ENGI 1313 Mechanics I

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1 ENGI 1313 Mechanics I Lecture 43: Course Material Review Shawn Kenny, Ph.D., P.Eng. ssistant Professor aculty of Engineering and pplied Science Memorial University of Newfoundland spkenny@engr.mun.ca

2 inal Exam ormulae Sheet Posted on course webpage Probably by end of Monday Coordinate with Dr. Rideout Not to be used in the final exam inal exam formulae sheet will be attached to the exam S. Kenny, Ph.D., P.Eng.

3 Example The wheel weighs 20 lb and rests on a surface for which μ B.2. cord wrapped around it is attached to the top of the 30-lb homogeneous block. If the coefficient of static friction at D is μ D.3, determine the smallest vertical force that can be applied tangentially to the wheel which will cause motion to impend S. Kenny, Ph.D., P.Eng.

4 Example (cont.) BD Possible riction nalysis Cases Impending motion at B Impending motion at D Impending motion at B & D ssumption at B B μ N B B P B T T ND C D S. Kenny, Ph.D., P.Eng.

5 Example (cont.) nalysis heel M 1.5P 1.5T 1.5 B 0 P T + B + y P + 20 P 20 + x T B B 6.67 lb T B P T + B 13.3lb μ N B T P B B S. Kenny, Ph.D., P.Eng.

6 Example (cont.) nalysis Block C + x D T N D lb + y T 6.67lb T C D N D S. Kenny, Ph.D., P.Eng.

7 Example (cont.) Check ssumptions Maximum friction force at Point D ( ) μ N.3( 30lb) 9lb D max D D Calculated force at Point D D 6.67lb ssumption ok as block C does not have D impending motion N D D < ( D ) max S. Kenny, Ph.D., P.Eng. T C

8 Example (cont.) Check ssumptions Block C tipping 3T C x ( 6.67lb) ( 30lb)x 3 x.667ft Therefore block does not tip x.667ft < 1.5ft 2 T C x N D S. Kenny, Ph.D., P.Eng.

9 Example (cont.) Conclusion Impending motion at B Block C stationary and does not tip over P 13.3lb P T T C B D ND S. Kenny, Ph.D., P.Eng.

10 Example The friction hook is made from a fixed frame which is shown colored and a cylinder of negligible weight. 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 of paper p can be held S. Kenny, Ph.D., P.Eng.

11 Example BD ssume impending motion at all contact points μ 1 N μ 2 N 2 N 1 N N 1 N S. Kenny, Ph.D., P.Eng.

12 Example nalysis of Paper BD + y μ 2 N 1 2μ 1 N 1 N N S. Kenny, Ph.D., P.Eng.

13 Example nalysis of Cylinder Objective is to ind μ Orient axes to contact surface M O 1 2 r r y x 2 r r θ 2 N 2 r 1 / 2 N 1 / 2μ θ S. Kenny, Ph.D., P.Eng.

14 Example nalysis of Cylinder Objective is to ind μ Orient axes to contact surface + x N 2 sinθ cosθ 2 2μ 1 N 2 sinθ + cosθ 2 μ 2 1 sinθ + cosθ μ 2 μ 1 sinθ + cosθ 2μ 2 μ 2 2 θ S. Kenny, Ph.D., P.Eng. y 2 N 2 1 / 2 1 cosθ 1 μ sinθ + cosθ μ. 176 sinθ θ x N 1 / 2μ

15 Example 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 μ.3, μ B 0.25, and μ C.4. Each cylinder has a radius of 150 mm S. Kenny, Ph.D., P.Eng.

16 Example (cont.) y x BD Impending Motion Point Point B Point C Point B and C P S. Kenny, Ph.D., P.Eng.

17 Example (cont.) y x nalysis ssume impending motion at point μ BD of roller r M O r C BD of cylinder r M O r B C B S. Kenny, Ph.D., P.Eng. P C N C r.15m r.15m B

18 Example (cont.) y x nalysis of Tube + x m N B 2 s N 367.9N 0 o ( 75kg ) 9.81 sin N μ 367.9N N 158N 0 0 μ B r.15m B C 157.7N N 525.7N μ N S. Kenny, Ph.D., P.Eng.

19 Example (cont.) y x nalysis of Tube + y o 157.7N 735.8N cos 30 0 r.15m 157.7N 637.2N 794.9N 795N 0 B μ B C 157.7N 158N S. Kenny, Ph.D., P.Eng.

20 Example (cont.) y x nalysis + y m N + 2 s N C N 849.6N o ( 100kg ) 9.81 cos 30 0 C N C 691.8N + x 692N o P 525.7N 157.7N 981N sin 30 P N 1174N P 0 μ B r.15m C 157.7N 158N C N C S. Kenny, Ph.D., P.Eng.

21 Example (cont.) Check ssumption Impending motion at μ N 158N 794.9N 795N B C y x N C 691.8N 692N ind maximum friction force at point B and C ( ) μ N.25( 795N) 199N B max B B ( ) μ N.4( 692N) 277N C max C C ( ) 158N 199N B max < ( ) 158N 277N C max < S. Kenny, Ph.D., P.Eng.

22 References Hibbeler (2007) mech_ S. Kenny, Ph.D., P.Eng.

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