Upload
others
View
2
Download
0
Embed Size (px)
Citation preview
STATIC EQUILIBRIUM OF A PARTICLE (3-D)
Learning Objectives
1). To draw a free body diagram (FBD) of an object that is
modeled as a particle.
2). To evaluate the forces required for static equilibrium of an
object that is modeled as a particle.
3). To do an engineering estimate of these quantities.
Force Classifications
External Forces: applied forces which are typically known or
prescribed (e.g., forces due to cables, springs, gravity, etc.).
Reaction Forces: constraining forces at supports, intended to
prevent motion (usually nonexistent unless system is externally
loaded).
Free Body Diagram (FBD)
Free Body Diagram (FBD): a graphical sketch of the system
showing a coordinate system, all
external/reaction forces and moments,
and key geometric dimensions.
Benefits:
1). Provides a coordinate system to establish a solution
methodology.
2). Provides a graphical display of all forces/moments acting on
the rigid body.
3). Provides a record of geometric dimensions needed for
establishing moments of the forces.
Newton’s First Law
Given no net force, a body at rest will remain at rest and a body
moving at a constant velocity will continue to do so along a
straight path ( )R F 0 .
Static Equilibrium
Vector Equation:
Component Equations:
N
R i x y z
i 1
F F F i F j F k 0
x y z0 0 0F F F
Problem Solving
1). Draw complete FBD.
2). Choose an xyz reference frame.
3). Evaluate the geometrical parameters.
4). Write equations of static equilibrium.
5). Count number of scalar equations and number of unknowns.
6). Solve equations of static equilibrium.
Note:
Fdrag = ½ ρ CD SA ν2
Where ρ = density of air
CD = Drag Coefficient
SA = Frontal Surface Area
ν = velocity
3-D Particle Equilibrium
Example 2
Given: A 500 lb crate is suspended in static equilibrium using rigid strut AD and cables AB and AC.
Find:
a) Write expressions for cables ABT and
ACT and strut DAF
in terms of their unknown magnitudes and their known unit vectors.
b) Write the equations of static equilibrium and determine the magnitudes of the tensions in cables AB and AC and the axial load in strut AD.
c) Is the axial load in strut AD in tension or compression?
3-D Particle Equilibrium
Group Quiz
Group #: ____________ Group Members: 1) ______________________________
(Present Only)
Date: ______________ Period: _________ 2) ______________________________
3) ______________________________
4) ______________________________
Given: A weather balloon is tethered by the lines AB, AC, and AD. The mass of the balloon and the
gas it contains is 80 kg. and the (upward) buoyancy force on the balloon is 1000 N.
Find: a) Draw a free body diagram of particle A.
b) Write force vectors ABF , ACF , ADF , and bF in terms of
their unknown tensions. c) Estimate the tensions in lines AB, AC, and AD. d) Set up the equilibrium equations and (if time permits)
solve for the unknown tension in each line.
Solution: