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Shawn Kenny, Ph.D., P.Eng.Assistant ProfessorFaculty of Engineering and Applied ScienceMemorial University of [email protected]
ENGI 1313 Mechanics I
Lecture 43: Course Material Review
2 ENGI 1313 Statics I – Lecture 43© 2007 S. Kenny, Ph.D., P.Eng.
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
3 ENGI 1313 Statics I – Lecture 43© 2007 S. Kenny, Ph.D., P.Eng.
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.
4 ENGI 1313 Statics I – Lecture 43© 2007 S. Kenny, Ph.D., P.Eng.
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
NB
FB
ND
FD
PT T
WA
WC
BBB NF
5 ENGI 1313 Statics I – Lecture 43© 2007 S. Kenny, Ph.D., P.Eng.
Example 43-01 (cont.)
Analysis Wheel A 0MA
0F5.1T5.1P5.1 B
BFTP
20PNB 0Fy
BN20P
0Fx
BFT NB
FB
PT
WA
Tlb67.6FB BBB NF
lb3.13FTP B
6 ENGI 1313 Statics I – Lecture 43© 2007 S. Kenny, Ph.D., P.Eng.
Example 43-01 (cont.)
Analysis Block C
ND
FD
T
WC
30ND
0Fy
lb67.6T
0Fx
lb67.6TFD
7 ENGI 1313 Statics I – Lecture 43© 2007 S. Kenny, Ph.D., P.Eng.
Example 43-01 (cont.)
Check Assumptions Maximum friction force
at Point D
Calculated force at Point D
Assumption ok as block C does not have impending motion
ND
FD
T
WC
lb9lb303.0NF DDmaxD
lb67.6FD
maxDD FF
8 ENGI 1313 Statics I – Lecture 43© 2007 S. Kenny, Ph.D., P.Eng.
Example 43-01 (cont.)
Check Assumptions Block C tipping
Therefore block does not tip
ND
T
WC
xWT3 C
x
xlb30lb67.63
ft667.0x
2
ft5.1ft667.0x
9 ENGI 1313 Statics I – Lecture 43© 2007 S. Kenny, Ph.D., P.Eng.
Example 43-01 (cont.)
Conclusion Impending motion at B Block C stationary and
does not tip over
NB
FB
ND
FD
PT T
WA
WC
lb3.13P
10 ENGI 1313 Statics I – Lecture 43© 2007 S. Kenny, Ph.D., P.Eng.
Example 43-02
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.
11 ENGI 1313 Statics I – Lecture 43© 2007 S. Kenny, Ph.D., P.Eng.
Example 43-02
FBD Assume impending motion
at all contact points
N1
F1
N1
F1
W
N1
F1
N2
F2
11 NF
22 NF
12 ENGI 1313 Statics I – Lecture 43© 2007 S. Kenny, Ph.D., P.Eng.
Example 43-02
Analysis of Paper FBD
N1
F1
N1
F1
W
WF2 1
0Fy
2
WF1
11 N2
WF
2W
N1
13 ENGI 1313 Statics I – Lecture 43© 2007 S. Kenny, Ph.D., P.Eng.
Example 43-02
Analysis of Cylinder Objective is to Find
Orient axes to contact surface
N1 = W / 2
F1 = W / 2
N2
F2
xy
0MO
0rFrF 12
r
2
WF2
0r2
WrF2
14 ENGI 1313 Statics I – Lecture 43© 2007 S. Kenny, Ph.D., P.Eng.
Example 43-02
Analysis of Cylinder Objective is to Find
Orient axes to contact surface
N1 = W / 2
F1 = W / 2
N2
F2
= 20
xy 0Fx
0cos2
Wsin
2
WN2
cos
1sin
2
WN2
cos
1sin
2
WF2
cos
1sin
2
W
2
W
2
WF2
cossin1 176.0sin
cos1
15 ENGI 1313 Statics I – Lecture 43© 2007 S. Kenny, Ph.D., P.Eng.
Example 43-03 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.
16 ENGI 1313 Statics I – Lecture 43© 2007 S. Kenny, Ph.D., P.Eng.
Example 43-03 (cont.)
FBD Impending Motion
Point A Point B Point C Point B and C
NA
FA
FA
NA
NAFA
NA
FA
P
W
W
xy
17 ENGI 1313 Statics I – Lecture 43© 2007 S. Kenny, Ph.D., P.Eng.
Example 43-03 (cont.)
Analysis Assume impending
motion at point A
FBD of roller
FBD of cylinder
FA
NA
NCFC
P
W 0MO
rFrF CA
r = 0.15m
AA NF
0MO
rFrF BA
NA
FA
NB
FB
Wr = 0.15m
CA FF
BA FF
xy
18 ENGI 1313 Statics I – Lecture 43© 2007 S. Kenny, Ph.D., P.Eng.
Example 43-03 (cont.)
Analysis of Tube
xy
030sins
m81.9kg75FN
2BA
0N9.367FN AA
0Fx
NA
FA
NB
FB
Wr = 0.15m
0N9.367FF
AA
A
0N9.367F3.0
FA
A
N158N7.157FA
AA NF
CBA FFF
N526N7.5253.0
N7.157FN
A
AA
19 ENGI 1313 Statics I – Lecture 43© 2007 S. Kenny, Ph.D., P.Eng.
Example 43-03 (cont.)
Analysis of Tube
AA NF
CBA FFF
xy
030cosN8.735N7.157NB
0N2.637N7.157NB NA
FA
NB
FB
Wr = 0.15m
N795N9.794NB
0Fy
N158N7.157FA
20 ENGI 1313 Statics I – Lecture 43© 2007 S. Kenny, Ph.D., P.Eng.
Example 43-03 (cont.)
Analysis
FA
NA
NCFC
P
W
r = 0.15m
xy
030coss
m81.9kg100FN
2AC
0Fy
0N6.849N7.157NC
AA NF
CBA FFF
N158N7.157FA N692N8.691NC
030sinN981N7.157N7.525P
0Fx
N1174N9.1173P
21 ENGI 1313 Statics I – Lecture 43© 2007 S. Kenny, Ph.D., P.Eng.
Example 43-03 (cont.)
Check Assumption Impending motion at A
Find maximum friction force at point B and C
xy
CBAA FFN158NF
N692N8.691NC
N795N9.794NB
N199N79525.0NF BBmaxB
N277N6924.0NF CCmaxC
N199N158F maxB
N277N158F maxC
22 ENGI 1313 Statics I – Lecture 43© 2007 S. Kenny, Ph.D., P.Eng.
References
Hibbeler (2007) http://wps.prenhall.com/
esm_hibbeler_engmech_1
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