Elements Of Electromagnetics
7th Edition
ISBN: 9780190698614
Author: Sadiku, Matthew N. O.
Publisher: Oxford University Press
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Please use equations attached
Transcribed Image Text:Q2(a) A box sliding at point B as shown in Figure Q2(a) with acceleration of 3.8 m/s².
Assume the coefficient of kinetic friction is same for each section. Detemine the
acceleration of the box at point A. Sketch the free body diagram at both points to help
you answer.
35
20
Figure Q2(a)
(b)
A ball with mass of 3kg is acted upon by four forces of magnitude with the direction as
shown in the Figure Q2(b). Given the forces as:
F1 = 50N, F2 = 25N, F3 = 8N, F4 = 5N,
(i)
Calculate the magnitude of the ball's acceleration and its direction.
(ii)
Relate the unbalanced forces in the system shown with the equation of motion.
40°
Figure Q2(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),](https://content.bartleby.com/qna-images/question/33488049-1422-455e-b50d-4d67f5321948/a8121053-711d-41c2-b5d6-dc297e83c179/gyrur_processed.png)
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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