Concept explainers
(a)
The acceleration of the centre of gravity.
Answer to Problem 16.131P
The acceleration of the centre of gravity is
Explanation of Solution
Given information:
Pole length,
Weight,
Angular velocity,
Horizontal force,
Pole mass,
Here,
Pole moment of inertia,
Acceleration tangential component between G and C.
Here,
Acceleration centripetal component between G and C.
Point G acceleration,
Force friction,
Here,
Moment at G,
Here,
Vertical component of forces,
Here,
Normal force between pole and ground,
Substitute,
So,
Forces horizontal component,
Here,
Therefore,
Acceleration at point G,
Resultant acceleration,
From equation D and E,
Substitute,
Resultant angle,
Conclusion:
The acceleration of the centre of gravity is
(b)
The normal force between pole and ground.
Answer to Problem 16.131P
The normal force between pole and ground is
Explanation of Solution
Given information:
Pole length,
Weight,
Angular velocity,
Horizontal force,
Pole mass,
Here,
Pole moment of inertia,
Acceleration tangential component between G and C
Here,
Acceleration centripetal component between G and C
Point G acceleration,
Force friction,
Here,
Moment at G,
Here,
Vertical component of forces,
Here,
Normal force between pole and ground,
Substitute,
So,
Conclusion:
The normal force between pole and ground is
Want to see more full solutions like this?
Chapter 16 Solutions
Vector Mechanics For Engineers
- A uniform 144-lb cube is attached to a uniform 136-lb circular shaft as shown, and a couple M with a constant magnitude is applied to the shaft when the system is at rest. Knowing that r = 4 in., L= 12 in., and the angular velocity of the system is 960 rpm after 4 s, determine the magnitude of the couple M.arrow_forwardA cylinder of radius r and weight W with an initial counterclockwise angular velocity w0 is placed in the corner formed by the floor and a vertical wall. Denoting by μk the coefficient of kinetic friction between the cylinder and the wall and the floor, derive an expression for the time required for the cylinder to come to rest.arrow_forwardA uniform rod BC of mass 4 kg is connected to a collar A by a 250-mm cord AB. Neglecting the mass of the collar and cord, determine (a) the smallest constant acceleration aA for which the cord and the rod will lie in a straight line, (b) the corresponding tension in the cord.arrow_forward
- A 48-kg advertising panel of length 2a = 2.4 m and width 2b = 1.6 m is kept rotating at a constant rate w1 about its horizontal axis by a small electric motor attached at A to frame ACB. This frame itself is kept rotating at a constant rate w2 about a vertical axis by a second motor attached at C to the column CD. Knowing that the panel and the frame complete a full revolution in 6 s and 12 s, respectively, express, as a function of the angle 0, the dynamic reaction exerted on column CD by its support at D.arrow_forwardA 9-kg uniform disk is attached to the 5-kg slender rod AB by means of frictionless pins at B and C. The assembly rotates in a vertical plane under the combined effect of gravity and of a couple M that is applied to rod AB. Knowing that at the instant shown the assembly has an angular velocity of 6 rad/s and an angular acceleration of 25 rad/s2 , both counterclockwise, determine (a) the couple M, (b) the force exerted by pin C on member ABarrow_forwardIn the engine system shown l = 250 mm and b = 100 mm. The connecting rod BD is assumed to be a 1.2-kg uniform slender rod and is attached to the 1.8-kg piston P. During a test of the system, crank AB is made to rotate with a constant angular velocity of (400) rpm CW with no force applied to the face of the piston. Determine the velocity and acceleration of the piston P when θ = 90°. (Neglect the effect of the weight of the rod.)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