Concept explainers
A uniform slender rod of length L is dropped onto rigid supports at A and B. Because support B is slightly lower than support A, the rod strikes A with a velocity
(a)
Calculate the angular velocity and mass center velocity of rob when rod strikes support A.
Answer to Problem 17.111P
While rod strikes support A,
Angular velocity of rod
Mass center velocity of rod
Explanation of Solution
For impact at A
As per kinematics,
Taking moment at A,
Further solving, we get
and mass center velocity of rod,
Conclusion:
Rod having length is supported by both end at A and B support B is lower than support A. Hence, rod with velocity v1strikes A before striking to B, assuming perfect elasticity between A and B.
Angular velocity of rod is
(b)
Calculate the angular velocity and mass center velocity of the rod when rod stricken supports B.
Answer to Problem 17.111P
When rod strikes support B,
The angular velocity of rod =
The mass center velocity of rod =
Explanation of Solution
As per kinematics,
Taking moment at B1
Now, mass center velocity of rod,
Conclusion:
Rod having length is supported by both end at A and B support B is lower than support A. Hence rod with velocity v1 strikes A before striking to B. assuming perfect elasticity between A and B.
The angular velocity of rod is
(c)
Calculate the angular velocity and mass center velocity of the rod when rod strikes A again?
Answer to Problem 17.111P
When rod strikes A again
The angular velocity of rod =
The mass center velocity of rod =
Explanation of Solution
For impact A again,
As per kinematics,
Taking moment about A,
And mass center velocity of rod,
Conclusion:
Rod having length is supported by both end at A and B support B is lower than support A. Hence rod with velocity v1 strikes A before striking to B assuming perfect elasticity between A and B.
The angular velocity of rod is
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Chapter 17 Solutions
Vector Mechanics for Engineers: Dynamics
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