Concept explainers
At the instant shown, the velocity of collar A is 0.4 m/s to the right and the velocity of collar B is 1 ms to the left, Determine (a) the angular velocity of bar AD. (b) the angular velocity of bar BD, (c) the velocity of point D.
Fig. P15.91
(a)
The angular velocity of bar AD.
Answer to Problem 15.97P
The angular velocity of bar AD is
Explanation of Solution
Given information:
Velocity of collar A is
Velocity of collar B is
Draw a diagram locating the instantaneous center C of bar AD and I of bar BD.
The velocity directions of point A, B and D are known where AC perpendicular to
Calculation:
According to the above diagram,
The length AD
The length BD
The angle
The angle
Apply sine rule for triangle
Rearrange
Apply sine rule for triangle
Rearrange
The length AC
The length BI
For bar AD,
The angular velocity of bar AD
For bar BD,
The angular velocity of bar BD
According to the above equations,
Rearrange,
Substitute,
Solve,
Substitute for
Therefore,
Then find
The angular velocity of bar AD
Conclusion:
According to the above explanation, the angular velocity of bar AD is
(b)
The angular velocity of bar BD.
Answer to Problem 15.97P
The angular velocity of bar BD is
Explanation of Solution
Given information:
Velocity of collar A is
Velocity of collar B is
Draw a diagram locating the instantaneous center C of bar AD and I of bar BD.
The velocity directions of point A, B, and D are known where AC perpendicular to
Calculation:
According to sub part a,
And,
Therefore,
Angular velocity of bar BD
Conclusion:
According to the above explanation, the angular velocity of bar BD is
(c)
The velocity of point D.
Answer to Problem 15.97P
The velocity of point D is
Explanation of Solution
Given information:
Velocity of collar A is
Velocity of collar B is
Draw a diagram locating the instantaneous center C of bar AD and I of bar BD.
The velocity directions of point A, B, and D are known where AC perpendicular to
Calculation:
According to sub part a,
And,
And,
Therefore, the length CD
The velocity of point D
Substitute,
The angle
Conclusion:
According to the above explanation, the velocity of point D is
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Chapter 15 Solutions
Vector Mechanics For Engineers
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