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**Lecture 43: Course Material Review**

ENGI 1313 Mechanics I Lecture 43: Course Material Review

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**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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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.

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**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

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

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

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**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

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**Example 43-01 (cont.) Check Assumptions Block C tipping**

Therefore block does not tip T WC x ND

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**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

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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.

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**Example 43-02 FBD Assume impending motion at all contact points F1 F1**

W F2 N1 N2

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

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**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

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**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

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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.

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**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

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**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

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

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

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

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**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

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**References Hibbeler (2007)**

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