can you name the second condition for
equilibrium?
Can you solve problems involving static
equilibrium?
QUESTIONS?
Homework
Part A, #1-14
Part B, #15-27