Concept explainers
(a)
Find the relative velocity of the block with respect to the each rod.
(a)
Answer to Problem 15.257RP
The relative velocity of the rod AE, BD, are
Explanation of Solution
Given information:
The value of the angle is
Calculation:
Consider the value of the angle as
Show the geometry of the assembly as shown in Figure 1.
Refer to Figure 1.
Show the relation between the distances
Calculate the distances
Consider the common angular velocity and angular acceleration of the rod AE and BD are
Consider the double slider H as a particle sliding along the rotating rod AH with relative velocity
Consider
Calculate the velocity at
Calculate the acceleration at
Calculate the corresponding coriolis acceleration as follows:
Show the velocity and acceleration at H as follows:
Consider the double slider H is a particle sliding along BD with relative velocity
Consider the point
Calculate the velocity and acceleration at
Calculate the corresponding coriolis acceleration as follows:
Show the velocity and acceleration at H as follows:
Equate vertical components of Equation (1) and (3).
Equate horizontal components of Equation (1) and (3).
Substitute
Equate the vertical component of Equation (5) and (6)
Equate the horizontal component of Equation (5) and (6)
Thus, the relative velocity of the rod AE, BD, are
(b)
Find the relative acceleration of each rod.
(b)
Answer to Problem 15.257RP
Thus, The relative acceleration of the rod AE and BD are
Explanation of Solution
Given information:
Calculation:
Refer Part (a).
The relative acceleration of the rod AE and BD are
Want to see more full solutions like this?
Chapter 15 Solutions
Loose Leaf for Vector Mechanics for Engineers: Statics and Dynamics
- Problem (5) The rectangular block shown rotates about the diagonal OA with a constant angular velocity of 6.76 rad/s. Knowing that the rotation is counterclockwise as viewed from A, determine the velocity and acceleration of point B at the instant shown. 240 mm 100 mm 312 mm B 312 mmarrow_forwardThe 200-mm-radius disk rolls without sliding on the surface shown. Knowing that the distance BG is 160 mm and that at the instant shown the disk has an angular velocity of 5.50 rad/s counterclockwise and an angular acceleration of 7.00 rad/s² clockwise, determine the acceleration of A. A 730 mm 200 mm Barrow_forwardRequired information NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. For a 5-m steel beam AE, the acceleration of point A is 2.5 m/s² downward and the angular acceleration of the beam is 1.5 rad/s2 counterclockwise. Knowing that at the instant considered the angular velocity of the beam is zero, determine the acceleration of cable B and cable D. A -1.5 m- B Determine the acceleration of cable B The acceleration of cable Bis 2 m 1.375 5 m/s2. D -1.5 m- Earrow_forward
- Both 15-cm-radius wheels roll without slipping on the horizontal surface. Knowing that the distance AD is 12.5 cm, the distance BE is 10 cm, that D has a velocity of 30 cm/s to the right and acceleration of E is 60 cm/s? to the left, determine the angular velocity and angular acceleration of link AB, angular velocity and angular acceleration of both wheels. Also determine the acceleration of point C. | 30 y Wheel 1 45 cm Wheel 2 /A 15cm 10 cm VD=30 cm/s B aE=60 cm/s2 15 cm 12.5 cmarrow_forwardProblem (8) The belt shown moves over two pulleys without slipping. At the instant shown the pulleys are rotating clockwise and the speed of point B on the belt is 4 m/s, increasing at the rate of 32 m/s?. Determine, at this instant, (a) the angular velocity and angular acceleration of each pulley, (b) the acceleration of point P on pulley C. B 160 mm fi00 mmarrow_forward5.- Knowing that at the instant shown bar AB has an angular velocity of 4 rad/s and an angular acceleration of 2 rad/s?, both clockwise, determine the angular acceleration (a) of bar BD, (b) of bar DE by using the vector approach. 100 mm 175 mm - B A 200 mm 75 mm D Earrow_forward
- If crank AB rotates with an angular velocity of wAB angular acceleration a AB = 6 rad/s? at the instant shown, determine: 1.1. The angular velocity of rod BC and the velocity of the slider block 1.2. The angular acceleration of rod BC and the linear acceleration of = 5 rad/s and an 0.5 m 0,3 m B 60° 30° WAB slider Block. 1.3. Locate the instantaneous center (IC) of the rod BC. CABarrow_forwardA series of small machine components being moved by a conveyor belt pass over a 120 mm radius idler pulley. At the instant shown, the velocity of Point A is 300 mm/s to the left and its acceleration is 180 mm/s2 to the right. Determine (a) the angular velocity and angular acceleration of the idler pulley, (b) the total acceleration of the machine component at B.arrow_forwardA Rod slides along the ground and the wall as shown. If the velocity of end B is 2 m/s downwards, Determine (a) the angular velocity of AB, (b) the velocity of end A. 500 mm 125 mm B 300 mmarrow_forward
- 0.2 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_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_forwardThe 200-mm-radius disk rolls without sliding on the surface shown. Knowing that the distance BG is 160 mm and that at the instant shown the disk has an angular velocity of 8.6 rad/s counterclockwise and an angular acceleration of 2.3 rad/s2 clockwise, determine the acceleration of A. 800 mm The acceleration of A is 11.55 200 mm B m/s²_arrow_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