Transcript Lecture 43 - Course Material Review REPOSTED

ENGI 1313 Mechanics I
Lecture 43:
Course Material Review
Shawn Kenny, Ph.D., P.Eng.
Assistant Professor
Faculty of Engineering and Applied Science
Memorial University of Newfoundland
[email protected]
Final Exam

Formulae Sheet

Posted on course webpage
• Probably by end of Monday
• Coordinate with Dr. Rideout
Not to be used in the final exam
 Final exam formulae sheet will be attached
to the exam

2
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 43
Example 43-01

The wheel weighs 20 lb
and rests on a surface for
which μB = 0.2. A cord
wrapped around it is
attached to the top of the
30-lb homogeneous block.
If the coefficient of static
friction at D is μD = 0.3,
determine the smallest
vertical force that can be
applied tangentially to the
wheel which will cause
motion to impend.
3
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 43
Example 43-01 (cont.)
FBD
 Possible Friction
Analysis Cases

Impending motion at B
 Impending motion at D
 Impending motion at
B&D


Assumption at B
FB  BNB
4
© 2007 S. Kenny, Ph.D., P.Eng.
T
P
T
WC
WA
FB
FD
NB
ENGI 1313 Statics I – Lecture 43
ND
Example 43-01 (cont.)

Analysis Wheel A
M
0
A
1.5P 1.5T 1.5FB  0
P  T  FB

F
0
y
NB  P  20
P  20  NB

F
x
T
P
WA
0
T  FB
FB  6.67lb  T
5
P  T  FB  13.3lb
© 2007 S. Kenny, Ph.D., P.Eng.
FB  BNB
FB
NB
ENGI 1313 Statics I – Lecture 43
Example 43-01 (cont.)

Analysis Block C

F
x
0
FD  T  6.67lb

F
y
0
ND  30
T  6.67lb
T
WC
FD
ND
6
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 43
Example 43-01 (cont.)

Check Assumptions

Maximum friction force
at Point D
FD max  DND  0.330lb  9lb

Calculated force at
Point D
T
WC
FD  6.67lb

Assumption ok as block
C does not have
impending motion
FD  FD max
7
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 43
FD
ND
Example 43-01 (cont.)

Check Assumptions

Block C tipping
3T  WC x
36.67lb  30lbx
x  0.667ft

T
WC
Therefore block does
not tip
x  0.667ft 
1.5ft
2
x ND
8
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 43
Example 43-01 (cont.)

Conclusion
Impending motion at B
 Block C stationary and
does not tip over

P  13.3lb
T
P
T
WC
WA
FB
FD
NB
9
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 43
ND
Example 43-02

10
The friction hook is made from a
fixed frame which is shown
colored and a cylinder of
negligible weight. A piece of paper
is placed between the smooth
wall and the cylinder. If θ = 20°,
determine the smallest coefficient
of static friction μ at all points of
contact so that any weight W of
paper p can be held.
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 43
Example 43-02

FBD

Assume impending motion
at all contact points
F1
F1   N1
F2   N2
F1
N1
N1
F1
F2
W
N1
N2
11
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 43
Example 43-02

Analysis of Paper FBD

F
y
0
2F1  W
W
2
W
F1 
  N1
2
W
N1 
2
F1 
12
© 2007 S. Kenny, Ph.D., P.Eng.
F1
F1
N1
N1
W
ENGI 1313 Statics I – Lecture 43
Example 43-02
Analysis of Cylinder
 Objective is to Find 


Orient axes to contact surface
M
O
0
F2r  F1r  0
W
r 0
2
W
F2 
2
y
F2 r 
13
© 2007 S. Kenny, Ph.D., P.Eng.
x
F2
r
F1 = W / 2
N1 = W / 2

N2
ENGI 1313 Statics I – Lecture 43

Example 43-02
Analysis of Cylinder
 Objective is to Find 

Orient axes to contact surface
 Fx  0
y

W
W
sin 
cos  0
2
2

W
1
N2   sin  cos 
2


N2 
F2



W
1
 sin  cos 
2


F2 
W
2
x
F1 = W / 2
F2
N1 = W / 2
 = 20
N2

1  cos

W W
1
 0.176
  sin  cos   1   sin  cos   
sin
2 2 


14
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 43
Example 43-03

15
Determine the minimum
force P needed to push the
tube E up the incline. The
tube has a mass of 75 kg
and the roller D has a mass
of 100 kg. The force acts
parallel to the plane, and
the coefficients of static
friction at the contacting
surfaces are μA = 0.3, μB =
0.25, and μC = 0.4. Each
cylinder has a radius of 150
mm.
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 43
Example 43-03 (cont.)
y
x
FBD
 Impending Motion

W
Point A
 Point B
 Point C
 Point B and C

NA
FA
FA
NA
W
FA
NA
P
FA
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© 2007 S. Kenny, Ph.D., P.Eng.
NA
ENGI 1313 Statics I – Lecture 43
Example 43-03 (cont.)

y
x
Analysis

Assume impending
motion at point A
W
r = 0.15m
FA   NA

FBD of roller
M
FAr  FC r
NB
W
FA
 FA  FC
NA
FBD of cylinder
M
O
FAr  FBr
17
FB
FA
0
O

NA
0
 FA  FB
© 2007 S. Kenny, Ph.D., P.Eng.
r = 0.15m
P
FC
NC
ENGI 1313 Statics I – Lecture 43
Example 43-03 (cont.)

y
x
Analysis of Tube

F
x
0
m

NA  FB  75kg  9.81 2  sin30  0
s 

NA  FA  367.9N  0
FA
 FA  367.9N  0
A
FA
 FA  367.9N  0
0.3
FA  157.7N  158N
W
NA
NB
FA   NA
FA  FB  FC
157.7N
NA 

 525.7N  526N
A
0.3
© 2007 S. Kenny, Ph.D., P.Eng.
FB
FA
FA
18
r = 0.15m
ENGI 1313 Statics I – Lecture 43
Example 43-03 (cont.)

y
x
Analysis of Tube

F
y
0
W
NB 157.7N  735.8N cos 30  0

NB 157.7N  637.2N  0
NB  794.9N  795N
r = 0.15m
NA
FB
FA
NB
FA   NA
FA  FB  FC
FA  157.7N  158N
19
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 43
Example 43-03 (cont.)

y
x
Analysis

F
0
y
m

NC  FA  100kg  9.81 2  cos 30  0
s 

NC 157.7N  849.6N  0
FA   NA
NC  691.8N  692N
FA  157.7N  158N

F
x
0
FA  FB  FC
W
FA
P  525.7N 157.7N  981N sin30  0
NA
P  1173.9N  1174N
r = 0.15m
P
FC
20
© 2007 S. Kenny, Ph.D., P.Eng.
NC
ENGI 1313 Statics I – Lecture 43
Example 43-03 (cont.)

y
x
Check Assumption

Impending motion at A
FA   NA  158N  FB  FC
NB  794.9N  795N
NC  691.8N  692N

Find maximum friction
force at point B and C
FB max  B NB  0.25795N  199N
FC max  C NC  0.4692N  277N
21
© 2007 S. Kenny, Ph.D., P.Eng.
 FB max  158N  199N
 FC max  158N  277N
ENGI 1313 Statics I – Lecture 43
References
Hibbeler (2007)
 http://wps.prenhall.com/esm_hibbeler_eng
mech_1

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© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 43