Concept explainers
A 1-Ib ball A and a 2-Ib ball B are mounted on a horizontal rod that rotates freely about a vertical shaft. The balls are held in the positions shown by pins. The pin holding B is suddenly removed and the ball moves to position C as the rod rotates. Neglecting friction and the mass of the rod and knowing that the initial speed of A is
(a)
Radial and transverse component of acceleration of ball B immediately after the pin is removed.
Answer to Problem 12.91P
Radial component:
Transverse component:
Explanation of Solution
Given:
Let
Constraint of rod:
Components of acceleration:
Sketch the free body diagrams of the balls showing the radial and transverse components of the forces acting on them.
Owing to frictionless sliding of B along the rod,
Radial component of acceleration of B.
Transverse components of acceleration,
Since the rod has no mass, it must be in equilibrium.
Draw its free body diagram, applying Newton’s third law:
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At
So that
From Eq. (1),
(b)
Acceleration of ball B relative to rod.
Answer to Problem 12.91P
Acceleration of ball B relative to rod:
Explanation of Solution
Given:
Acceleration of B relative to the rod,
At
(c)
Acceleration of ball B relative to rod.
Answer to Problem 12.91P
Acceleration of ball B relative to rod:
Explanation of Solution
Given:
Speed of A:
Substituting
Integrating with respect to time,
Applying to the final state with ball B moved to the stop at C,
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