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551203 Engineering Dynamics
Semester 2/2019
November 2019 – February 2020
ส ำหรบนกศกษำหลกสตรวศวกรรมเมคคำทรอนกส
ประมวลการสอนรายวชา 551203
ภาคการศกษา 3/2561
1. รายวชา พลศำสตรวศวกรรม (ENGINEERING DYNAMICS) รหสวชำ 551203 4 (4-0-8) หนวยกต
2. ผรบผดชอบรายวชา อ.ดร.เอกรงค สขจต
3. เวลาและสถานท วนเสำร เวลำ 13.00-17.00 น. หอง B1207 อำคำรเรยนรวม 1
4. ต าราประกอบการเรยนการสอน
เอกสารประกอบการเรยนหลก Vector Mechanics for Engineers: Dynamics (10th Edition in SI Units, 2013) โดย F.B.Beer, E.R.Johnston,
P.J.Cornwell เอกสารประกอบการเรยนแนะน า เพอใชในการทบทวนเนอหาและท าโจทยเพมเตม
[1] Engineering Mechanics: Dynamics โดย J. L. Meriam และ L. G Kraige [2] Engineering Mechanics: Dynamics โดย R. C. Hibbeler
5. เนอหาโดยสงเขป รายวชาบงคบกอน: 551201 ENGINEERING STATICS
รำยวชำพลศำสตรวศวกรรม (ENGINEERING DYNAMICS) จะศกษำกำรเคลอนทของอนภำคและวตถแขงเกรงในระนำบและกำรเคลอนททวไป ทเปนคเนเมตกต (Kinematics) และคเนตกต (Kinetics) โดยอำศยกฎกำรเคลอนทของนวตน วธงำน-พลงงำน และวธอมพลส-โมเมนตม
6. แผนการสอนรายสปดาห
สปดาห / ชวโมง
หวขอการสอน (องตำมเอกสำรประกอบกำรเรยนหลก) การวดผล การประเมนผล
1 (4 ชวโมง)
Chapter 11: Kinematics of particles Rectilinear motion of particles 11.1 Introduction to dynamics 11.2 Position, velocity and acceleration 11.3 Determination of the motion of a particle 11.4 Uniform rectilinear motion 11.5 Uniformly accelerated rectilinear motion 11.6 Motion of several particles
กำรบำน ตรวจใหคะแนน
2 (4 ชวโมง)
Chapter 11: Kinematics of particles Curvilinear motion of particles 11.11 Rectangular components 11.12 Motion relative to a frame in translation 11.13 Tangential and normal components 11.14 Radial and transverse components
กำรบำน ตรวจใหคะแนน
3 (4 ชวโมง)
Chapter 12: Kinetics of particles: Newton’s second law 12.2 Newton’s second law of motion 12.4 Systems of units 12.5 Equations of motion: rectangular and normal-tangential components 12.8 Equations of motion: radial-transverse components
กำรบำน ตรวจใหคะแนน
4 (4 ชวโมง)
Chapter 13: Kinetics of particles: Energy and momentum methods Energy method 13.2 Work of force 13.3 Kinetic energy of particle: Principle of Work and energy 13.5 Power and efficiency 13.6 Potential energy
กำรบำน ตรวจใหคะแนน
5 (4 ชวโมง)
Chapter 13: Kinetics of particles: Energy and momentum methods Momentum method 13.10 Principle of impulse and momentum 13.11 Impulsive motion 13.12 Impact 13.13 Direct central impact 13.14 Oblique central impact
กำรบำน ตรวจใหคะแนน
6 (4 ชวโมง)
ทบทวนเนอหา ส าหรบสอบกลางภาค
7 สอบกลำงภำค 8
(4 ชวโมง) Chapter 15: Kinematics of rigid bodies 15.2 Translation 15.3 Rotation about a fixed axis 15.4 Equations defining the rotation of a rigid body about a fixed axis 15.5 General plane motion 15.6 Absolut and relative velocity in plane motion 15.7 Instantaneous center of rotation in plane motion
กำรบำน ตรวจใหคะแนน
สปดาห / ชวโมง
หวขอการสอน (องตำมเอกสำรประกอบกำรเรยนหลก) การวดผล การประเมนผล
9 (4 ชวโมง)
Chapter 15: Kinematics of rigid bodies 15.8 Absolute and relative acceleration in plane motion 15.10 Rate of change of a vector with respect to a rotating frame 15.11 Plane motion of a particle relative to a rotating frame
กำรบำน ตรวจใหคะแนน
10 (4 ชวโมง)
Chapter 16: Plane motion of rigid bodies: Forces and accelerations 16.2 Equations of motion for a rigid body 16.3 Angular momentum of a rigid body in plane motion 16.4 Plane motion of a rigid body: D’Alembert’s principle 16.8 Constrained plane motion
กำรบำน ตรวจใหคะแนน
11 (4 ชวโมง)
Chapter 17: Plane motion of rigid bodies: Energy and momentum methods Energy method 17.2 Principle of work and energy for a rigid body 17.3 Work of forces acting on a rigid body 17.4 Kinetic energy of a rigid body in plane motion 17.5 Systems of rigid bodies 17.6 Conservation of energy 17.7 Power
กำรบำน ตรวจใหคะแนน
12 (4 ชวโมง)
Chapter 17: Plane motion of rigid bodies: Energy and momentum methods Momentum method 17.8 Principle of impulse and momentum for the plane motion of a rigid body 17.10 Conservation of angular momentum 17.12 Eccentric impact
กำรบำน ตรวจใหคะแนน
13 สอบประจ ำภำค
7. วธการสอน 7.1 บรรยำยในหองเรยนสปดำหละ 4 ชวโมง 7.2 พำท ำแบบฝกหดในหองเรยน และใหกำรบำน 7.3 ทดสอบยอย
8. วธการวดผลและน าหนกคะแนน
8.1 คะแนนเกบระหวำงเรยน 20% - เขำเรยน และ Quiz 10% - Worksheet 10%
8.2 สอบกลำงภำค 40% 8.3 สอบปลำยภำค 40%
หมายเหต: เวลำเขำเรยนจะตอง > 80% (ขำดไมเกน 4 ครง) มฉะนนจะไมมสทธสอบปลำยภำค
9. เกณฑการประเมนผล ระดบคะแนน แตมระดบคะแนน คะแนนรวม A 4.0 80 ขนไป B+ 3.5 73-79.9 B 3.0 66-72.9 C+ 2.5 59-65.9 C 2.0 52-58.9 D+ 1.5 45-51.9 D 1.0 38-44.9 F 0.0 ต ำกวำ 38 หมำยเหต: อำจมกำรปรบชวงคะแนนตำมควำมเหมำะสม ซงจะตองพจำรณำควำมอยำก-งำยของขอสอบ
Chapter 11: Kinematics of particles
Answer t = 1.000 s, 𝓍1 = 15.00 m, a1 = -6.00 m/s2; t = 2.00 s, 𝓍 2 = 14.00 m, a2 = 6.00 m/s2
Answer (a) 𝓍1 = 102.9 mm, 𝒱1 = -35.6 mm/s, a1 = -11.40 mm/s2, (b) 𝒱max = -36.1 mm/s, amax = 72.1 mm/s2
Answer (a) 𝓍0 = 0 mm, 𝒱0 = 960 mm/s , a0 = 9220 mm/s2 .
(b) 𝓍0.3 = 14.16 mm , 𝒱0.3 = 87.9 mm/s , a0.3 = 3110 mm/s2 or 3.11 mm/s2 .
Answer t = 0.667 s, 𝓍2/3 = 0.259 m, v2/3 = -8.56 m/s.
Answer (a) 𝒱0 = 24.5 m/s2. (b) tf = 8.17 s.
Answer (a) a = -0.0525 m/s2. (b) t3 – t1 = 6.17 s.
Answer (a) 𝒱1 = 76.8 m/s. (b) ymax = 328 m.
Answer (a) t1 = 14.548 s, 𝓍A = .203 m. (b) 𝒱A = 64.3 km/h . 𝒱B = 35.1 km/h .
Answer (a) 𝒱C= 8.00 m/s . (b) 𝒱W =4.00 m/s . (c) 𝒱C/E =12.00 m/s. (d) 𝒱W/E 8.00 m/s .
Answer (a) 𝒱B = 2.00 m/s . (b) 𝒱D = 2.00 m/s . (c) 𝒱C/D = 8.00 m/s .
Answer (a) 𝒱A= 200 mm/s . (b) 𝒱C = 600 mm/s . (c) 𝒱D = 200 mm/s . (d) 𝒱C/A = 400 mm/s .
Answer (a) 𝒱L = 16.67 mm/s. (b) 𝒱B/L = 16.67 mm/s.
Answer (a) 𝒱 = 6.28 m/s 37.2º. (b) 𝓍 = 7.49 m.
Answer d = 353 m.
Answer (a) d = 330 m. (b) h = 149.9 m.
Answer 0 ≤ d ≤ 0.5173 m.
Answer 0.244 m < h < 0.386 m.
Answer (a) yC > 2.43 m (height of net) ⟹ ball clears net. (b) b = (16.01-9.00) m = 7.01 m from the net.
Answer d = 233 m.
Answer (A) 𝒱0 = 8.96 m/s. (b) 𝒱0 =8.87 m/s.
Answer 33.7 m/s < 𝒱0 < 44.3 m/s.
Answer (a) vB/A = 91.0 ft/s 47.0º. (b) rB/A = 364 ft 47.0º. (c) Distance between autos = 293 ft.
Answer ρ = 500 m.
Answer (𝒱max)AB = 97.6 km/h.
Answer (a) a = 10.20 mm/s2. (b) t = 25.2 s.
Answer (a) 𝒱B = 83.8 km/h. (b) a = 3.71 m/s2
Answer (a) vB/A = 189.5 km/h 54.0º. (b) aB/A 21.8 m/s2 5.3º
Answer (a) vB/A = 501 km/h 68.9º. (b) aB/A = 82.2 m/s2 25.1º
Answer
2 2cos0
min Bg
Q.E.D. (b)
min
3cosC Q.E.D.
Answer (a) vA = - (25 mm/s)er - (250 mm/s)e , (b) aB = - (490 mm/s2)er + (100 mm/s2)e , (c) aB/OA = (10 mm/s2)er .
2 2120 / , 0.0900 / , 34.8 / , 0.0156 /Answer r m s rad s r m s rad s
Chapter 12: Kinetics of particles
Newton’s second law
Answer (a) aA =2.49 m/s2 →, aB = 0.831 m/s2, (b) = 74.8 N
Answer a2 = 6.63 m/s2 ←. (b) xp/belt = 0.321 m →
Answer µs > 0.300
Answer (a) = 33.6 N. (b) aA = 4.76 m/s2 →, aB = 3.08 m/s2, aC = 1.401 m/s2 ←.
Answer (a) mC = 1.426 kg. (b) aA = 1.503 m/s2→, aB =0.348 m/s2→, aC = 1.759 m/s2.
Answer (a) = 201 m. (b) N = 612 N.
Answer (a) N = 2.905 N. (b) = 13.09º.
Answer (a) = 43.5º. (b) µ =0.408. (c) 𝒱 = 121.8 km/h
12.5
Answer (a) Fr = 0.49 N, Fθ =0.1 N. (b) Fr = -0.249 N, Fθ = -0.250 N.
Answer (a) aB/rod = 72 m/s2 radically outward. (b) Fθ = 1.25 N.
Answer (a) T = 126.6 N. (b) aA = 5.48 m/s2→ (c) aB = 4.75 m/s2 ↑.
Chapter 13: Kinetics of particles
Work & Energy
Answer d = 6.71 m.
Answer v0 = 4.61 m/s 15˚.
Answer (a) vB = 2.34 m/s←. (b) d = 235 mm.
Answer (a) d = 11.88 m. (b) T 5.05 kN.
Answer (a) vB = 1.510 m/s←. (b) F = 96.0 N.
Answer (a) 𝒱 = 0.597 m/s. (b) 𝒱max = 0.617 m/s.
Answer (a) P =58.9 kW. (b) P = 52.9 kW.
Answer 𝒱2 = 1.481 m/s↓.
Answer 𝓍 = 0.269 m.
Chapter 13: Kinetics of particles
Impulse & momentum
Answer (a) F = 7940 N. (b) t =3.00 s.
Answer (a) t = 0.549 s. (b) T = 56.8 N.
Answer (a) A was going faster. (b) 𝒱A = 115.2 km/h
Answer FAV = 65.0 kN.
Answer (a) plate = 1.694 m/s↓. (b) Energy lost = (1.3272 – 1.1653)J = 0.1619 J.
Answer (a) vA = 0.594 m/s ←,vB = 1.156 m/s→. (b) T1 –T2 = 2.99 J.
Answer T1 –T2 = (1 – e2)m𝒱2.
Answer ./338.0,/013.1,/150.0 smvsmvsmv BAC
Answer 0 00.711 39.3 , 0.636 45 .A B
Answer 6.37 / 72.2 , 1.802 / 40 .A Bm s m s
Answer d = 15.94 m.
Answer h h = 0.156 m.
Chapter 15: Kinematics of rigid bodies
Answer (a) ωB = 300 rpm , ωC = 100 rpm . (b) aB = 4.3 m/s2 ←, aC = 16.45 m/s2→.
Answer (a) A: ωA = 15.0 rad/s ; B; ωB = 7.50 rad/s .
Answer vC = 0, vB = 44.4 m/s→, vD = 42.9 m/s 15°, vE = 31.4 m/s 45°.
Answer (a) ωAB = 3.62 rad/s . (b) vA = 1.963 m/s ↓.
Answer (a) ωB = 48 rad/s . (b) vD = 3.39 m/s 45°.
Answer (a) r = 1.5 mm. (b) an = 0.457 x 10-3 mm/s2. (c) an = 2.74 x 10-3 mm/s2.
Answer (a) ωAD = (6.0 rad/s)k = 6.0 rad/s . (b) vB = (360 mm/s)i - (672 mm/s)j = 762 m/s 61.8°.
Answer (a) r = 1.5 mm. (b) an = 0.457 x 10-3 mm/s2. (c) an = 2.74 x 10-3 mm/s2.
Answer (a) ωAD = (6.0 rad/s)k = 6.0 rad/s . (b) vB = (360 mm/s)i - (672 mm/s)j = 762 m/s 61.8°.
Answer
2
DABD
B tan)b(.cos
rv)a( .
Answer (a) ωBD = 1.500 rad/s . (b) vD = 450 mm/s ↑.(c) vM = -(168.8 mm/s)i + (255 mm/s)j = 281 mm/s 53.1°.
Answer (a) vP = 0, ωBD = 39.3 rad/s . (b) ωBD = 0, vP = 6.28 m/s ↓.
Answer (a) ωBD = 12.00 rad/s . (b) vM = 3.90 m/s 67.4°.
Answer (a) ωBD = 3.33 rad/s . (b) vF = 2.00 m/s 56.3°
Answer vF = 369 mm/s i = 369 mm/s →.
Answer (a) vB = 338 mms←, ωAB = 0. (b) vB = 710 mm/s←, ωAB = 2.37 rad/s .
Answer (a) ωBCD = 2.84 rad/s . (b) vE = 1.817 m/s 82.4°.
Answer (a) ω= 5.13 rad/s . (b) vD = 0.924 m/s←. (c) vA = 1.870 m/s 34.7°
Answer (a) aB = 1430 m/s2 ↓. (b) aC = 1430 m/s2 ↓. (c) aD = 1430 m/s2 60°.
Answer aP = 148.3 m/s2 ↓.
Answer aD = 1558 m/s2 45°.aE = 337 m/s2 45°.
Answer aD = 59.8 m/s2 ↑, aD = 190.6 m/s2↑.
Answer aD = 6.038 m/s2 ←, aG = 10.064 m/s2 72.5°
Answer (a) αAB = 0.718 rad/s2 . (b) aB = 125.0 mm/s2 →.
Answer aD = 1.745 m/s2 68.2°.
Answer (a) αBD = 4.18 rad/s2 . (b) αDE = 2.43 rad/s2 .
Chapter 16: Plane motion of rigid bodies
Forces and accelerations
Answer (a) a = 7.85 m/s2. (b) a = 3.74 m/s2. (c) a = 4.06 m/s2→.
Answer (a) 5270 N↑. (b) 4120 N (compression).
Answer Cy = -194.0 N, By = 194.0 N.
Answer (a) A = 15.14 rad/s2 . (b) FA =21.8 N↗.
Answer aA = 0.885 m/s2, aB = 2.60 m/s2 ↑.
Answer (a) = 107.1 rad/s2 . (b) Cy = 39.2 N↑, CX = 21.4 N ←.
Answer (a) B
9a g .
7 (b)
4C mg .
7
Answer (a) C = 72.4 rad/s2 . (b) aB = 7.24 m/s2 .
Answer (a) aA = aB = 1.923 m/s2 ←. (b) Dx = 4.33 N←.
Answer A = 6.40 N←.
Answer D = 171.7 N→.
Answer (a) M = 36.3 N · m . (b) C = 231 N ←+ 524 N.
Answer B = 805 N←, D = 426 N→.
Answer B = 8.61 N↑, Ay = 8.13 N↑.
Answer Bx = 120 N→, By = 88.2 N↑, M = 15 N · m .
Chapter 17: Plane motion of rigid bodies
Work & Energy
Answer A = 1.063 rev
Answer (a) ω2 = 3.995 rad/s . (b) R = 32.4 N.
Answer ω2 = 11.13 rad/s .
Answer vAB = 292 mm/s →.
Answer vA = 0.775 gL ←, vB = 0.775 gL 60º.
Answer ω2 = 84.7 rpm .
Answer vB =3.25 m/s.
Answer (a) MAB = 39.8 N · m. (b) MCD = 95.5 N · m. (c) MEF = 229 N · m.
Chapter 17: Plane motion of rigid bodies
Impulse & Momentum
Answer ω = 3.87 rad/s.
Answer M = 1.081 N· m.
Answer 2 k
tg
Answer (a) 2
2 2
r gt sinv .
r k
(b)
2
2 2s
k tan
r k
Answer h = 2
5r .
Answer (a) ω = 22.7 rad/s . (b) C = 4540 N →.
