Jw Physics 2111 Understanding Physics Chapter 12 1 Fundamentals of Physics Chapter 12 Equilibrium & Elasticity 1.Equilibrium 2.The Requirements of Equilibrium.

jw Physics 2111 Understanding Physics

Chapter 12 1

Fundamentals of Physics

Chapter 12 Equilibrium & Elasticity

1. Equilibrium

2. The Requirements of Equilibrium

3. The Center of Gravity

4. Some Examples of Static Equilibrium

Problem Solving Tactics

5. Indeterminate Structures

6. Elasticity

Tension & Compression

Shearing

Hydraulic Stress

Review & Summary

Questions

Exercises & Problems


Chapter 12 2

Equilibrium

Equilibrium: P and L are constant.

Static Equilibrium:

P

L

0LP

Stable Static Equilibrium: body returns to static equilibrium after being displaced by a force.

Unstable Equilibrium: a “small” force can displace the body and end the equilibrium,


Chapter 12 3

Requirements of Equilibrium

Requirements for Equilibrium:• The vector sum of all the external forces that act on the body must be zero.• The vector sum of all the external torques that act on the body, measured about

any possible point, must be zero.

Simplification in Chapter 12: forces are in the xy-plane (torques in z-direction)

Newton’s 2nd Law:

vector equations

0dt

PdFnet

0dt

Ldnet


Chapter 12 4

Center of Gravity

The gravitational force Fg on a body effectively acts at a stable

point, called the Center of Gravity of the body.

If g is the same for all parts of a body, then the body’s Center of

Gravity is coincident with the body’s Center of Mass.

gF


Chapter 12 5

Equilibrium

Stable Equilibrium Neutral Equilibrium


Chapter 12 6

Equilibrium & Center of Gravity

cog over the base of support

cog beyond the base of support


Chapter 12 7

Problem Solving:

• Draw a picture relevant to the problem.

• Choose the system: e.g. “the ladder & man”

• Draw the corresponding free-body diagram for the system.

– Forces

– Distances

• Choose coordinate axes.

– Component Force Equations along axes.

– Torque Equations (Choose the axis).

• Algebraically solve the equations.

– Solve for the unknowns.

– Check that units are correct.

• Plug in the numbers.

• Set significant figures for the answer(s).


Chapter 12 8

What are the forces on the ladder from the wall and pavement?

half-way up ladder

frictionless wall

L = 12 m

ML = 45 kg

h = 9.3 m

com = L/3 from bottom

MF = 72 kg climbs halfway up

Forces on ladder from wall, pavement


Chapter 12 9

Fireman on the Ladder

Choose rotation axis here

hFww

2agMMg

3agmmg

0pypx FF

Fr

net 0

h


Chapter 12 10

Elasticity

A rigid body is a 3D matrix of atoms (or molecules) held together by inter-atomic forces.

All rigid bodies are elastic - deform under stress.

Stress = “Modulus of Elasticity” X Strain

Force Stress Deformation Strain


Chapter 12 11

Elasticity

Apply a stretching force to a bar:

This force gets distributed over the surface area of the bar:

Force per unit area is defined as the stress.


Chapter 12 12

Elasticity

If this sample bar is pulled on, what happens?


Chapter 12 13

Elasticity

Tension & Compression

Shearing Hydraulic

Stress

Young’s Modulus(aka Y)

Shear Modulus Bulk Modulus

L

LE

A

F L

xG

A

F

V

VB

A

Fp


Chapter 12 14

tension in rope & normal force from wall?

N

T

mg

T N

T mg

sin

cos

0

0

Tmg L r

L

Nmgr

L

2 2

cos L

L r2 2

Equilibrium: Fnet 0

vector equation


Chapter 12 15

forces on the 4 tires of a car?

mg

Ffront

Frear

L

Lcog

Vertical forces: 2 2F F mgfront rear

F x Nfront 2 77 103. F x Nrear 389 103.

car

m

mL

kgm

78.1L

wheelbase""05.3

1360

cog

Torque about rear axle: 0)(2)L-(Lmg- cog LFfront


Chapter 12 16

Example: biceps lifts a weight; force on elbow?

mg N60

?mF

?elbowF

elbowF


Chapter 12 17

Example: biceps lifts a weight; force on elbow?

0

34 30 0

530

about O gives F

F cm mg cm

F N

m

m

m

.

.

elbowF

mg N60

NF

mgFFF

elbow

elbowmy

470

0


Chapter 12 18

R h

FN

Fe

mg

F when the wheel is about to go over the edgeN 0, .

Take torques about the edge F R h Mg x

trigonometry x R h R

:

:

02 2 2

F

Mg h R h

R h

2

Example: force to raise the wheel over the edge?

Forces on the wheel


Chapter 12 19

T = ? Force on Hinge = ?

mg

Mg

T

FX

FY

T L M g L mgL

T M m g

T N

O O O

O

O

sin sin sin

sin

sin.

15 452

45 0

45

156 63 10

12

3

F T

F T Mg mgX

O

Y

O

cos

sin

30 0

30 0

F N

F NX

Y

574 10

596 10

3

3

.

.

Mm

mstrut=25kg


Chapter 12 20

nut cracks @ 40 N on both sides; F ?

Torques about hinge:

F F

F Nnut 2 6 12 0

8 7

.

.

“Mechanical Advantage”: F

Fnut

4 6.


Chapter 12 21

T N

T T

O

O

1

2 1

35 40 0

35 0

cos

sin

T T

TX

Y

2 0

50 0TX

TY

T N

T N1

2

49

28

tan

T

TX

Y

O29

????321 TTT

2223 yx TTT

NT 573

Suspended Blocks

Jw Physics 2111 Understanding Physics Chapter 12 1 Fundamentals of Physics Chapter 12 Equilibrium & Elasticity 1.Equilibrium 2.The Requirements of Equilibrium.

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