-
8/6/2019 MAE 241-Lec4-Summer 2011
1/14
MAE 241 - Statics
Summer 2011
Dr. Konstantinos A. Sierros
Office Hours: M and W 10:30 11:30 (263 ESB new add)
[email protected]
Teaching Blog: http://wvumechanicsonline.blogspot.com
-
8/6/2019 MAE 241-Lec4-Summer 2011
2/14
Chapter 3: Equilibrium of a particle
Chapter objectives
Introduction of the concept
of free body diagram (FBD)for a particle
Solve particle equilibrium
problems using equations of
equilibrium
-
8/6/2019 MAE 241-Lec4-Summer 2011
3/14
3.1 Condition for the equilibrium of a particle
A particle is said to be in equilibrium if it remains at rest
(if it isoriginally at rest) or has a constant velocity (if it is
originally in
motion)
To maintain equilibrium it is necessary to satisfy Newtons 1st
Law
which requires the resultant force acting on a particle to
bezero
F= 0
but also from Newtons 2nd Law we know that F = ma
Which means that a = 0 (i.e particle does not have
acceleration)
-
8/6/2019 MAE 241-Lec4-Summer 2011
4/14
3.2 The free body diagram (FBD)
A drawing that shows the particle with all the forces that act
on
it is called afree body diagram
In particle equilibrium problems we may have two types of
connections
1. Springs
If a linearly elastic springof initial length lo is
used to support a particle, the length of the
spring will change linearly with the force F
acting on it.F = ks (where s = l-lo and k is stiffness of
spring)
-
8/6/2019 MAE 241-Lec4-Summer 2011
5/14
3.2 The free body diagram (FBD)
In particle equilibrium problems we may have two types of
connections
2. Cables and pulleys
We assume that cables have negligible weightand they cannot
stretch
Also, we assume that a cable can support only
a tension or pulling force
Pulleys are frictionless
For any angle , the cable is subjected to aconstant tension T
throughout its length (will
prove that in Chapter 5)
-
8/6/2019 MAE 241-Lec4-Summer 2011
6/14
3.2 The free body diagram (FBD)
Steps for drawing a free body diagram
1. Draw outlined shape
Imagine the particle to be isolatedor cut free from its
surroundings
by drawing its outlined shape2. Show all forces that act on the
particle (both active forces and
reactive forces).Active forces tend to set the particle in
motion and
reactive forces are the result of constraints or supports that
tend to
prevent motion
3. Identify each forceLabel known forces with their magnitudes
and directions. Use letters
to represent the unknown forces
-
8/6/2019 MAE 241-Lec4-Summer 2011
7/14
3.2 The free body diagram (FBD)
-
8/6/2019 MAE 241-Lec4-Summer 2011
8/14
-
8/6/2019 MAE 241-Lec4-Summer 2011
9/14
-
8/6/2019 MAE 241-Lec4-Summer 2011
10/14
3.3 Coplanar force systems
If a particle is subjected to a system of coplanar forces that
lie in thex-y plane, then each force can be resolved into its i
andj components
Fx = 0
Fy = 0
-
8/6/2019 MAE 241-Lec4-Summer 2011
11/14
3.3 Coplanar force systems
make sure you always define positive/negative direction
(+ ) Fx = 0
-
8/6/2019 MAE 241-Lec4-Summer 2011
12/14
-
8/6/2019 MAE 241-Lec4-Summer 2011
13/14
-
8/6/2019 MAE 241-Lec4-Summer 2011
14/14
3.3 Three dimensional (3D) force systems
In the case of 3-D systems, weneed to resolve forces into
the
respective i,j,kcomponents so
that:
Fxi+ Fyj+ Fzk= 0
Fx=
0Fy = 0
Fz = 0
