The crank arm AB turms about z axis through its pinned end A with the clockwise angular velocity w = 3 rad/s and counterclockwise angular acceleration a = track. At the given instant, determine (a) position vector, řB/a, and velocity and acceleration at point B, vg and äg, (b) position vector, ře/n. velocity at point C, vc, and angular velocity of the link BC, õnc, and (c) acceleration at point C, åc, and angular acceleration of the link BC, ägc. 2 rad/s? at the instant shown. The block C slides in the vertical B 30 2m 50 3 m 3 rad (7] (a) faya = (10] (b) ře/m = [8] (c) âc = -2rad
The crank arm AB turms about z axis through its pinned end A with the clockwise angular velocity w = 3 rad/s and counterclockwise angular acceleration a = track. At the given instant, determine (a) position vector, řB/a, and velocity and acceleration at point B, vg and äg, (b) position vector, ře/n. velocity at point C, vc, and angular velocity of the link BC, õnc, and (c) acceleration at point C, åc, and angular acceleration of the link BC, ägc. 2 rad/s? at the instant shown. The block C slides in the vertical B 30 2m 50 3 m 3 rad (7] (a) faya = (10] (b) ře/m = [8] (c) âc = -2rad
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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I attached a formula sheet of the only formulas that can be used to solve problems. Will leave a vote!
![Position, Velocity, Acceleration
Rectangular Coordinate:
i = xỉ + yj + zk
ü = v,i + v,j + v,k = xi + ÿj + żk
a = a,i + a,j + a,k = xï + ÿj+ žk
Projectile Motion
a = -gj
v = vĩ + v,j = voxī+(-gt + voy)j
Kinematic Equations for Two Points on the Same
Rigid Body:
%3D
/A
Pure Rolling:
vc = rw; ac = ra, consistent with the rolling direction;
v¡ = 0; a¡ = rw² toward C
7 = xĩ + yỹ = (Voxt + xo)ï + (–gt2 + voyt + Yo)j Eq. of Motion for a Rigid Body in Planar Motion:
1
gt²
ΣF -
Tangent and Normal Coordinate:
* = 7(s)
i = vũ; = sū;
à = a,ū, + a„īn = šū, +ūn
= māg
ΣΜ 1ς α
ΣΜΟ-10α
EMQ = Iga + (Fc/ × mãc),
= lọa + (Tc/Q × māo), Q: any point
G: mass center
O: pivot point or instantaneous center
213/2
1+]
|d²y|
p =
Kinetic Energy of a Rigid Body
dx2
T =mv,² +Igw²
2
Cylindrical Coordinate:
= rū, + zū,
v = v,ũ, + vgũg + v,ū, = rū, + rôūo + żū,
à = a,ūr + agūg + azūz
= (* – rô?)ũ, + (rö + 2řė)ūg + žū,
T =
Work Done on a Rigid Body
- [ Fds + f Mdo
U =
Newton's Second Law:
2F = mã
Work-Energy Principle:
T; +U.-2 = T2
1
kinetic energy: T =
mv²
work done: U =
F• dr
*work of the force exerted by a spring:
U1-2 = k(sỉ – s3)
*work of the force exerted by friction:
U1-2 = -fd
Conservative Force Field:
T1 + Vị = T2 + V2
T: kinetic energy
V:potential energy](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd4a02593-47b6-4253-beb0-7c85972c9833%2F3310d4b7-a0a8-430c-a472-b181852b9354%2Fyikcvr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Position, Velocity, Acceleration
Rectangular Coordinate:
i = xỉ + yj + zk
ü = v,i + v,j + v,k = xi + ÿj + żk
a = a,i + a,j + a,k = xï + ÿj+ žk
Projectile Motion
a = -gj
v = vĩ + v,j = voxī+(-gt + voy)j
Kinematic Equations for Two Points on the Same
Rigid Body:
%3D
/A
Pure Rolling:
vc = rw; ac = ra, consistent with the rolling direction;
v¡ = 0; a¡ = rw² toward C
7 = xĩ + yỹ = (Voxt + xo)ï + (–gt2 + voyt + Yo)j Eq. of Motion for a Rigid Body in Planar Motion:
1
gt²
ΣF -
Tangent and Normal Coordinate:
* = 7(s)
i = vũ; = sū;
à = a,ū, + a„īn = šū, +ūn
= māg
ΣΜ 1ς α
ΣΜΟ-10α
EMQ = Iga + (Fc/ × mãc),
= lọa + (Tc/Q × māo), Q: any point
G: mass center
O: pivot point or instantaneous center
213/2
1+]
|d²y|
p =
Kinetic Energy of a Rigid Body
dx2
T =mv,² +Igw²
2
Cylindrical Coordinate:
= rū, + zū,
v = v,ũ, + vgũg + v,ū, = rū, + rôūo + żū,
à = a,ūr + agūg + azūz
= (* – rô?)ũ, + (rö + 2řė)ūg + žū,
T =
Work Done on a Rigid Body
- [ Fds + f Mdo
U =
Newton's Second Law:
2F = mã
Work-Energy Principle:
T; +U.-2 = T2
1
kinetic energy: T =
mv²
work done: U =
F• dr
*work of the force exerted by a spring:
U1-2 = k(sỉ – s3)
*work of the force exerted by friction:
U1-2 = -fd
Conservative Force Field:
T1 + Vị = T2 + V2
T: kinetic energy
V:potential energy
![The crank arm AB tums about z axis thrdugh its pinned end A with the clockwise angular velocity w = 3 rad/s
and counterclockwise angular acceleration a = 2 rad/s² at the instant shown. The block C slides in the vertical
track. At the given instant, determine (a) position vector, îa/a, and velocity and acceleration at point B, vg and
äg, (b) position vector, ře/B, velocity at point C, vc, and angular velocity of the link BC, ögc, and (c)
acceleration at point C, år, and angular acceleration of the link BC, đgc.
B
30°
*50
3 m
o- 3 rad's
a-2 zad v
A
(7] (a) řbya =
(10] (b) ře/u =
[8] (c) âc =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd4a02593-47b6-4253-beb0-7c85972c9833%2F3310d4b7-a0a8-430c-a472-b181852b9354%2Fixi1qq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The crank arm AB tums about z axis thrdugh its pinned end A with the clockwise angular velocity w = 3 rad/s
and counterclockwise angular acceleration a = 2 rad/s² at the instant shown. The block C slides in the vertical
track. At the given instant, determine (a) position vector, îa/a, and velocity and acceleration at point B, vg and
äg, (b) position vector, ře/B, velocity at point C, vc, and angular velocity of the link BC, ögc, and (c)
acceleration at point C, år, and angular acceleration of the link BC, đgc.
B
30°
*50
3 m
o- 3 rad's
a-2 zad v
A
(7] (a) řbya =
(10] (b) ře/u =
[8] (c) âc =
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