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Q1(a) A car in Figure Q1(a) travels in a straight line with acceleration shown in the graph. The car starts from the origin with vo = -18 m/s. By assume t' = 8.4s, sketch the v-t and s-t graphs. a (m/s*) 6. 3 t (s) 4 12 -5

Q1(a) A car in Figure Q1(a) travels in a straight line with acceleration shown in the graph. The car starts from the origin with vo = -18 m/s. By assume t' = 8.4s, sketch the v-t and s-t graphs. a (m/s*) 6. 3 t (s) 4 12 -5

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Use t'=20.4 instead of 8.4 and use the formulas attached 

Q1(a) A car in Figure Q1(a) travels in a straight line with acceleration shown in the graph. The car starts from the origin with vo = -18 m/s. By assume t' = 8.4s, sketch the v-t and s-t graphs. a (m/s") 3 t (s) 4 12 -5 Figure Q1(a) (b) The rod OA in Figure Q1(b) rotates clockwise with a constant angular velocity. Two- pin-connected slider blocks, located at B, moves freely on OA and the curved rod is describe by the equation r = 100(1 – cos 8) mm. (i) Determine the speed of the slider blocks at e = 120° (11) Calculate its magnitude of acceleration when e = 120° 6 rad/s 400 mm 600 mm 200 mm Figure Q1(b)
Transcribed Image Text:Q1(a) A car in Figure Q1(a) travels in a straight line with acceleration shown in the graph. The car starts from the origin with vo = -18 m/s. By assume t' = 8.4s, sketch the v-t and s-t graphs. a (m/s") 3 t (s) 4 12 -5 Figure Q1(a) (b) The rod OA in Figure Q1(b) rotates clockwise with a constant angular velocity. Two- pin-connected slider blocks, located at B, moves freely on OA and the curved rod is describe by the equation r = 100(1 – cos 8) mm. (i) Determine the speed of the slider blocks at e = 120° (11) Calculate its magnitude of acceleration when e = 120° 6 rad/s 400 mm 600 mm 200 mm Figure Q1(b)
Fundamental Equation of Dynamics KINAMATICS Equations of Motion: Particle Rectilinear motion: Constant a = de EF = ma EF, = m(ag), EF, = m(ag), Variable a Particle dv ds v = vo + at 1 Rigid Body (Plane Motion) dt s = , + vạt +at 12 = vỷ + 2a.(s - 50) ads = vdv EMG = Iça a EMp = E(M)p Particle Curvilinear Motion: Principle of Work and Energy: T, + U,-2 = T, Cartesian Coordinates (1,y,z) V = * a, = * Vy = ý ay = jỹ Kinetic Energy Particle T = : T=mvå + lgw?² or T= 1,w? Polar Coordinates (r,8,z) Rigid Body a, = # - re? ag = rê + 2rẻ (Plane Motion) V = ré Work Uş = SF cos e de U, = (F cos 8)As Uw = -WAy Variable Force : Normal-Tangential Coordinates (n,t,b) Constant Force: a = i = v, Weight U, = -(kei -kei) Spring [1+ (dy/dx)*]a/2 |d²y/dx*| Couple of Moment: UM = M AO Where p= Power and Efficiency du Uout Pout P = = Fv, E= Pin Conservation of Energy Theorem !! dt Relative Motion VB = VA + VB/A T +V = T2 + V2 Potential Energy Rigid Body Motion About a Fixed Axis V = V, + V. Where: V = ± Wy , V, = +ks? Иariable a Constant a = de Principle of linear Impulse and Momentum: dw w = w, +at a = dt 1 e = 0, + wat + w? = w3 + 2a.(0 - 0.) mv, +ES Fåt = mvz Rigid Body: m(vc)ı +ES Fdt = m(va)a Particle de dt wdw = ade For Point P Conservation of Linear Momentum: s= er, v= wr. a = ar, an = w'r Σ(mv), Σ (mv), Relative General Plane Motion-Translating Coefficient of Restitution (v3), – (v)2 Axes Vg = VA + vn/Acpin) B = Ga+ aB/Apin) Principle of Angular Impulse and Momentun: : (H,), +ES M,dt = (H,)2 Where H, = (d)(mv) Relative General Plane Motion-Tran. And Rot. Axis Particle Vg = VA + w X TB/a + (VB/A)vz ag = an + i x P/a +w x (w x rayA) + 2w x (V8/A)v Rigid Body : (H.h +ES M,dt = (H)2 (Plane Motion) + Where He = Igw Kineties (H.)1 + M,dt = (H,)2 Mass Moment of Inertia Parallel-Axis Theory 1= [r*dm 1 = lg + m d? Where H, = 1,w Conservation of Angular Momentum Radius of Gyration k = Σ(Η), Σ (Η),
Transcribed Image Text:Fundamental Equation of Dynamics KINAMATICS Equations of Motion: Particle Rectilinear motion: Constant a = de EF = ma EF, = m(ag), EF, = m(ag), Variable a Particle dv ds v = vo + at 1 Rigid Body (Plane Motion) dt s = , + vạt +at 12 = vỷ + 2a.(s - 50) ads = vdv EMG = Iça a EMp = E(M)p Particle Curvilinear Motion: Principle of Work and Energy: T, + U,-2 = T, Cartesian Coordinates (1,y,z) V = * a, = * Vy = ý ay = jỹ Kinetic Energy Particle T = : T=mvå + lgw?² or T= 1,w? Polar Coordinates (r,8,z) Rigid Body a, = # - re? ag = rê + 2rẻ (Plane Motion) V = ré Work Uş = SF cos e de U, = (F cos 8)As Uw = -WAy Variable Force : Normal-Tangential Coordinates (n,t,b) Constant Force: a = i = v, Weight U, = -(kei -kei) Spring [1+ (dy/dx)*]a/2 |d²y/dx*| Couple of Moment: UM = M AO Where p= Power and Efficiency du Uout Pout P = = Fv, E= Pin Conservation of Energy Theorem !! dt Relative Motion VB = VA + VB/A T +V = T2 + V2 Potential Energy Rigid Body Motion About a Fixed Axis V = V, + V. Where: V = ± Wy , V, = +ks? Иariable a Constant a = de Principle of linear Impulse and Momentum: dw w = w, +at a = dt 1 e = 0, + wat + w? = w3 + 2a.(0 - 0.) mv, +ES Fåt = mvz Rigid Body: m(vc)ı +ES Fdt = m(va)a Particle de dt wdw = ade For Point P Conservation of Linear Momentum: s= er, v= wr. a = ar, an = w'r Σ(mv), Σ (mv), Relative General Plane Motion-Translating Coefficient of Restitution (v3), – (v)2 Axes Vg = VA + vn/Acpin) B = Ga+ aB/Apin) Principle of Angular Impulse and Momentun: : (H,), +ES M,dt = (H,)2 Where H, = (d)(mv) Relative General Plane Motion-Tran. And Rot. Axis Particle Vg = VA + w X TB/a + (VB/A)vz ag = an + i x P/a +w x (w x rayA) + 2w x (V8/A)v Rigid Body : (H.h +ES M,dt = (H)2 (Plane Motion) + Where He = Igw Kineties (H.)1 + M,dt = (H,)2 Mass Moment of Inertia Parallel-Axis Theory 1= [r*dm 1 = lg + m d? Where H, = 1,w Conservation of Angular Momentum Radius of Gyration k = Σ(Η), Σ (Η),
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