e14 - applied mechanics: statics - stanford universitybiomechanics.stanford.edu/e14/e14_s06.pdf ·...
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1mon/wed/fri, 12:50-2:05pm, 370-370
e14 - applied mechanics: statics
YOU’RE BUSY WITH YOUR 2ND HOMEWORK.
2syllabus
e14 - applied mechanics: statics
second homework
due first midterm:takehome
3homework #02
e14 - applied mechanics: statics
4homework #02
e14 - applied mechanics: statics
textbook.russell c. hibbelerprentice hall, 12th editionengineering mechanics staticsread chapters 3 and 4for homework #2
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63. equilibrium of a particle
• to introduce the concept ofthe free-body diagram for aparticle• to show how to solveparticle equilibrium problemsusing the equations ofequilibrium• when cables are used forhoisting loads, the must beselected so that they do notfail. today, we will show howto calculate cable forces forsuch cases
what we‘ve done so far…
73.1 equilibrium condition of a particle
newton‘s three laws of motion
• first law equilibrium if ∑F = 0 then v = const.
FAB
FBA
• second law accelerated motion F = m · a
• third law actio = reactio FAB = - FBA
= 0
83.2 free body diagram
procedure for drawing a FBD
I. isolate the particle ofinterest - easy ;-)here shown for particle A
II. show all forces - tricky!3 cables, 3 tension forcesassume directions
III. label each force - easy ;-)
93.3 coplanar force systems
conceptual problem 3-1show that the longer the cables,the less the forces in each cable.
FAB FAC
WFAB FAC
W
2!
xy
for longer cables, the angle !becomes smaller, cos! becomesbigger, and FAB and FAC becomesmaller.
W
FAB
FAC
W
FAB
FAC
! !
104. force system resultants
• to discuss the concept of amoment of a force• to calculate the moment ofa force in 2d and 3d using thescalar formulation• to discuss the cross productas a tool to calculate moments• to calculate the moment ofa force in 2d and 3d using thevector formulation
today‘s objectives
114.1 moment - scalar formulation
engineering intuition
largest moment smaller moment no moment
M0 = F · d [M] = N!m = lb!ft
O … fixed pointF … forced … moment arm
124.1 moment - scalar formulation
example 4.1determine the moment M0 of the force F about point O
use positive M0 !+
134.1 moment - scalar formulation
example 4.2
144.2 cross product
right-handed system
C = A ! B = A · B · sin! uC
C = A ! B = det Ay By yAx Bx x
Az Bz z
C = Az Bx - Ax Bz
Ay Bz - Az By
Ax By - Ay Bx
• C is a vector• C is orthogonal to A and B• C is the area enclosed by A and B, i.e., A · B · sin!
+
154.2 cross product
right-handed system
y
z
… if your thumb is the x axis…
… and your middle finger is the z axis…
x
… then your index finger is…
164.2 cross product
right-handed system
y
z
x
… pointing right at your abs …
174.3 moment - vector formulation
right-handed system
MO = r ! F = r · F · sin! uM
MO = r ! F = det ry Fy yrx Fx x
rz Fz z
MO = rz Fx - rx Fz
ry Fz - rz Fy
rx Fy - ry Fx
• MO is a vector• MO is orthogonal to r and F• MO is the area enclosed by r and F, i.e., r · F · sin!
+
+
184.4 principle of moments
example 4.5
determine the moment M0 of the force F about point O
use two different approaches and compare the results!
+
194.4 principle of moments
example 4.5
determine the moment M0 of the force F about point O+
204.4 principle of moments
example 4.5
determine the moment M0 of the force F about point O+