mekanika teknik mektek_polije
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MEKANIKA TEKNIK
OLEH:
AHMAD ROBIUL AWAL UDIN, ST., MT
TEKNIK OTOMOTIF POLITEKNIK NEGERI JEMBER
SEMESTER III, 2013/2014
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Mechanics
Rigid Bodies
(Things that do not change shape)
Deformable Bodies
(Things that do change shape)Fluids
Statics Dynamics Incompressible Compressible
Apa itu Mekanika?
Cabang ilmu fisika yang berbicara tentang
keadaan diam atau geraknya benda-benda
yang mengalami kerja atau aksi gaya
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Bagaimana evaluasinya ?
Tugas : 15 %
Pemb. Alat Peraga + absensi : 25 %
UTS : 30 % UAS : 30 %
Tidak mento ler irsegala ben tuk kecurangan
Tap i tetap bo lehcross check
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KONSEP DASAR MEKANIKA TEKNIK
Partikel
Suatu jumlah benda yang sangat kecil (benda yang ukurannya mendekati nol)
sehingga dapat dianalisa sebagai sebuah titik yang memiliki massa. Benda tegar / kaku
Gabungan dari jumlah besar partikel yang membentuk suatu struktur tetap.
Massa
Kelembaman benda yang merupakan tahanan terhadap perubahan gerak.
Gaya
Suatu yang menjadi sebab perubahan dalam keadaan diam atau keadaan bergerak
terhadap benda
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Apa pentingnya mekanika teknik (statik)
/ keseimbangan ?
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Apa perbedaan Partikel dan Benda
Tegar/Kaku?
Partikel:
Mempunyai suatu
massa namun
ukurannya dapatdiabaikan, sehingga
geometri benda tidak
akan terlibat dalam
analisis masalah
Benda Tegar/Kaku:
Kombinasi sejumlah
partikel yang mana
semua partikelberada pada suatu
jarak tetap terhadap
satu dengan yang lain
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Contoh Partikel
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Contoh Benda Tegar
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Review Sistem Satuan
Four fundamental physical quantities. Length, Time, Mass, Force.
We will work with two unit systems in statics: SI & US Customary.
Bagaimana konversi dari SI ke US atau sebaliknya ?
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Hukum Newton
1.Hukum Pertama: setiap benda akan memiliki kecepatan yang konstan kecuali
ada gaya yang resultannya tidak nol bekerja pada benda tersebut. Berarti jika
resultan gaya nol, maka pusat massa dari suatu benda tetap diam, atau bergerak
dengan kecepatan konstan (tidak mengalami percepatan).
2.Hukum Kedua: sebuah benda dengan massa M mengalami gaya resultan
sebesar F akan mengalami percepatan (a) yang arahnya sama dengan arah
gaya, dan besarnya berbanding lurus terhadap F dan berbanding terbalik
terhadap M. atau F=Ma. Bisa juga diartikan resultan gaya yang bekerja pada
suatu benda sama dengan turunan dari momentum linear benda tersebut
terhadap waktu.
3.Hukum Ketiga: gaya aksi dan reaksi dari dua benda memiliki besar yang sama,dengan arah terbalik, dan segaris. Artinya jika ada benda A yang memberi gaya
sebesar F pada benda B, maka benda B akan memberi gaya sebesarF kepada
benda A. F danF memiliki besar yang sama namun arahnya berbeda. Hukum ini
juga terkenal sebagai hukum aksi-reaksi, dengan F disebut sebagai aksi dan F
adalah reaksinya.
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Apa yang harus dilakukan supaya
Mekanika Teknik menjadi mudah ?
Banyak dan ser ing menyelesaikan soal-soal
Prosedur mengerjakan soal:
1. Baca soal dengan cermat2. Buat free body diagram dan tabulasikan data soal
3. Tuliskan prinsip dasar / persamaan yang relevan dengan
soal
4. Selesaikan persamaan sepraktis mungkin sehingga didapathasil yang signifikan dan jangan lupa disertai sistem satuan
5. Pelajari jawaban dengan akal sehat, masuk akal atau tidak
6. Jika ada waktu, coba pikirkan cara lain untuk menyelesaikan
soal tersebut.
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THE WHAT, WHY AND HOW OF A
FREE BODY DIAGRAM (FBD)
Free Body Diagrams are one of the most important things for
you to know how to draw and use.
What ?- It is a drawing that showsall external forces acting on the
particle.
Why ?- It helps you write the
equations of equilibrium used to
solve for the unknowns (usually
forces or angles).
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How ?
1. Imagine the particle to be isolated or cut free from its
surroundings.
2. Show all the forces that act on the particle.
Active forces: They want to move the particle.
Reactive forces: They tend to resist the motion.
3. Identify each force and show all known magnitudes
and directions. Show all unknown magnitudes and /
or directions as variables .
FBD at A
Note : Engine mass = 250 Kg
A
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PENJUMLAHAN VEKTORKonsep vektor digunakan untuk besaran-besaran dalam
mekanika yang mempunyai besar dan arah. Adapun konsep
skalar digunakan untuk besaran besaran dalam fisika yangmempuyai besar saja
Vektor dapat digambarkan
dengan sepenggal garis berarah, di mana panjang penggalan
garis menyatakan besar vektor dan arah panah menyatakan arahvektor.
Gambar di bawah menggambarkan vektor AB (AB ) dengan titik A
sebagai titik tangkap vektor AB
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Fundamental Principles
The parallelogram law for the addition of forces: Two
forces acting on a particle can be replaced by a single
force, called resultant, obtained by drawing the diagonal
of the parallelogram which has sides equal to the given
forces
f1
f2
f1+f2
Parallelogram Law
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Fundamental Principles (cont)
The principle of transmissibility: A force acting at a pointof a rigid body can be replaced by a force of the the samemagnitude and same direction, but acting on at a different
point on the line of action
f1
f2
f1 and f2 are equivalent if theirmagnitudes are the same and the
object is rigid.
Principle of Transmissibility
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APPLICATION OF VECTOR
ADDITION
There are four
concurrent cable forces
acting on the bracket.How do you determine
the resultant force acting
on the bracket ?
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Penjumlahan Vektor
Trapezoid rule for vector addition
Triangle rule for vector addition
B
B
C
C
QPR
BPQQPR
cos2222
Law of cosines,
Law of sines,
P
C
QP
B
Q
A sinsinsin
Vector addition is commutative,
PQQP
Vector subtraction
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Sample Problem
The two forces act on a bolt at
A. Determine their resultant.
SOLUTION:
Trigonometric solution - use the triangle
rule for vector addition in conjunction
with the law of cosines and law of sines
to find the resultant.
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Sample Problem (cont) Trigonometric solution - Apply the triangle rule.
From the Law of Cosines,
155cosN60N402N60N40
cos2
22
222 BPQQPR
A
A
R
QBA
R
B
Q
A
20
04.15
N73.97
N60155sin
sinsin
sinsin
N73.97R
From the Law of Sines,
04.35
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ADDITION OF SEVERAL VECTORS
Step 3 is to find the magnitude
and angle of the resultant vector.
Step 1 is to resolve each forceinto its components
Step 2 is to add all the x
components together and add all
the y components together. Thesetwo totals become the resultant
vector.
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Example of this
process,
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You can also represent a 2-D vector with a
magnitude and angle.
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EXAMPLE
Given: Three concurrent forces
acting on a bracket.Find: The magnitude and
angle of the resultant
force.
Plan:
a) Resolve the forces in their x-y components.
b) Add the respective components to get the resultant vector.
c) Find magnitude and angle from the resultant components.
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EXAMPLE (continued)
F1= { 15 sin 40 i+ 15 cos 40j} kN
= { 9.642 i+ 11.49j} kN
F2= { -(12/13)26 i+ (5/13)26j} kN
= { -24 i+ 10j} kN
F3= { 36 cos 30 i36 sin 30j} kN
= { 31.18 i18j} kN
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EXAMPLE (continued)
Summing up all the iandjcomponents respectively, we get,
FR= { (9.64224 + 31.18) i+ (11.49 + 1018)j} kN
= { 16.82 i+ 3.49j} kN
x
y
FRFR= ((16.82)2 + (3.49)2)1/2 = 17.2 kN
= tan-1(3.49/16.82) = 11.7
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Sample Problem
Four forces act on boltA as shown.Determine the resultant of the force
on the bolt.
SOLUTION:
Resolve each force into rectangular
components.
Calculate the magnitude and direction
of the resultant.
Determine the components of the
resultant by adding the corresponding
force components.
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Sample Problem (cont)SOLUTION:
Resolve each force into rectangular components.
1.4N1199
N314tan
.
.
R
R
x
y
Calculate the magnitude and direction.
N6.199sin
N3.14
R
1.4
Determine the components of the resultant by
adding the corresponding force components.
1.199xR 3.14yR
9.256.96100
0.1100110
2.754.2780
0.759.129150
4
3
2
1
F
F
F
F
compycompxmagforce
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READING QUIZ
1. The subject of mechanics deals with what happens to a body
when ______ is / are applied to it.
A) magnetic field B) heat C) forces
D) neutrons E) lasers
2. ________________ still remains the basis of most of todays
engineering sciences.
A) Newtonian Mechanics B) Relativistic Mechanics
C) Euclidean Mechanics C) Greek Mechanics
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READING QUIZ
3. Which one of the following is a scalar quantity?
A) Force B) Position C) Mass D) Velocity
4. For vector addition you have to use ______ law.
A) Newtons Second
B) the arithmetic
C) Pascals
D) the parallelogram
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CONCEPT QUIZ
5. Can you resolve a 2-D vector along two directions, whichare not at 90 to each other?
A) Yes, but not uniquely.
B) No.
C) Yes, uniquely.
6. Can you resolve a 2-D vector along three directions (sayat 0, 60, and 120)?
A) Yes, but not uniquely.B) No.
C) Yes, uniquely.
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ATTENTION QUIZ
7. Resolve Falong x and y axes and write it in
vector form. F= { ___________ } N
A) 80 cos (30) i - 80 sin (30)j
B) 80 sin (30) i + 80 cos (30)j
C) 80 sin (30) i - 80 cos (30)j
D) 80 cos (30) i+ 80 sin (30)j
8. Determine the magnitude of the resultant (F1+ F2)
force in N when F1= { 10 i+ 20j} N and F2 =
{ 20 i+ 20j} N .
A) 30 N B) 40 N C) 50 N
D) 60 N E) 70 N
30
xy
F = 80 N
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