ENGR-1100 Introduction to Engineering Analysis

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ENGR-1100 Introduction to Engineering Analysis

• Lecture 4

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Lecture Outline

• Free body diagram.
• Equilibrium of a particle - two dimensional
  problems.

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A Particle

• Large bodies or small bodies can be referred to
  as particles when the size and shape of the body
  have no effect on the response of the body to a
  system of forces.
• The mass of the body can be assumed to be
  concentrated at a point and the shape can be
  neglected.
• A necessary and sufficient condition for
  equilibrium
• RSF0
• Where SF is the sum of all forces acting on a
  particle.

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Free Body Diagram

• A carefully prepared drawing that shows a body
  of interest separated from all interacting
  bodies.
• The forces exerted by all other bodies must be
  determined and shown on the diagram.

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The procedure for drawing free-body diagram
Essential Steps

• Make a decision regarding what body is to be
  isolated and analyzed.
• Prepare a sketch of the external boundary of the
  selected body.
• Present all forces, known and unknown, that are
  applied by other bodies with vectors in the
  correct position.

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What should be the body of interest of the
following problem?
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How to deal with unknown forces?

• If a force has a known line of action but unknown
  magnitude and direction, the direction of the
  force can be assumed.
• If both magnitude and direction of the force are
  unknown it might be convenient to show the two
  rectangular components of the force.

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Procedure to construct a complete and correct
free-body diagram

• 1) Decide which body or combination of bodies is
  to be shown on the free-body diagram.
• 2) Prepare a drawing of the outline of the
  free-body.
• 3) Carefully trace around the boundary of the
  free body and identify all the forces exerted by
  contacting or attracting bodies that were removed
  during the isolation process.
• 4) Choose the set of coordinate axes to be used
  in solving the problem and indicate their
  direction on the free-body diagram.

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Equilibrium of a Particle Two Dimensions
R Rx Ry Rn Rt Rxi Ryj Rnen
Rtet SFxi SFyj SFnen SFtet 0
The equation can only be satisfied if
Rx RxiSFxi0 Ry RyjSFyj0 Rn
RnenSFnen0 Rt RtetSFtet0
or
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Example P3-4
A homogeneous cylinder with mass of 250 kg is
supported against a smooth surface by a cable as
shown in Fig. 3-4. Determine the forces exerted
on the cylinder by the cable and by the smooth
surface at contact point C.
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Solution
1) Free body diagram
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1) Equilibrium equations
a
How many unknowns? How many equations?
2
2
SFx0
FCB-FAB sin(a)0
SFy0
FAB cos(a)-2509.80
FAB 2509.8/cos(a) 2525.4 N
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Class Assignment Exercise set 3-3 please submit
to TA at the end of the lecture
A homogeneous cylinder weighing 500 lb rests
against two smooth planes that form a trough as
shown in Fig. P3-3. Determine the forces exerted
on the cylinder by the plane at contact A and B.
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Solution
1) Free body diagram
a) Choose the body
b) Prepare the drawing
d) Choose coordinate axes
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1) Equilibrium equations
How many unknowns? How many equations?
SFx0
FA-FB sin(300)0
SFy0
FB cos(300)-5000
FB 500/cos(300) 577.4 lb
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Example P3-17
A continuous cable is used to support blocks A
and B as shown in Fig. P3-17. Block A is
supported by a small wheel that is free to roll
on the cable. Determine the displacement y of
block A for equilibrium if the weight of block A
and B are 50 lb and 75 lb, respectively.
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Solution
1) Free body diagram body B
T
y
75 lb
SFy0
T -750
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1) Free body diagram body A
How many unknowns? How many equations?
Two a and b Two SFx0, SFy0
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SFx0
T cos(a) - T cos(b) 0
SFy0
T sin(a)T sin(a) - 500
sin(a) 50/150
a 19.50
y10/2tan(19.50)1.77 ft
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Class Assignment Exercise set 3-13 please submit
to TA at the end of the lecture
Two flower pots are supported with cables as
shown in Fig. P13-3. If pot A weighs 10 lb and
pot B weighs 8 lb, determine the tension of the
cables and the slope of cable BC.
Answer TABTCD12.73 lb a6.340 TBC9.06 lb
B
A