Concept explainers
(a)
Find the angular velocity of the member ABD.
(a)
Answer to Problem 15.92P
The angular velocity of the member ABD is
Explanation of Solution
Given information:
The angular velocity of the arm DE is
Calculation:
Show the member ABD as shown in Figure 1.
Refer to Figure 1.
Calculate the velocity at D as follows:
Substitute
Consider the velocity of the point B as follows:
Consider the velocity at point B and D are denoted by
The perpendiculars to
The perpendicular BC and DC intersect at C. Then,
The point C is the instantaneous centre of ABD.
Refer to Figure 1.
Calculate the distances BD and DK as follows:
Calculate the value of the angle
Substitute
Calculate the value of the angle
Consider the triangle BCD.
Apply law of sine.
Calculate the distance BC and CD as follows:
Consider the triangle ABC.
Apply law of cosine.
Substitute
Apply law of sine.
Substitute
Calculate the angular velocity of the member ABD as follows:
Substitute
Thus, the angular velocity of the member ABD is
(b)
Find the velocity of A.
(b)
Answer to Problem 15.92P
The velocity at A is
Explanation of Solution
Given information:
Calculation:
Refer to Part (a).
Calculate the velocity of A using the relation:
Substitute
The velocity
Thus, the velocity at A is
Want to see more full solutions like this?
Chapter 15 Solutions
VEC MECH 180-DAT EBOOK ACCESS(STAT+DYNA)
- The outer gear A rotates with an angular velocity of 6 rad/s counterclockwise. Knowing that the angular velocity of the intermediate gear B is 3 rad/s clockwise, determine: 1. The angular velocity of the arm ABC 2. The angular velocity of the outer gear C. 5 in. 10 in. C B -15 in.- -15 in.- Select one: O A. arm = 3 rad/s (CW); and @c = 1.5 rad/s (CW) O B. Warm = 5 rad/s (CW); and @c = 3 rad/s (CW) O C.o arm = 0 rad/s ; and @c = 1.5 rad/s (CCW) O D. warm = 1 rad/s (CW); and wc = 0 rad/sarrow_forward0.2 m 0.25 m D E 0.6 m- Knowing that at the instant shown the angular velocity of rod AB is 15 rad/s clockwise, determine (a) the angular velocity of rod BD. (b) the velocity of the midpoint of rod BD. In the position shown, bar AB has an angular velocity of 4 rad/s clockwise. Determine the angular velocity of bars BD and DE. 200 mm 75 mm D 175 mm - 100 mm Earrow_forwardKnowing that at the instant shown the angular velocity of rod BE is 4 rad/s counterclockwise, determine (a) the angular velocity of rod AD, (b) the velocity of collar D, (c) the velocity of point A. A 240 mm EO 192 mm 30° 360 mm Darrow_forward
- Knowing that at the instant shown the angular velocity of rod BE is 4 rad/s counterclockwise, determine (a) the angular velocity of rod AD, (b) the velocity of collar D, (c) the velocity of point A. E 192 mm В 240 mm 30° D 360 mmarrow_forward15.89 The pin at B is attached to member ABD and can slide freely along the slot cut in the fixed plate. Knowing that at the instant shown the angular velocity of arm DE is 3 rad/s clockwise, determine (a) the angular velocity of member ABD, (b) the velocity of point A. A 2X) mm Fig. P15.89 E 120 mm 160 mmarrow_forwardRod BDE is partially guided by a roller at D that moves in a vertical track. Knowing that atthe instant shown the angular velocity of crank AB is 5 rad/s clockwise and that β = 25°, determine (a) the angular velocity of the rod, (b) the velocity of point E.arrow_forward
- 15.113 The 360-mm-radius flywheel is rigidly attached to a 30-mm- radius shaft that can roll along parallel rails. Knowing that at the instant shown the center of the shaft has a velocity of 24 mm/s and an acceleration of 10 mm/s, both directed down to the left, determine the acceleration (a) of point A, (b) of point B. A 2₂x 360 mm- 20° Barrow_forwardThe outer gear A rotates with an angular velocity of 3 rad/s counterclockwise. Knowing that the angular velocity of the intermediate gear B is 3 rad/s clockwise, determine: 1. The angular velocity of the arm ABC 2. The angular velocity of the outer gear C. 5 in. 10 in. 15 in. 15 in. Select one: O A.Wa= l rad/s (CW); and we O rad/s E B. warm =0 rad/s; and wc = 1.5 rad/s (CCW) O C.warm =5 rad/s (CW); and wc = 3 rad/s (CW) D:Warm =3 rad/s (CW): and wc =1.5 rad/s (CW). 9:17 PM AGO eA ENG 17-Apr-2021arrow_forward2.8 in. 15.57 Knowing that the disk has a constant angular velocity of 15 rad/s clockwise, determine the angular velocity of bar BD and the velocity of collar D when (a) 0 = 0, (b) 0 = 90°. (c) 0 = 180°. 10 in. D Fig. P15.57 and P15.58arrow_forward
- The outer gear A rotates with an angular velocity of 9 rad/s counterclockwise. Knowing that the angular velocity of the intermediate gear B is 6 rad/s clockwise, determine: 1. The angular velocity of the arm ABC ut of 2. The angular velocity of the outer gear C. ,5 in. 10 in. B 15 in. 15 in.- Select one: O A. warm =5 rad/s (CWI: and we = 3 rad/s (CW) OB.Wurm=1 rad/s (CW) and we = 0 radis 2Cwn=0 radis and w=1.5 rad/s (CCW)arrow_forwardQUESTIONS A rod BC is attached by pins to two uniform disks as shown. The lenght of rod Q.1. BC is 350 mm and the disks roll without sliding. The center A of the disk on the left side has a velocity of v4=0.3 m/s directed to the right. At the instant shown, determine (a) the velocities of points B and C of the rod, (b) the angular velocities of the disks. 75 mm 150 mm A 75 mm Barrow_forwardChapter 15 Problem 50P Done The outer gear A rotates with an angular velocity of 3 rad/s counterclockwise. Knowing that the angular velocity of the intermediate gear B is 6 rad/s clockwise, determine the angular velocity of (a) the arm ABC, (b) the outer gear C. 5 in. 10 in. -15 in.- -15 in. Fig. P15.50 Fig. P15.50arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY