move to the left Can you sce what happens to le motion of the conneting Tod at that point? You can also solve this problem using the vector shown in
move to the left Can you sce what happens to le motion of the conneting Tod at that point? You can also solve this problem using the vector shown in
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
Related questions
Question
Please answer the highlighted portion of the second page.
![In the engine system shown, the crank AB has a constant clockwise angular
velocity of 2000 rpm. For the crank position shown, detemine (a) the
angular velocity of the connecting od BD, (b) the velocity of the piston P.
1%3D8 in
r53 in
140 t
STRATEGY: Connecting rod BD is undergoing general motion, so use
rigid-body kinematics. Crank AB is undergoing fixed axis rotation, and
piston P is translating. The motion of the piston is the same as the end D
of the connecting rod.
D.
MODELING and ANALYSIS:
Motion of Crank AB. The crank AB rotates about point A. Expressing
WAR in rad/s and writing v rwa you have (Fig. 1)
in.
I min27 rad
I rev
50
rev
2000
min
209.4 rad/s
AB
60 s
- AB)o - (3 in.)(2094 rad/s) - 628.3 in./s
VA 628.3 in./s 50°
Fig. 1 Crank AB is
undergoing fixed
axis rotation.
Motion of Connecting Rod BD. Consider this as a general plane
motion. Using the law of sines, compute the angle 3 bet ween the con-
necting rod and the horizontal as
sin 40
sin 3
3= 13.95
%3D
8 in.
3 in.
The velocity V, of point D where the rod is attached to the piston must
be horizontal, while the velocity of point B is equal to the velocity va
obtained previously. Expressing the relation between the velocities Vp. Va.
and von: you have
V = V + Vpn
(continued)
1004 Kinematics of Rigid Bodies
This equation is shown pictorially in kig. 2 where the motion of BD is
resolved into a translation of B and a rotation about B.
AD B-13.95
(fixed)
76.05
30°
50
Plane motion
Translation
Rotation
+]
Fig. 2 The general plane motion of the connecting rod can be modelled as a
translation plus a rotation.
Draw the vector diagram comresponding to this equation (Fig. 3). Recalling
that 8 = 13.95°, you can determine the angles of the triangle and write
No
so
76.05
50
A-13.95
Vp
sin 53.95
628.3 in./s
sin 50
sin 76.05
Von- 495.9 in.s
Vp- 5234 in/s- 43.6 fVs
Voa- 495.9 in.A 76.05
Vp-43.6 ft/s→
Vp- Vp- 43.6 fs
53.95
Since vpa= lanp. you have
Fig. 3 Vector triangle showing the
rel ationship between the velocities of
8 and D.
495.9 in./s (8 in. Jop
aD- 62.0 rad/s 4
REFLECT and THINK: Note that as the crank continues to move
clockwise below the center line, the piston changes direction and starts to
move to the left Can you see what happens to e motion of the connecting
rod at that point? You can also solve this problem using the vector
relationship expressed in Eq. (15.17'); this type of approach is shown in
Sample Prob. 15.8.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8700fa5c-0cb9-46f9-817d-473369b2beec%2F7d083e6b-b816-4daa-aa6a-dca45209c235%2Fop3dnvn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In the engine system shown, the crank AB has a constant clockwise angular
velocity of 2000 rpm. For the crank position shown, detemine (a) the
angular velocity of the connecting od BD, (b) the velocity of the piston P.
1%3D8 in
r53 in
140 t
STRATEGY: Connecting rod BD is undergoing general motion, so use
rigid-body kinematics. Crank AB is undergoing fixed axis rotation, and
piston P is translating. The motion of the piston is the same as the end D
of the connecting rod.
D.
MODELING and ANALYSIS:
Motion of Crank AB. The crank AB rotates about point A. Expressing
WAR in rad/s and writing v rwa you have (Fig. 1)
in.
I min27 rad
I rev
50
rev
2000
min
209.4 rad/s
AB
60 s
- AB)o - (3 in.)(2094 rad/s) - 628.3 in./s
VA 628.3 in./s 50°
Fig. 1 Crank AB is
undergoing fixed
axis rotation.
Motion of Connecting Rod BD. Consider this as a general plane
motion. Using the law of sines, compute the angle 3 bet ween the con-
necting rod and the horizontal as
sin 40
sin 3
3= 13.95
%3D
8 in.
3 in.
The velocity V, of point D where the rod is attached to the piston must
be horizontal, while the velocity of point B is equal to the velocity va
obtained previously. Expressing the relation between the velocities Vp. Va.
and von: you have
V = V + Vpn
(continued)
1004 Kinematics of Rigid Bodies
This equation is shown pictorially in kig. 2 where the motion of BD is
resolved into a translation of B and a rotation about B.
AD B-13.95
(fixed)
76.05
30°
50
Plane motion
Translation
Rotation
+]
Fig. 2 The general plane motion of the connecting rod can be modelled as a
translation plus a rotation.
Draw the vector diagram comresponding to this equation (Fig. 3). Recalling
that 8 = 13.95°, you can determine the angles of the triangle and write
No
so
76.05
50
A-13.95
Vp
sin 53.95
628.3 in./s
sin 50
sin 76.05
Von- 495.9 in.s
Vp- 5234 in/s- 43.6 fVs
Voa- 495.9 in.A 76.05
Vp-43.6 ft/s→
Vp- Vp- 43.6 fs
53.95
Since vpa= lanp. you have
Fig. 3 Vector triangle showing the
rel ationship between the velocities of
8 and D.
495.9 in./s (8 in. Jop
aD- 62.0 rad/s 4
REFLECT and THINK: Note that as the crank continues to move
clockwise below the center line, the piston changes direction and starts to
move to the left Can you see what happens to e motion of the connecting
rod at that point? You can also solve this problem using the vector
relationship expressed in Eq. (15.17'); this type of approach is shown in
Sample Prob. 15.8.
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