Lecture 43: Course Material Review ENGI 1313 Mechanics I Lecture 43: Course Material Review

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

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.

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 T T P WC WA FB FD NB ND

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

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

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 T WC FD ND

Example 43-01 (cont.) Check Assumptions Block C tipping Therefore block does not tip T WC x ND

Example 43-01 (cont.) Conclusion Impending motion at B Block C stationary and does not tip over T T P WC WA FB FD NB ND

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.

Example 43-02 FBD Assume impending motion at all contact points F1 F1 W F2 N1 N2

Example 43-02 Analysis of Paper FBD F1 F1 N1 N1 W

Example 43-02 Analysis of Cylinder Objective is to Find  Orient axes to contact surface y x F1 = W / 2 r F2 N1 = W / 2  N2 

Example 43-02 Analysis of Cylinder Objective is to Find  Orient axes to contact surface y x F1 = W / 2 F2 N1 = W / 2  = 20 N2 

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.

Example 43-03 (cont.) FBD Impending Motion Point A Point B Point C y x FBD Impending Motion Point A Point B Point C Point B and C W NA FA FA NA W FA NA P FA NA

Example 43-03 (cont.) Analysis Assume impending motion at point A FBD of roller FBD of cylinder W r = 0.15m NA FB FA NB W FA NA r = 0.15m P FC NC

Example 43-03 (cont.) y x Analysis of Tube W r = 0.15m NA FB FA NB

Example 43-03 (cont.) y x Analysis of Tube W r = 0.15m NA FB FA NB

Example 43-03 (cont.) y x Analysis W FA NA r = 0.15m P FC NC

Example 43-03 (cont.) Check Assumption Impending motion at A y x Check Assumption Impending motion at A Find maximum friction force at point B and C

References Hibbeler (2007) http://wps.prenhall.com/esm_hibbeler_engmech_1