DEVIL PHYSICSTHE BADDEST CLASS ON

CAMPUSPRE-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

0F

maF

Static Equilibrium

FN

Fg

gN FF

F

0

Static Equilibrium

Now What?

Static Equilibrium

First Condition for Equilibrium (which is really three)

0

0

0

z

y

x

F

F

F

Static Equilibrium

What forces are at work here?

Static Equilibrium

What forces are at work here?

FT-2

FT-1

Fg

Static Equilibrium

FT-2

FT-1

Fg

?xF ?yF

Static Equilibrium

xTT

x

FF

F

12

0

mgF

FF

F

g

gyT

y

1

0

FT-2

FT-1

Fg

FT-1-y

FT-1-x

?1 xTF

Static Equilibrium

xTT

x

FF

F

12

0

mgF

FF

F

g

gyT

y

1

0

FT-2

FT-1

Fg

FT-1-y

FT-1-x

tan

tan

tan

1

1

1

1

mgF

FmgFF

xT

xT

xT

yT

Static Equilibrium

xTT FF 12mgF yT 1

FT-2

FT-1

Fg

FT-1-y

FT-1-x

tan1mgF xT

?1 TF

Static Equilibrium

xTT FF 12mgF yT 1

FT-2

FT-1

Fg

FT-1-y

FT-1-x

tan1mgF xT

212

11 yTxTT FFF

Static Equilibrium

Piece a’ cake, right? Well, if you don’t feel a

little torqued by now, you will shortly

Static Equilibrium

FN

Fg-B

FNFg-T

BgTgN FFF

F

2

0

Static Equilibrium

FN-2Fg-BFN-1

Fg-T

BgTgNN FFFF

F

21

0

Now What?

Static Equilibrium

Second condition of equilibrium

0

Static Equilibrium

BgTgNN FFFF

F

21

0

23

21

2321

0

NBT

NBT

FrFrFr

FrFrFr

FN-2

Fg-BFN-1Fg-T

Static Equilibrium

What is FT? Fg-2

FT

Fg-1

FW ???

Static Equilibrium

Fg-2

FT

Fg-1

FT-y

FT-x

FW

21

0

0

ggyWyT

y

xWxT

x

FFFF

F

FF

F

Static Equilibrium

Fg-2

FT

Fg-1

FT-y

FT-x

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.

Static Equilibrium

Fg-2

FT

Fg-1

FT-y

FT-x

yTgg

yTgg

Fr

rFrF

rFrFrF

3

2112

32112

0

Static Equilibrium

Fg-2

FT

Fg-1

FT-y

FT-x

yTgg

yTgg

Fr

rFrF

rFrFrF

3

2112

32112

0

sin

sin

yTT

T

yT

FF

FF

Solving Problems with Statics1. 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 Statics1. 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 Statics5. 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?

Part A, #1-14Part B, #15-27

Homework