Concept explainers
(a)
Find the velocity and acceleration of point E.
(a)
Answer to Problem 15.245P
The velocity of point E is
The acceleration of point E is
Explanation of Solution
Given information:
The radius of disk is
The length of rod CD is
The constant rate of rotation of the rod-and-disk with respect to arm AB is
The constant rate of rotation of the rod-and-disk is
Calculation:
Calculate the position of E with respect to B
Calculate the position of E with respect to D
Calculate the rate of rotation of the frame Bxyz
Substitute
The angular velocity of motion relative to x axis is
Calculate the velocity at the point
Substitute
Calculate the velocity at the point E with respect to the frame
Substitute
Calculate the velocity at the point E
Substitute
Hence, the velocity of point E is
Calculate the acceleration at the point
Substitute
Calculate the acceleration at E with respect to the frame
Substitute
Calculate the Coriolis acceleration
Substitute
Calculate the acceleration at E
Substitute
Therefore, the acceleration of A is
(b)
Find the velocity and acceleration of point F.
(b)
Answer to Problem 15.245P
The velocity of point F is
The acceleration of point F is
Explanation of Solution
Given information:
The radius of disk is
The length of rod CD is
The constant rate of rotation of the rod-and-disk with respect to arm AB is
The constant rate of rotation of the rod-and-disk is
Calculation:
Calculate the position of F with respect to B
Calculate the position of F with respect to D
Calculate the rate of rotation of the frame Bxyz
Substitute
The angular velocity of motion relative to x axis is
Calculate the velocity at the point
Substitute
Calculate the velocity at the point F with respect to the frame
Substitute
Calculate the velocity at the point F
Substitute
Hence, the velocity of point F is
Calculate the acceleration at the point
Substitute
Calculate the acceleration at F with respect to the frame
Substitute
Calculate the Coriolis acceleration
Substitute
Calculate the acceleration at F
Substitute
Therefore, the acceleration of F is
Want to see more full solutions like this?
Chapter 15 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
- At the instant shown in Fig. TT1.3, during deceleration, the velocity of an automobile is 13.3 m/s to the right. Knowing that the velocity of the contact point A of the wheel with the ground is 2.2 m/s to the right, determine the location of the instantaneous center of rotation of the wheel below point O in mm. Fig. TT1.3: A wheel in contact with the ground.arrow_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_forwardThe earth makes one complete revolution on its axis in 23 h 56 min.Knowing that the mean radius of the earth is 3960 mi, determine the linear velocity and acceleration of a point on the surface of the earth (a) at the equator, (b) at Philadelphia, latitude 40° north, (c) at the North Pole.arrow_forward
- Knowing 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_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_forwardIn 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_forward
- Knowing 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_forwardThe bucket of a backhoe is the element AB of the four-bar linkage system ABCD. Assume that the points A and D are fixed and that the bucket rotates with a constant angular velocity WAB = 0.25 rad/s. In addition, suppose that, at the instant shown, point B is aligned vertically with point A, and C is aligned horizontally with B. Determine the acceleration of point C at the instant shown along with the angular acceleration of the elements BC and CD. Let h= 0.66 ft, e= 0-46 ft, l= 0.9 ft, and w= 1.0 ft.arrow_forwardA 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_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_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_forwardThe rated speed of drum B of the belt sander shown is 2400 rpm. When the power is turned off, it is observed that the sander coasts from its rated speed to rest in 10 s. Assuming uniformly decelerated motion, determine the velocity and acceleration of point C of the belt, (a) immediately before the power is turned off, (b) 9 s later.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