Concept explainers
(a)
Angular acceleration of bar BD.
Answer to Problem 15.132P
The angular acceleration of bar BD is
Explanation of Solution
Given information:
Angular velocity of bar AB is
Angular acceleration of bar AB is
The absolute value of point A
The relative velocity of A with respect to B is defined as
The absolute acceleration of point B is defined as:
The tangential acceleration is defined as:
The normal acceleration is defined as:
In above equations:
Calculation:
Position vector of B relative to A:
Position vector of D relative to B:
Position vector of D relative to E:
For bar AB:
Velocity of point B:
For bar BD:
Velocity of point D:
For bar DE:
Velocity of point D:
Equate above equations
Equate components:
Therefore:
For bar AB:
Acceleration of point B
We know that:
Therefore:
For bar BD:
Acceleration of point D:
Substitute:
Therefore:
For bar DE
Acceleration of point D:
Substitute:
Therefore:
Equate above equations
Equate components:
Solve above equations:
Conclusion:
The angular acceleration of bar BD is
(b)
Angular acceleration of bar DE
Answer to Problem 15.132P
The angular acceleration of bar DE is
Explanation of Solution
Given information:
Angular velocity of bar AB is
Angular acceleration of bar AB is
The absolute value of point A
The relative velocity of A with respect to B is defined as
The absolute acceleration of point B is defined as
The tangential acceleration is defined as
The normal acceleration is defined as
In above equations
Calculation:
According to sub part a
Acceleration of point D for bar BD
Acceleration of point D for bar DE
Equate above equations
Equate components
Therefore
Conclusion:
The angular acceleration of bar DE is
Want to see more full solutions like this?
Chapter 15 Solutions
Vector Mechanics For Engineers
- In Prob. 15.14, determine the velocity and acceleration of point E , assuming that the angular velocity is 26 rad/s and increases at the rate of 65 rad/s2.Reference to Problem 15.14:A circular plate of 120-mm radius is supported by two bearings A and B as shown. The plate rotates about the rod joining A and B with a constant angular velocity of 26 rad/s. Knowing that, at the instant considered, the velocity of point C is directed to the right, determine the velocity and acceleration of point E.arrow_forwardKnowing that at the instant shown the angular velocity of bar AB is 15 rad/s clockwise and the angular velocity of bar EF is 10 rad/s clockwise, determine (a) the angular velocity of rod DE, (b) the relative velocity of collar B with respect to rod DE.arrow_forwardProblem 1: In a four bar mechanism, the dimensions of the links are as given below: AB = 50 mm, BC = 66 mm CD = 56 mm and AD = 100 mm At a given instant when |DAB 60o the angular velocity of link AB is 10.5 r/s in CCW direction. Determine, i) Velocity of point C ii) Velocity of point E on link BC when BE = 40 mm iii) The angular velocity of link BC and CD iv) The velocity of an offset point F on link BC, if BF = 45 mm, CF = 30 mm and BCF is read clockwise. v) The velocity of an offset point G on link CD, if CG = 24 mm, DG = 44 mm and DCG is read clockwise. vi) The velocity of rubbing of pins A, B, C and D. The ratio of the pins are 30 mm, 40 mm, 25 mm and 35 mm respectively.arrow_forward
- In a four-link mechanism, the dimensions of the links are given as AB=50mm, BC=66mm, CD=56mm, and AD=100mm. At the instant when <DAB = 60° , the link AB has an angular velocity of 10.5 rad/sec in the counterclockwise direction. Both A and D lies in the horizontal plane.For the given configuration of the mechanism, determine the following: angular velocity of the link CD, angular velocity of the link BC, velocity of an offset point G on the link CD if CG=24mm,DG=44mm Instructions: configuration diagram Scale: 1:1 velocity diagram. Scale: 1m/s : 95mmarrow_forwardIn a four bar mechanism, the dimensions of the links are as given below:AB = 50 mm, BC = 66 mmCD = 56 mm and AD = 100 mmAt a given instant when | DAB=60°the angular velocity of link AB is 10.5rad/sec in CCW direction.Determine,i) Velocity of point Cii) Velocity of point E on link BC when BE = 40 mmiii) The angular velocity of link BC and CDiv) The velocity of an offset point F on link BC, if BF = 45 mm,CF = 30 mm and BCF is read clockwise.v) The velocity of an offset point G on link CD, if CG = 24mm, DG = 44 mm and DCG is read clockwise.vi) The velocity of rubbing of pins A, B, C and D. The ratios ofthe pins are 30 mm, 40 mm, 25 mm and 35 mmrespectively.arrow_forwardKnowing that at the instant shown the angular velocity of rod AB is 15 rad/s clockwise, write down the equation of velocity of point B relative to point A. -V_Bi=(-15k)x(-0.2j) +V_Bj=V_Ai-(15k) x (0.6i+0.25j) -V_Bi=V_A+(-15k)x(0.2j) +V_Bj=V_Ai-(omega_BDk) x (-0.6i-0.25j)arrow_forward
- In order to uncoil electrical wire from a 0.6-m-radius spool fixed to a truck, a worker drives to the left with a speed of vA = 5 m/s. At the same time, a second worker holds the cable as he walks to the right with a speed of vB = 3 m/s. Knowing that at the instant shown the thickness of wire on the spool is 40 mm, determine (a) the instantaneous center of rotation of the spool, (b) the velocity of point D on the inside of the spool.arrow_forwardA juggling club is thrown vertically into the air. The center of gravity G of the 20-in. club is located 12 in. from the knob. Knowing that at the instant shown, G has a velocity of 4 ft/s upward and the club has an angular velocity of 30 rad/s counterclockwise, determine (a) the speeds of points A and B, (b) the location of the instantaneous center of rotation.arrow_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
- A chain is looped around two gears of radius 40 mm that can rotate freely with respect to the 320-mm arm AB. The chain moves about arm AB in a clockwise direction at the constant rate of 80 mm/s relative to the arm. Knowing that in the position shown arm AB rotates clockwise about A at the constant rate ω = 0.75 rad/s, determine the acceleration of each of the chain links indicated Links 1 and 2.arrow_forwardA painter is half way up a 10-m ladder when the bottom starts sliding out from under him. Knowing that point A has a velocity vA = 2 m/s directed to the left when 0= 60°, determine (a) the angular velocity of the ladder, (b) the velocity of the painter.arrow_forwardAt the instant shown, the velocity of collar A is 0.4 m/s to the right and the velocity of collar B is 1 m/s to the left. Determine (a) the angular velocity of bar AD, (b) the angular velocity of bar BD, (c) the velocity of point D.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