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Shawn Kenny, Ph.D., P.Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland ENGI 1313 Mechanics I Lecture 43:Course Material Review

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ENGI 1313 Statics I – Lecture 43© 2007 S. Kenny, Ph.D., P.Eng. 2 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

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ENGI 1313 Statics I – Lecture 43© 2007 S. Kenny, Ph.D., P.Eng. 3 Example The wheel weighs 20 lb and rests on a surface for which μ B = 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 μ D = 0.3, determine the smallest vertical force that can be applied tangentially to the wheel which will cause motion to impend.

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ENGI 1313 Statics I – Lecture 43© 2007 S. Kenny, Ph.D., P.Eng. 4 Example (cont.) FBD Possible Friction Analysis Cases Impending motion at B Impending motion at D Impending motion at B & D Assumption at B NBNB FBFB NDND FDFD P T T WAWA WCWC

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ENGI 1313 Statics I – Lecture 43© 2007 S. Kenny, Ph.D., P.Eng. 5 Example (cont.) Analysis Wheel A NBNB FBFB P T WAWA

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ENGI 1313 Statics I – Lecture 43© 2007 S. Kenny, Ph.D., P.Eng. 6 Example (cont.) Analysis Block C NDND FDFD T WCWC

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ENGI 1313 Statics I – Lecture 43© 2007 S. Kenny, Ph.D., P.Eng. 7 Example (cont.) Check Assumptions Maximum friction force at Point D Calculated force at Point D Assumption ok as block C does not have impending motion NDND FDFD T WCWC

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ENGI 1313 Statics I – Lecture 43© 2007 S. Kenny, Ph.D., P.Eng. 8 Example (cont.) Check Assumptions Block C tipping Therefore block does not tip NDND T WCWC x

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ENGI 1313 Statics I – Lecture 43© 2007 S. Kenny, Ph.D., P.Eng. 9 Example (cont.) Conclusion Impending motion at B Block C stationary and does not tip over NBNB FBFB NDND FDFD P T T WAWA WCWC

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ENGI 1313 Statics I – Lecture 43© 2007 S. Kenny, Ph.D., P.Eng. 10 Example 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.

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ENGI 1313 Statics I – Lecture 43© 2007 S. Kenny, Ph.D., P.Eng. 11 Example FBD Assume impending motion at all contact points N1N1 F1F1 N1N1 F1F1 W N1N1 F1F1 N2N2 F2F2

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ENGI 1313 Statics I – Lecture 43© 2007 S. Kenny, Ph.D., P.Eng. 12 Example Analysis of Paper FBD N1N1 F1F1 N1N1 F1F1 W

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ENGI 1313 Statics I – Lecture 43© 2007 S. Kenny, Ph.D., P.Eng. 13 Example Analysis of Cylinder Objective is to Find Orient axes to contact surface N 1 = W / 2 F 1 = W / 2 N2N2 F2F2 xy r

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ENGI 1313 Statics I – Lecture 43© 2007 S. Kenny, Ph.D., P.Eng. 14 Example Analysis of Cylinder Objective is to Find Orient axes to contact surface N 1 = W / 2 F 1 = W / 2 N2N2 F2F2 = 20 xy

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ENGI 1313 Statics I – Lecture 43© 2007 S. Kenny, Ph.D., P.Eng. 15 Example 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 μ A = 0.3, μ B = 0.25, and μ C = 0.4. Each cylinder has a radius of 150 mm.

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ENGI 1313 Statics I – Lecture 43© 2007 S. Kenny, Ph.D., P.Eng. 16 Example (cont.) FBD Impending Motion Point A Point B Point C Point B and C NANA FAFA FAFA NANA NANA FAFA NANA FAFA P W W x y

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ENGI 1313 Statics I – Lecture 43© 2007 S. Kenny, Ph.D., P.Eng. 17 Example (cont.) Analysis Assume impending motion at point A FBD of roller FBD of cylinder FAFA NANA NCNC FCFC P W r = 0.15m NANA FAFA NBNB FBFB W x y

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ENGI 1313 Statics I – Lecture 43© 2007 S. Kenny, Ph.D., P.Eng. 18 Example (cont.) Analysis of Tube x y NANA FAFA NBNB FBFB W r = 0.15m

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ENGI 1313 Statics I – Lecture 43© 2007 S. Kenny, Ph.D., P.Eng. 19 Example (cont.) Analysis of Tube x y NANA FAFA NBNB FBFB W r = 0.15m

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ENGI 1313 Statics I – Lecture 43© 2007 S. Kenny, Ph.D., P.Eng. 20 Example (cont.) Analysis FAFA NANA NCNC FCFC P W r = 0.15m x y

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ENGI 1313 Statics I – Lecture 43© 2007 S. Kenny, Ph.D., P.Eng. 21 Example (cont.) Check Assumption Impending motion at A Find maximum friction force at point B and C x y

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ENGI 1313 Statics I – Lecture 43© 2007 S. Kenny, Ph.D., P.Eng. 22 References Hibbeler (2007) mech_1

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