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SNMPTN 2012 Matematika Doc. Name: SNMPTN2012MATDAS999 Version : 2013-04 halaman 1 01. Jika a dan b adalah bilangan bulat positif yang memenuhi ab = 220 - 219, maka nilai a+b adalah …. (A) 3 (B) 7 (C) 19 (D) 21 (E) 23 02. Jika 4log3 = k , maka 2log27 adalah … (A) k 6 (B) (C) (D) (E) k 6k 6 k6 k 03. Jika p+1 dan p-1 adalah akar-akar persamaan x2 - 4x + a = 0, maka nilai a adalah …. (A) 0 (B) 1 (C) 2 (D) 3 (E) 4 04. Jika f adalah fungsi kuadrat yang grafiknya melalui titik (1,0), (4,0), dan (0,-4), maka nilai f(7) adalah …. (A) -16 (B) -17 (C) -18 (D) -19 (E) -20 Kunci dan pembahasan soal ini bisa dilihat di www.zenius.net dengan memasukkan kode 2429 ke menu search. Copyright © 2012 Zenius Education SNMPTN 2012 Matematika, Kode Soal doc. Name: SNMPTN2011MATDAS999 version : 2013-04 | halaman 2 05. Semua nilai x yang memenuhi (x + 3)(x - 1) ≥ (x - 1) adalah (A) 1 ≤ x ≤ 3 (B) x ≤ -2 atau x ≥ 1 (C) -3 ≤ x ≤ -1 (D) -2 ≥ x atau x ≥ 3 (E) -1 ≥ x atau x ≥ 3 06. Jika 2x - z = 2, x + 2y = 4, dan y + z = 1, maka nilai 3x + 4y + z adalah …. (A) 4 (B) 5 (C) 6 (D) 7 (E) 8 07. Jika diagram batang di bawah ini memperlihatkan frekuensi kumulatif hasil tes matematika siswa kelas XII, maka persentase siswa yang memperoleh nilai 8 adalah…. (A) (B) (C) (D) (E) 12 % 15 % 20 % 22 % 80 % Kunci dan pembahasan soal ini bisa dilihat di www.zenius.net dengan memasukkan kode 2429 ke menu search. Copyright © 2012 Zenius Education SNMPTN 2012 Matematika, Kode Soal doc. Name: SNMPTN2011MATDAS999 version : 2013-04 | halaman 3 08. Ani telah mengikuti tes matematika sebanyak n kali. Pada tes berikutnya ai memperoleh nilai 83 sehingga nilai rata-rata Ani aalah 80, tetapi jika nilai tes tersebut adalah 67, maka rata-ratanya adalah 76. Nilai n adalah …. (A) 2 (B) 3 (C) 4 (D) 5 (E) 6 09. Nilai maksimum fungsi objektif (tujuan) f(x,y) = 3x + 2y dengan kendala x + 2y ≤ 12, x ≥ 2, dan y ≥ 1 adalah …. (A) 16 (B) 18 (C) 32 (D) 36 (E) 38 10. Jika dan , maka determinan matriks AB - C adalah …. (A) -5 (B) -4 (C) 5 (D) 6 (E) 7 11. Agar tiga bilangan a + 2, a - 3, a - 4 merupakan barisan aritmatika, maka suku ke dua harus ditambah dengan …. (A) -3 (B) -2 (C) -1 (D) 1 (E) 2 Kunci dan pembahasan soal ini bisa dilihat di www.zenius.net dengan memasukkan kode 2429 ke menu search. Copyright © 2012 Zenius Education SNMPTN 2012 Matematika, Kode Soal doc. Name: SNMPTN2011MATDAS999 version : 2013-04 | halaman 4 12. Jika suku pertama barisan aritmatika adalah -2 dengan beda 3, Sn adalah jumlah n suku pertama deret aritmatika tersebut, dan Sn+2 - Sn = 65, maka nilai n adalah …. (A) 11 (B) 12 (C) 13 (D) 14 (E) 15 13. Jika suatu persegi dengan sisi satu satuan dibagi menjadi 5 persegi panjang dengan luas yang sama seperti ditunjukkan pada gambar di bawah ini, maka panjang ruas garis AB adalah … (A) 3 5 (B) 2 3 (C) 2 5 (D) (E) 1 5 1 5 14. Di suatu kandang tedapat 40 ekor ayam, 15 ekor diantaranya jantan. Di antara ayam jantan tersebut, 7 ekor berwarna putih. Jika banyak ayam berwarna putih adalah 22 ekor, maka banyak ayam betina yang tidak berwarna putih adalah … (A) 5 (B) 7 (C) 8 (D) 10 (E) 15 Kunci dan pembahasan soal ini bisa dilihat di www.zenius.net dengan memasukkan kode 2429 ke menu search. Copyright © 2012 Zenius Education SNMPTN 2012 Matematika, Kode Soal doc. Name: SNMPTN2011MATDAS999 version : 2013-04 | halaman 5 15. Jika f(x) = ax + 3, a ≠ 0 dan f-1 (f-1(9)) = 3, maka nilai a2 + a + 1 adalah … (A) 11 (B) 9 (C) 7 (D) 5 (E) 3 Kunci dan pembahasan soal ini bisa dilihat di www.zenius.net dengan memasukkan kode 2429 ke menu search. Copyright © 2012 Zenius Education
1340cm3 in-line 4-cylinder fuel-injected, liquid-cooled DOHC engine built to deliver a broad wave of torque for effortless acceleration. Suzuki Clutch Assist System (SCAS) serves as back-torque-limiting system for smooth downshifts and also contributes to a light clutch pull. U-shaped cutouts in the cylinder-bore sides allow air below descending pistons to escape to adjacent cylinders to reduce internal pumping pressure and mechanical power losses. Advanced aerodynamics offering superb wind protection both for normal and completely tucked-in seating positions. Lightweight titanium valves allow use of light valve springs and high lift while maintaining accurate valve control. Iridium spark plugs produce more complete combustion. Curved radiator with a compact, dense-core design and engine-management-computer-controlled two ring-type electric fans mounted on the rear of the radiator, increasing the control accuracy and keeping engine temperature stable. Suzuki Dual Throttle Valve (SDTV) fuel injection results in improved power delivery and a more linear response. This system uses engine-computer-operated secondary valves to maintain optimum intake-air velocity for maximum combustion efﬁciency. Two 12-hole ﬁne-spray injectors on each throttle body improve fuel atomization for better combustion efﬁciency and while reducing fuel consumption. Suzuki Drive Mode Selector (S-DMS) enables the rider to choose from three different engine power characteristics according to personal preference. Speciﬁcations, appearance, colors (including body color), equipment, materials and other aspects of the “SUZUKI” products shown in this catalogue are subject to change by Suzuki at any time without notice, and they may vary depending on local conditions or requirements. Some models are not available in some regions. Each model may be discontinued without notice. Please inquire at your local dealer for details of any such changes. Always wear a helmet, eye protection and protective clothing. Enjoy riding safely. Read your Owner's Manual carefully. Never ride under the inﬂuence of alcohol or other drugs. PRINTED IN JAPAN Hayabusa 1300 (GSX1300R) Leaﬂet 99999-A0021-121 SEP.'11 300 Takatsuka-cho, Minami-ku, Hamamatsu City, JAPAN 432-8611 Electronic ignition (Transistorized) 21.0 L (5.5 US gal) Colors Functional Instrument cluster Inverted cartridge front forks featuring Diamond-Like Coating (DLC) surface treatment to reduce stiction and improve reaction to small surface irregularities. The front forks and the single rear shock absorber both have fully adjustable spring preload, compression and rebound damping. 310mm (12.2-in) dual-ﬂoating-disc front brakes with efﬁcient, race-proven aluminum-piston, radial-mount brake calipers, and 260mm (10.2-in) single-disc rear brake with single-piston brake caliper. Four analog gauges including step-motor-driven tachometer and speedometer. Round LCD panel includes clock, gear position indicator, S-DMS map indicator, odometer and dual trip meters. Engine-rpm indicator, programmable to blink or stay on between 4,000 and 11,500 rpm.
MSRP: $13,999 The Suzuki Hayabusa is a machine so dominant, that it created an entirely new category of motorcycle in the industry – Ultimate Sport. With performance credentials that have established it as the most exciting sportbike on the planet, it's designed for serious sport riders who will settle for nothing less than the best. If that's you, and if you choose to ride the Hayabusa, you'll be rewarded with a riding experience you'll never forget. Its combination of unsurpassed power, crisp handling and superb aerodynamics creates the ultimate sport bike. For 2012, the Hayabusa is available with new graphics and colors - Glass Sparkle Black, Pearl Glacier White and limited edition Candy Sonoma Red. TOP 10 FEATURES The Hayabusa is equipped with a 1340cc, in-line, DOHC liquid-cooled engine with 16-valves, and Twin Swirl Combustion Chambers (TSCC) for eﬃcient, powerful acceleration and top end performance. The Hayabusa’s engine is fed via Suzuki’s Suzuki Dual Throttle Valve (SDTV) fuel injection system uses engine-computer-operated secondary valves to maintain optimum intake-air velocity for maximum combustion eﬃciency. Two 12-hole ﬁne-spray injectors on each throttle body improve fuel atomization for better combustion eﬃciency and while reducing fuel consumption. Lightweight aluminum alloy pistons with a compression ratio of 12.5:1 are used for maximum performance in all conditions with stunning acceleration and top end power. Hard, smooth chrome-nitride Physical Vapor Deposition (PVD) coating on the upper compression and oil control rings on each piston reduces friction while improving cylinder sealing. Lightweight titanium valves allow the use of light valve springs and high lift while maintaining accurate valve control. Iridium spark plugs are used for high combustion eﬃciency and consistent performance. The Hayabusa comes with an constant mesh 6-speed transmission, with close gear ratios for outstanding performance. Oil spray to the 4th, 5th and 6th gears reduces wear and mechanical noise during highway cruising. Suzuki Clutch Assist System (SCAS) serves as a back-torque-limiting system for smooth downshifts and also contributes to a light clutch pull. A lightweight and rigid twin-spar aluminum frame minimizes weight while maintaining high torsional strength, and is designed to allow a compact riding position for exceptional handling and control on the road. Rear subframe is made of rectangular steel tubing for suﬃcient weight carrying capacity. Lightweight Showa Big Piston front Fork (BPF) features a 37.6mm upper piston riding inside the 41mm fork tube. This endurance-race-proven design, along with a lightweight fully adjustable Showa rear shock, delivers more eﬀective, linear damping performance, resulting in better feedback to the rider for unmatched handling. A bridged aluminum alloy swingarm features a cross-sectional shape for increased rigidity, which improves rear tire grip and increases engine output. The Hayabusa’s fully adjustable rear shock absorber has a 43mm piston and 14mm rod diameter. Radial-mount Tokico front brake calipers oﬀer maximum braking performance using dual 310mm front brake rotors, resulting in reduced unsprung weight and improved handling. A lightweight single piston rear brake caliper works in conjunction with a 260mm rear brake disc. S-DMS (Suzuki Drive Mode Selector) allows the rider to choose from three diﬀerent engine settings, depending on riding conditions or rider preferences. For example, the rider can choose one map for tight, twisty roads and another for high-speed cruising.
The Economical CNC Grinding Machine The economical CNC grinding machine The affordable tool grinding package The ANCA FastGrind is an entry level CNC tool grinder and a popular machine in the ANCA range. This machine offers all of the benefits that ANCA customers have enjoyed for many years at an extremely affordable price. The FastGrind is a versatile and flexible machine and is suited to a wide variety of industries and applications. It is popular with regrinders and provides opportunities for companies to reduce costs by bringing regrinding in-house. It is also ideally suited to companies looking for reduced risk in making the transition into CNC grinding technology. The FastGrind has all of the essential elements the industry demands for cost-effective tool grinding, including:Quick and easy set-up Superior tool accuracy High quality surface finish Flexibility to grind a large variety of tool types Machine reliability and accuracy Direct-drive technology The double-ended wheel spindle is based on a directdrive, bi-directional motor design capable of 10,000 rpm. With a HSK40F taper, constant power of 3.7 kW (5.0 HP) and peak power of 8.0 kW (10.0 HP), it offers enough power for any resharpening task. There are no belts, pulleys or gears, resulting in superior surface finish on the ground tool and higher machine reliability. All linear and rotary machine axes, including workhead, use direct-drive technology giving greater positional accuracy. the affordable choice Flexibility and speed The FastGrind is both small and compact, yet has a large working envelope making it suitable for a wide range of tool types, geometries and shapes. The FastGrind also has both the flexibility and speed to tackle a wide range of different high-precision cutting and drilling tools in one set-up. For resharpening, the standard probe system digitises the features and geometry of the tool, ensuring accurate and precise grinding.
Contents Unit 1 Reasoning and Proof Unit 2 nequalities and Linear I Programming Unit 3 Similarity and Congruence Unit 4 Samples and Variation Unit 5 olynomial and Rational P Functions Unit 6 ircles and Circular C Functions Unit 7 Recursion and Iteration Unit 8 nverse Functions I Visit us at www.glencoe.com ISBN: 978-0-07-877261-0 MHID: 0-07-877261-3 www.glencoe.com Algebra and Functions Geometry and Trigonometry Statistics and Probability Discrete Mathematics 2nd Edition James T. Fey • Christian R. Hirsch • Eric W. Hart Harold L. Schoen • Ann E. Watkins with Beth E. Ritsema • Rebecca K. Walker • Sabrina Keller Robin Marcus • Arthur F. Coxford • Gail Burrill i_TP_FM_877261.indd This material is based upon work supported, in part, by the National Science Foundation under grant no. ESI 0137718. Opinions expressed are those of the authors and not necessarily those of the Foundation. Copyright © 2009 by the McGraw-Hill Companies, Inc. All rights reserved. Except as permitted under the United States Copyright Act, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without prior permission of the publisher. Send all inquiries to: Glencoe/McGraw-Hill 8787 Orion Place Columbus, OH 43240-4027 ISBN: 978-0-07-877261-0 (Student Edition) MHID: 0-07-877261-3 (Student Edition) Core-Plus Mathematics Contemporary Mathematics in Context Course 3 Student Edition Printed in the United States of America. 5 6 7 8 9 10 WDQ 17 16 15 14 13 12 11 Core-Plus Mathematics 2 Development Team Senior Curriculum Developers James T. Fey Advisory Board Diane Briars Collaborating Teachers Mary Jo Messenger University of Maryland Pittsburgh Public Schools Christian R. Hirsch (Director) Jeremy Kilpatrick Howard County Public Schools, Maryland Western Michigan University University of Georgia Eric W. Hart Robert E. Megginson Maharishi University of Management University of Michigan Harold L. Schoen University of Cambridge Jacqueline Stewart Okemos, Michigan Graduate Assistants Allison BrckaLorenz Christopher Hlas Kenneth Ruthven University of Iowa David A. Smith Ann E. Watkins University of Iowa Duke University California State University, Northridge Contributing Curriculum Developers Beth E. Ritsema Western Michigan University Mathematical Consultants Deborah Hughes-Hallett University of Arizona / Harvard University Stephen B. Maurer University of Maryland Swarthmore College Rebecca K. Walker William McCallum Grand Valley State University University of Arizona Sabrina Keller Doris Schattschneider Michigan State University Moravian College Robin Marcus Richard Scheaffer University of Maryland Gail Burrill Michigan State University (First edition only) Principal Evaluator Steven W. Ziebarth Dana Cox Dana Grosser Anna Kruizenga Nicole Lanie Diane Moore Western Michigan University University of Florida Arthur F. Coxford (deceased) University of Michigan Madeline Ahearn Geoffrey Birky Kyle Cochran Michael Conklin Brandon Cunningham Tim Fukawa-Connelly Evaluation Consultant Norman L. Webb University of Wisconsin-Madison Technical Coordinator James Laser Undergraduate Assistants Cassie Durgin University of Maryland Rachael Kaluzny Jessica Tucker Western Michigan University Western Michigan University Western Michigan University
Engineering Mechanics major – Course Dependency Map 550.291 Linear Algebra / Differential Equations (or 110.201 and 110.302) Mathematics elective – 4 credits 560.348 or 550.310 Statistics 110.202 Calculus III or 110.211 Honors Multivariable Calculus 110.109 Calculus II Humanities / Social Science elective 6* * Humanities/Social Science Electives - total 18 credits required, some electives may carry more than 3 credits, so the electives might be achieved in less than six courses. Humanities / Social Science elective 5 Humanities / Social Science elective 4 * Technical Electives - total 18 credits required, some electives may carry more than 3 credits, so the elective requirements might be achieved in less than six courses. Technical Elective 5 - 3 credits Humanities / Social Science elective 3 Basic Science, Mathematics, and Humanities / Social Science in other departments: some courses have science and math prerequisites not mapped here. See isis.jhu.edu/classes for info. Technical Elective 4 – 3 credits Technical Elective 3 – 3 credits Humanities / Social Science elective 2 500.200 Computing for Engineers or other intro to programming options Humanities / Social Science elective 1 110.108 Calculus I 510.101 Intro to Materials Chemistry or 030.101 Intro to Chemistry 530.101/102, 530.105/106 Freshman Experiences I and Jaafar's DARPA Labs or other intro to engineering options BEGIN HERE Technical Elective 6* - 3 credits 171.102 / 173.112 Physics II and Lab 530.202 Dynamics 530.103/104 Intro to Mechanics I / II or 171.101 / 173.111 Physics I and Lab Key Required Course 530.201 Statics of Mechanics and Materials Tech Elective Required for next course: EM/ES Electives Concurrent: Technical Elective 2 – 3 credits 530.231 / 232 Thermodynamics and Lab 530.327 / 329 Intro to Fluid Mechanics and Lab 530.215 / 216 Mechanics Based Design and Lab or 530.405 Mechanics of Solids H/S Electives Basic Science and Math Suggested for next course: Technical Elective 1 – 3 credits 530.403/404 Senior Design I/II Engineering Mechanics elective 2 Engineering Mechanics elective 1 Engineering Science – solids / fluids elective Engineering Science – dynamics/ materials elective Engineering Science – fluids elective Engineering Science – solids elective ...
Equation Sheet for Engineering Mechanics 12—Dynamics Note: vectors are indicated by boldface type. Miscellaneous If ax2 + bx + c = 0, then x = −b ± √ b2 − 4ac 2a. Rectilinear (1-D) Motion Position: s(t); Velocity: v = s = ds/dt; Acceleration: a = s = dv/dt = d2 s/dt2 = vdv/dx. For ˙ ¨ constant acceleration ac : 2 v 2 = v0 + 2ac (s − s0 ) s = s0 + v0 t + 1 ac t2 2 v = v0 + ac t 2D Motions—Cartesian Coordinates Position: r = xˆ + yˆ Velocity: v = dr/dt = xˆ + yˆ Acceleration: a = dv/dt = d2 r/dt2 = xˆ + yˆ ı ; ˙ ı ˙ ; ¨ı ¨ 2D Motions—Normal-Tangential (Path) Coordinates ˙ v = ρθ v = vˆt e a = atˆt + anˆn e e ˙ an = ρθ2 = v 2 /ρ at = v ˙ 2D Motions—Polar Coordinates r = rˆr e v = vr ˆr + vθ ˆθ e e 2 ˙ ar = r − rθ ¨ a = ar ˆr + aθ ˆθ e e ˙ vθ = r θ vr = r ˙ ¨ aθ = rθ + 2rθ ˙˙ Newton’s Second Law F = ma; Fx = max ; Fy = may ; Fn = man ; Ft = mat ; Fr = mar ; Fθ = maθ Work-Energy Principle U1–2 = L F · dr Vg = W y T = 1 mv 2 2 T1 + U1–2 = T2 Ve = 1 kδ 2 2 T1 + V1 + (U1–2 )nc = T2 + V2 Linear Impulse-Momentum Principle p = mv F= dp dt t2 L1–2 = t1 F dt = mv2 − mv1 Impact of Smooth Particles For a coeﬃcient of restitution e, in the direction along to the line of impact (LOI) or n direction: vseparate vB − vA2 e= = 2 vapproach vA1 − vB1 Total linear momentum is conserved in the n direction: (mA vA1 + mB vB1 = mA vA2 + mB vB2 )n . Velocity of each particle is conserved perpendicular to the LOI (t direction):(vA1 = vA2 )t and (vB1 = vB2 )t . Angular Impulse-Momentum Principle ˙ hO = mr2 θ ˙ MA = hA + vA × mvG hA = rP/A × mv t2 (AA )1–2 = t1 r × F dt = t2 t1 MA dt = h2 − h1 Rigid Body Kinematics vB = vA + vB/A aB = aA + aB/A vB = vA + ω × rB/A aB = aA + α × rB/A + ω × (ω × rB/A ) vB = vA + Ω × rB/A + (vB/A )xyz where xyz refers to the rotating frame (B) ˙ aB = aA + Ω × rB/A + Ω × (Ω × rB/A ) + (aB/A )xyz + 2Ω × (vB/A )xyz Moments of Inertia (IG )disk = 1 mr2 2 (IG )rod = 2 1 12 ml (IG )plate = 2 1 12 m(a + b2 ) (IG )sphere = 2 mr2 5 2 Parallel Axis Theorem: IA = IG + md2 ; Radius of Gyration: IA = mkA Angular Momentum and Equations of Motion for a Rigid Body Angular Momentum hA = IG ω + rG/A × mvG hA = IA ω + rG/A × mvA Equations of Motion MG = IG α and for a ﬁxed point O: For the mass center G: MA = IG α + rG/A × maG MO = IO α. For an arbitrary point A: MA = IA α + rG/A × maA (MA )FBD = (MA )MAD Work-Energy for a Rigid Body The work-energy principle is the same as that for particles. The kinetic energy of a rigid body is: 2 y ¯ T = 1 mvA + 1 IA ω 2 − mω(¯vAx − xvAy ) 2 2 Vibrations Undamped free vibration: Equation of motion: x + p2 x = 0, p = k/m, x(t) = x0 cos pt + ¨ (v0 /p) sin pt. Period: τ = 2π/p. Frequency: f = 1/τ = p/2π. Damped free vibration: Equation of motion: m¨ + cx + kx = 0, ζ = c/ccr = c/(2mp), x ˙ √ √ 2 2 x(t) = A1 e(−ζ+ ζ −1)pt + A2 e(−ζ− ζ −1)pt , and for ζ < 1: x(t) = Ee−ζpt sin(ωd t + α), where E and α are constants and ωd = p 1 − ζ 2 . Harmonic Forcing: Equation of motion: x + p2 x = P0 sin ωt with solution: ¨ P0 /k x(t) = E sin(pt + α) + sin ωt 1 − (ω/p)2 Damped Forced Vibration: Equation of motion: m¨ + cx + kx = P0 sin ωt with solution: x ˙ x(t) = X sin(ωt + φ), where P0 /k X= [1 − (ω/p)2 ]2 + (2ζω/p)2 2ζω/p φ = tan−1 1 − (ω/p)2
Engineering Mechanics for Microsystems Design Structural integrity is a primary requirement for any device or engineering system regardless of its size. The theories and principles of engineering mechanics are used to assess: (1) Induced stresses in the microstructure by the intended loading, and (2) Associated strains ( or deformations) for the dimensional stability, and the deformation affecting the desired performance by this microstructural component. Accurate assessment of stresses and strains are critical in microsystems design not only for the above two specific purposes, but also is required in the design for signal transduction, as many signals generated by sensors are related to the stresses and strains Induced by the input signals. Static bending of thin plates Mechanical vibration analysis Thermomechanical analysis Fracture mechanics analysis Thin film mechanics Overview of finite element analysis Mechanical Design of Microstructures Theoretical Bases: ● Linear theory of elasticity for stress analysis ● Newton’s law for dynamic and vibration analysis ● Fourier law for heat conduction analysis ● Fick’s law for diffusion analysis ● Navier-Stokes equations for fluid dynamics analysis Mathematical models derived from these physical laws are valid for microcomponents Mechanical Design of Microsystems Common Geometry of MEMS Components Beams: Microrelays, gripping arms in a micro tong, beam spring in micro accelerometers Plates: ● Diaphragms in pressure sensors, plate-spring in microaccelerometers, etc ● Bending induced deformation generates signals for sensors and relays using beams and plates Tubes: Capillary tubes in microfluidic network systems with electro-kinetic pumping (e.g. electro-osmosis and electrophoresis) Channels: Channels of square, rectangular, trapezoidal cross-sections in microfluidic network. • Component geometry unique to MEMS and microsystems: Multi-layers with thin films of dissimilar materials Recommended Units (SI) and Common Conversion Between SI and Imperial Units in Computation Units of physical quantities: …
System of Coplanar forces Resultant of Concurrent forces, Parallel forces, Non-concurrent Non-parallel system of forces, Moment of force about a point, Couples, Varignon’s Theorem. Distributed Forces in plane (04 marks) Equilibrium of system of coplanar forces Condition of equilibrium for concurrent forces, parallel forces and Nonconcurrent Non-parallel general forces and Couples (04 marks) Friction Introduction to Laws of friction, Cone of friction, Equilibrium of bodies on inclined plane, Application to problems involving wedges, ladders. (04 marks) Kinematics of Particle Velocity & acceleration in terms of rectangular co-ordinate system, Rectilinear motion, Motion along plane curved path, Tangential & Normal component of acceleration, Motion curves (a-t, v-t, s-t curves), Projectile motion, Relative velocities (04 marks) Kinetics of a Particle: Force and Acceleration D’Alembert’s Principle, Equations of dynamic equilibrium, Newton’s second law of motion (04 marks) System of Coplanar forces Resultant of Concurrent forces, Parallel forces, Non-concurrent Non-parallel system of forces, Moment of force about a point, Couples, Varignon’s Theorem. Distributed Forces in plane (06 marks) Equilibrium of system of coplanar forces Condition of equilibrium for concurrent forces, parallel forces and Nonconcurrent Non-parallel general forces and Couples (08 marks) Kinetics of a Particle: Impulse and Momentum Principle of Linear Impulse and Momentum. Law of Conservation of momentum. Impact and collision (06 marks) Center of Gravity and Centroid for plane Laminas (08 marks) Forces in space Resultant of Non-coplanar force systems: Resultant of Concurrent force system, Parallel force system and Non-concurrent non-parallel force system Resultant of Concurrent force system, Parallel force system and Non-concurrent non-parallel force system Equilibrium of Non-coplanar force systems: Equilibrium of Concurrent force system, Parallel force system and Non-concurrent nonparallel force system (06 marks) ...