Shawn Kenny, Ph.D., P.Eng.Assistant ProfessorFaculty of Engineering and Applied ScienceMemorial University of Newfoundlandspkenny@engr.mun.ca

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