Chapter 15

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29 Νοε 2013 (πριν από 3 χρόνια και 8 μήνες)

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1

Statics and Dynamics

Chapter 15

2

SFA Courses

Physics 250
-

Statics


Physics 321
-

Dynamics


Free Body Diagrams

How many forces are involved in the
following?


A book on a table ______


A weight hanging from a string ______


A block on an inclined plane ______

3

Free Body Diagrams

Draw free body diagrams for the
following:


A book on a table


A weight hanging from a string


A block on an inclined plane

4

5

15.1 Statics

Study of forces on stationary objects

Sum of the forces…




0
F

6

15.1 Statics

Vector Notation

k
ˆ
F
j
ˆ
F
i
ˆ
F
F
z
y
x




7

15.1 Statics

Magnitude of a Force

2
z
2
y
2
x
F
F
F
F
F





8

15.1 Statics

Magnitude of a Force in 2D

2
y
2
x
F
F
F
F




j
ˆ
F
i
ˆ
F
F
y
x














x
y
1
F
F
tan
9

Example Problems

See handout…


10

Moment (a.k.a. Torque)



sin
rF
M
r

F



11

Right Hand Rule

-

Clockwise

+

Counterclockwise

12

Example Problems

See handout…


13

Moment (a.k.a. Torque)



0
M

For no rotation (static)…

14

Example Problem #4

A lever is 20ft long with the fulcrum at
the center.

Three weights are on it at the same
time: 50, 75 and 65 lb. The two
heaviest are at opposite ends of the
lever.

Where should the lightest weight be
placed to balance the lever?

15

Have you ever wondered?

Will the elevator cable break today?

16

15.3 Strength of Materials

F

Tension Stress

A
F
tension
tension


Fracture

17

F

Fracture

A
F
n
compressio
n
compressio


Compression Stress

18

F

Fracture

Shear Stress

A
F
shear


19

15.3 Strength of Materials

Tension Stress


Compression Stress


Shear Stress

A
F
tension
tension


A
F
n
compressio
n
compressio


A
F
shear


What are the units for stress?

20

15.3 Strength of Materials

Strain


the change in length
d

per unit original length L

L
d


What are the units for strain?

21

15.3 Strength of Materials

Stress Versus Strain Plots


Allowable Stress


Proportional Limit


Elastic Limit


Yield Strength


Ultimate Strength


Fracture

22

15.3 Strength of Materials

Modulus of Elasticity (E)


The slope of the


versus


plot




E
tension
How much will a ¼” rod of structural
steel stretch if the tension force is
1000lbs?

23

15.3 Strength of Materials

Safety Factor

Stress

Allowable
Strength

Yield
Factor
Safety

Are high or low safety factors desirable?

24

Announcements

Homework 3 is due today.


Homework 4 is due on Monday.



RAT 3
-

5 Minutes

1. Find the magnitude of the vector below.

2. Find the direction of the vector below.



3. Find the magnitude of the vector below.

4. Find the direction of the vector below.



5. Did you bring a calculator today?

j
ˆ
)
N
4
(
i
ˆ
)
N
3
(
F



j
ˆ
)
N
12
(
i
ˆ
)
N
5
(
F