tutorials 2010 mechanics
TRANSCRIPT
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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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Engineering Mechanics I
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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Engineering Mechanics I
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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Engineering Mechanics I
Tutorial SessionTopic:
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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Engineering Mechanics I
Tutorial SessionTopic: Cont.
Force system resultants
Moment of a force about a point
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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Engineering Mechanics I
Tutorial SessionTutorial sheet: 27/09/2010 (on work given 0n 23/09/2010)
Topic: Cont.
Force system resultants
Moment of a force about a point
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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Engineering Mechanics I
Tutorial SessionTopic:
Force system resultants
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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Engineering Mechanics I
Tutorial SessionTopic:
Force system resultants
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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Engineering Mechanics I
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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Engineering Mechanics I
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.