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

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

3. 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.

4. 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

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

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

7. 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

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

9. 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

10. 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.

11. Example 43-02 FBD Assume impending motion at all contact points F1 F1W F2 N1 N2

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

13. 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 

14. 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 

15. 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.

16. Example 43-03 (cont.) FBD Impending Motion Point A Point B Point Cy 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

17. 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

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

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

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

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

22. References Hibbeler (2007)