Concept explainers
Ring C has an inside radius of 55 mm and an outside radius of 60 mm and is positioned between two wheels A and B, each of 24-mm outside radius. Knowing that wheel A rotates with a constant angular velocity of 300 rpm and that no slipping occurs, determine (a) the angular velocity of ring C and of wheel B, (b) the acceleration of the points on A and B that are in contact with C.
Fig. . P15.26
(a)
The angular velocity of ring
Answer to Problem 15.26P
The angular velocity of ring
The angular velocity of wheel
Explanation of Solution
Given information:
Inside radius of ring
Outside radius of ring
Outside radius of wheels
Wheel
No slipping occurs.
Concept used:
The velocity
Calculation:
The velocity of the point
The point of ring
Here, the outer radius of the ring
The ponit of wheel
Here, the inner radius of the ring
The angular velocity of ring
The angular velocity of wheel
Conclusion:
The angular velocity of ring
The angular velocity of wheel
(b)
The accelerations of the points on
Answer to Problem 15.26P
The accelerations of the point on
The accelerations of the point on
Explanation of Solution
Given information:
Inside radius of ring
Outside radius of ring
Outside radius of wheels
Wheel
No slipping occurs.
Concept used:
The acceleration
Calculation:
The acceleration of the point
Consider the point on
Consider the point on
The accelerations of the point on
The accelerations of the point on
Conclusion:
The accelerations of the point on
The accelerations of the point on
Want to see more full solutions like this?
Chapter 15 Solutions
Vector Mechanics For Engineers
- Problem 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_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) An overhead door is guided by wheelsn at A and B that roll in horizontal and vertical tracks. Knowing that when θ= 40° the velocity of wheel B is 0.5 m/s upward, determine (a) the angular velocity of the door, (b) the velocity of end D of the door.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_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_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_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_forwardThe 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. Select one: A. ωarm=3 ω a r m = 3 rad/s (CW); and ωC=1.5 ω C = 1.5 rad/s (CW) B. ωarm=5 ω a r m = 5 rad/s (CW); and ωC=3 ω C = 3 rad/s (CW) C. ωarm=0 ω a r m = 0 rad/s ; and ωC=1.5 ω C = 1.5 rad/s (CCW) D. ωarm=1 ω a r m = 1 rad/s (CW); and ωC=0 ω C = 0 rad/sarrow_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_forward
- In a four bar mechanism, the dimensions of the links are given as AB = 50 mm, BC = 66 mm, CD = 56 mm and AD = 100 mm. At a given instant when <DAB=600 . The angular velocity of link AB is 10.5r/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 (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_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