e14 - applied mechanics: staticsbiomechanics.stanford.edu/e14/e14_s04.pdf · e14 - applied...
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1mon/wed/fri, 12:50-2:05pm, 370-370
e14 - applied mechanics: staticswhat e14 students ask vs. what they are really asking
2syllabus
e14 - applied mechanics: statics
first homework
due
3homework #01
e14 - applied mechanics: statics
4homework #01
e14 - applied mechanics: statics
textbook.russell c. hibbelerprentice hall, 12th editionengineering mechanics staticsread chapters 1 and 2for homework #1
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5homework #01
e14 - applied mechanics: statics
6homework #01
force resultant in cartesian coordinates• we can easily add and subtractforces using a Cartesian coordinatesystem
• we can determine the magnitudeof a force using Pythagoras (2d)
• we can determine the direction of a force using trigonometry
FRx = !FxFRy = !Fy
FRxFRy
FR =
FR = " [ FRx2 + FRy2 ]
! = tan-1[ FRy / FRx ]
Fx = |F| cos !Fy = |F| sin !
FxFy
F =
(1)(2)
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• we can easily add and subtractforces using a Cartesian coordinatesystem
• we can determine the magnitudeof a force using Pythagoras (3d)
• we can determine the direction ofa force using trigonometry
homework #01
FRx = !FxFRy = !FyFRz = !Fz
FxFyFz
F =
FR = " [ FRx2 + FRy2 + FRz2 ]
" = cos-1[ FRx / F ]
Fx = |F| cos "Fy = |F| cos !Fz = |F| cos " FRx
FRyFRz
FR =F
Fy y
Fz z
Fx x
force resultant in cartesian coordinates
(1)(2)(3)
cos2" +cos2! + cos2"=1
8e14 t-shirt design context
e14 - applied mechanics: statics design your own E14 statics t-shirt!• designs can only be single color.• designs can cover both front and back, but could also be single sided• everybody who uploads one or more designs into the drop box will receive 5 extra bonus points for this homework• the top three designs will receive another 5 extra bonus points• the best design will be elected as our E14 shirt• everybody in class will receive a free shirt upload your design into the drop box on coursework!
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9e14 t-shirt design context
design your own e14 t-shirt!
©maisy wieman
10e14 t-shirt design context
design your own e14 t-shirt!
©blake crowe
11e14 t-shirt design context
design your own e14 t-shirt!
@brandon skerda
12e14 t-shirt design context
design your own e14 t-shirt!
©julie mai
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13e14 t-shirt design context
e14 - applied mechanics: staticsas part of the following homework sets, we will ask you toupload photos of yourself or yourself with some of your classmates, wearing your statics t-shirts and illustrating forces.towards the end of this class, we will make a music videofrom the best photos.
• list the size of your t-shirt order, i.e., men or women, and small, medium, large, or extra large
• list your favorite song for the E14 video. it can be a “force”-related song, or just any song you like
• if you would like to be part of the E14 video team, and participate in photo selection, song selection or song composition, and video making, send us an email or talk to us for details after class
143. 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
today‘s objectives
153.1 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
163.2 free body diagram
assumptions - cables and pulleys
• cables. unless otherwise stated,we will assume that all cableshave a negligible weight andcannot stretch. they can onlysupport tension along their axis.
• pulleys. for now, we assumethat pulleys are frictionless, i.e.,the tension force of a cable thatpasses over a pulley may changeits direction but not itsmagnitude.
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173.2 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 ;-)
183.3 coplanar force systems
example 3.2determine the tension in cables BA
and BC to support the 60kg cylinder!
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