ENGI 1313 Mechanics I Lecture 43 Course Material

Final Exam n Formulae Sheet Ø Posted on course webpage • Probably by end

Example 43 -01 n The wheel weighs 20 lb and rests on a surface

Example 43 -01 (cont. ) FBD n Possible Friction Analysis Cases n Impending motion

Example 43 -01 (cont. ) n Analysis Wheel A T P WA FB NB

Example 43 -01 (cont. ) n Analysis Block C T WC FD ND 6

Example 43 -01 (cont. ) n Check Assumptions Ø Maximum friction force at Point

Example 43 -01 (cont. ) n Check Assumptions Ø Block C tipping T Ø

Example 43 -01 (cont. ) n Conclusion Impending motion at B Ø Block C

Example 43 -02 n 10 The friction hook is made from a fixed frame

Example 43 -02 n FBD Ø Assume impending motion at all contact points F

Example 43 -02 n Analysis of Paper FBD F 1 N 1 W 12

Example 43 -02 Analysis of Cylinder n Objective is to Find n Ø Orient

Example 43 -03 n 15 Determine the minimum force P needed to push the

Example 43 -03 (cont. ) y x FBD n Impending Motion n W Point

Example 43 -03 (cont. ) n y x Analysis Ø Ø Assume impending motion

Example 43 -03 (cont. ) n y x Analysis of Tube W r =

Example 43 -03 (cont. ) n y x Analysis W FA r = 0.

Example 43 -03 (cont. ) n 21 y Check Assumption Ø Impending motion at

References Hibbeler (2007) n http: //wps. prenhall. com/esm_hibbeler_eng mech_1 n 22 © 2007 S.

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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 spkenny@engr. mun. ca

Final Exam n Formulae Sheet Ø Posted on course webpage • Probably by end of Monday • Coordinate with Dr. Rideout Not to be used in the final exam Ø Final exam formulae sheet will be attached to the exam Ø 2 © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 43

Example 43 -01 n 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 n Possible Friction Analysis Cases n Impending motion at B Ø Impending motion at D Ø Impending motion at B&D Ø n Assumption at B T P WC WA FB FD NB 4 © 2007 S. Kenny, Ph. D. , P. Eng. T ENGI 1313 Statics I – Lecture 43 ND

Example 43 -01 (cont. ) n Check Assumptions Ø Maximum friction force at Point D Ø Calculated force at Point D Ø 7 Assumption ok as block C does not have impending motion © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 43 T WC FD ND

Example 43 -02 n 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 Analysis of Cylinder n Objective is to Find n Ø Orient axes to contact surface y x F 2 F 1 = W / 2 N 1 = W / 2 = 20 N 2 14 © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 43

Example 43 -03 n 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. ) n y x Analysis Ø Ø Assume impending motion at point A W NA FBD of roller NB FA NA FBD of cylinder r = 0. 15 m P FC 17 FB FA W Ø r = 0. 15 m © 2007 S. Kenny, Ph. D. , P. Eng. NC ENGI 1313 Statics I – Lecture 43