ENGI 1313 Mechanics I

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 N1 N1 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.) 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.) y x • 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 W FA NA r = 0.15m P FC NC

Example 43-03 (cont.) 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

ENGI 1313 Mechanics I