TUTORIALS 2010 Mechanics

8/4/2019 TUTORIALS 2010 Mechanics

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UNIVERSITY OF NAMIBIA

FACULTY OF ENGINEERING AND

INFORMATION TECHNOLOGY

Engineering Mechanics I: Statics

Tutorial session

ADDITION OF A SYSTEM OF COPLANAR FORCES

Date: 10/08/2010

By Ithete yaHango


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1. Determine thexand y components ofF1 and

F2 acting on the boom shown below. Express

each force as a Cartesian vector.


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2. The link in figure below is subjected to two

forces F1 and F2.Determine the magnitude anddirection of the resultant force.


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3. The end of the boom 0 in the figure below is

subjeted to three concurrent and coplanar

forces.

Determine the magnitude and direction of the

resultant force.


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6. The force F= 450 N acts on the frame. Resolve

this force into components acting along memberAB andAC. and determine the magnitude of

each component.


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Engineering Mechanics I

Tutorial SessionTopics:

Cartesian Vectors

Addition and subtraction of Cartesian Vectors

Date: 17/08/201


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7. Given the forces as F1= (60 i 50j + 40k) N

and F2 = ( 40 i 85j + 30k) N.

(a) Sketch each force on anx, y, z reference.

(b) Determine the magnitude and coordinate

direction angles of the resultant force.


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8. Two forces act on the hook shown in below.

Specify the magnitude of F2 and its coordinate

direction angles ofF2 that the resultant force FRacts along the positive y axis and has a

magnitude of 800 N.


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Home work

1. Revise the topic you have done so far.

2. Do example 2.10 on page 49

3. Do exercise 2-58 and 2- 59 on page 51

4. Read with understanding:

Position vectors

Force vector directed along a line


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Tutorial SessionTopics:

Position Vectors

Force Vector Directed along a Line

Date: 24/08/201


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1. The Man shown below pulls on the cord with a force of 350 N. Find

the coordinates of the end points (A and B) of the cord, hence plot

the position vector r.


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2. Represent the position vector r acting from

pointA (3m, 5m, 6m) to point B (5m, - 2m, 1m)

in Cartesian vector form. Determine its

coordinate direction angles and find thedistance between pointsA and B.


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3. Determine the magnitude and coordinate

direction angles of the resultant force.


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Home work

Please revise until the penultimate topics

Read Dot products and its applications

Chapter 3


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Tutorial SessionTopic:

Equilibrium of a Particle: Three Dimensional ForceSystems

Date: 31/08/201


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1. The joint of a space frame is subjected to four forces.

Strut OA lies in thex-yplane and strut OB lies in the y-z

plane. Determine the forces acting in each of the three

struts required for equilibrium. F= 2kN.


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2. The 100 kg crate as shown below is supported by

three cords, one of which is connected to a spring.

Determine the tension in each cord and the stretchof the spring.


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Home Work

1. Revise the examples in chapter 3

2. Revise the examples in chapters 1 23. Do problems 3.7, 3.12, 3.17 and 3.45

(Hibbeler 11th Edition)

4. Revise Chapters 1 3.


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Force system resultants

Moment of a force about a point

Cross product

Date: 21/09/2010

1 D i h i d d di i l f h


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1. Determine the magnitude and directional sense of the

resultant moment of the forces at A and B

about point O. 1= 300, 2= 45

0, a = 5 m, b = 13 m, c = 3 m, d= 6

m, e = 3 m,f= 6 m, F1= 40 N, F2= 60 N

2 Determine the moment of each force about the bolt


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2. Determine the moment of each force about the bolt

located atA.

FB= 40 N a = 2.5 m = 200 = 30 0

FC= 50 N b = 0.75 m = 250


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3. The Snorkel Co. produces the articulating boom platform that

can support weight W. If the boom is in the position shown,

determine the moment of this force about pointsA, B and C. W =

550N, a = 3 m, b = 16 m, c = 15 m,1= 300, 2= 70

0.


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Tutorial SessionTopic: Cont.



Cross product

Date: 23/09/2010


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4. The boom has length L, weight Wb, and mass center at G. If

the maximum moment that can be developed by the motor

at A is M, determine the maximum load W, having a mass

center at G', that can be lifted. L= 30 m, Wb= 800 N

a = 14 m, b = 2 m, = 30 0 and M = 20 103 N M.


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5. Determine the moment of the force atA about point O.

Express the result as a Cartesian vector. F =(60i 30j 20k) N

a=4m, b = 7m, c = 3 m, d= 4 m, e = 6 m andf= 2 m

6 The pole supports a traffic light of weight W Using


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6. The pole supports a traffic light of weight W. Using

Cartesian vectors, determine the moment

of the weight of the traffic light about the base of the

pole atA. W= 22 N, a = 12 m and = 30

0

E i i M h i I


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Tutorial SessionTutorial sheet: 27/09/2010 (on work given 0n 23/09/2010)

Topic: Cont.



Cross product

Date: 27/09/2010


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Problem 4-31

The worker is using the bar to pull two pipes together in order to complete the

connection. If he applies a horizantal force F to the handle of the lever, determine the

moment of this force about the end A. What would be the tension T in the cable

needed to cause the opposite moment about point A. F= 80 N 1= 400

2 = 200

a =0.5 m and b = 4.5 m.


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Problem 4-39

The curved rod lies in the x-yplane and has a radius r. If a force F acts at its end as

shown, determine the moment of this force about point B. F= 80 N, c = 3 m, a = 1 m

and r= 3 m. b = 2 m = 45 0


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Problem 4-23

The Y-type structure is used to support the high voltage transmission cables. If

the supporting cables each exert a force Fon the structure at B, determine the

moment of each force about pointA. Also, by the principle of transmissibility,

locate the forces at points Cand D and determine the moments. F= 275 N, a =85 m, = 30 0.


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Problem 4-41

The pole supports a traffic light of weight W. Using Cartesian vectors, determine the

moment of the weight of the traffic light about the base of the pole atA. W= 22 N, a =

12 m and = 30 0.


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Problem 4-43

Determine the smallest force Fthat must be applied along the rope in order to cause

the curved rod, which has radius r, to fail at the support C. This requires a moment to

be developed at Cof magnitude M. r= 5 m,

M = 80 N m, = 60 0, a = 7 m and b = 6 m.


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Moment of a force along an axis

Moment of a couple

Date: 05/10/2010

1 Determine the moment of the force F about the Oa axis


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1. Determine the moment of the force F about the Oa axis.

Express the result as a Cartesian vector. F={50i 20j + 20k}N, a =

6 m, b = 2 m, c = 1 m, d= 3 m. e = 4 m.


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2. The hood of the automobile is supported by the strut

AB, which exerts a force F on the hood. Determine the

moment of this force about the hinged axis y. F= 24 N

a = 2 m b = 4 m c = 2 m d= 4 m.


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3. Determine the magnitude and direction of the

couple moment acting on the gear as shown

below.


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Moment of a couple

Date: 11/10/2010

1 Express the moment of the couple acting on the pipe assembly in


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1. Express the moment of the couple acting on the pipe assembly in

Cartesian vector form. Find the moment by (a) using M = r x F, (b)

summing the moment of each force about point O. F = {25k} N, a =

300 mm, b = 150 mm, c = 400 mm, d= 200 mm, e = 200 mm


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2. Determine the magnitude and sense of the

couple moment. F= 5 kN, = 30 0, a = 0.5 m,

b = 4 m, c = 2 m and d= 1 m.


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3. Determine the couple moment acting on the

pipe shown below. SegmentAB is directed 300

below the x-y plane.


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Homework

1. Solve problems F4 24 and 4 94.

2. Read:

Simplification of a Force and Couple System

Reduction of a Simple Distributed Loading


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Tutorial SessionTopic: Structural Analysis

The Method of Joints

The Method of Sections

Date: 27/10/2010


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1. The truss, used to support a balcony, is subjected to

the loading shown. Approximate each joint as a pin

and determine the force in each member. State

whether the members are in tension orcompression.

P1= 600 N, P2= 400 N, a = 4 m, = 450


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2. Determine the force in each member of the

double scissors truss in terms of the load P

and state if the members are in tension orcompression.


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Hints to Q 2

3 The Howe bridge truss is subjected to the loading


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3. The Howe bridge truss is subjected to the loading

shown. Determine the force in members DE, EH,

and HG, and state if the members are in tension or

compression. F1= 30 kN, F2= 20 kN, F3= 20 kN,F4= 40 kN, a = 4 m, b = 4 m

4 D i h f i b BG HG d BC f


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4. Determine the force in members BG, HG, and BCof

the truss and state if the members are in tension or

compression. F1= 6 kN, F2= 7 kN, F3= 4 kN,

a = 3 m, b = 3 m, c = 4.5 m.

h


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Tutorial Session

Topic: Friction

Date: 02/11/2010


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1. The horizontal force is P. Determine the

normal and frictional forces acting on the

crate of weight W. The friction coefficientsare kand s are 0.2 and 0.3. W= 300 N, P =

80 N and = 20 0.


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2. The 80 N boy stands on the beam and pulls on the

cord with a force of 40 N. If (s)D = 0.4, determine

the frictional force between his shoes and the beam

and the reactions at A and B. The bean is uniform

and has a weight of 100 N. Neglect the size of the

pulleys and the thickness of the beam.

Documents

TUTORIALS 2010 Mechanics