Concept explainers
Two rods AB and DE are connected as shown. Knowing that point D moves to the left with a velocity of 40 in./s, determine (a) the angular velocity of each rod, (b) the velocity of point A.
(a)
The angular velocity of the rod AB at instant.
The angular velocity of the rod DE at instant.
Answer to Problem 15.98P
The angular velocity of the rod AB is
The angular velocity of the rod DE is
Explanation of Solution
Given information:
The velocity of the point D is
The following figure represents two instantaneous centers of the given system.
Figure-(1)
Write the expression for the distance between the point
Here, the distance between the point
Write the equation for the distance between the point
Here, the horizontal distance between the point
The following figure represents the instantaneous centre of the rod AB.
Figure-(2)
Write the expression for the horizontal distance between the point
Here, the point
Write the expression for the velocity of the point D.
Here, the velocity of the point D is
Write the expression for the velocity of the point B.
Here, the velocity of the point B is
Write the expression for the velocity of the point B.
Here, the angular velocity of the rod DE is
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Conclusion:
The angular velocity of the rod DE is
The angular velocity of the rod AB is
(b)
The velocity at the point A.
Answer to Problem 15.98P
The velocity at the point A is
Explanation of Solution
Write the expression for the horizontal distance between the point
Here, the vertical distance between the point
Write the expression for the velocity of the point A.
Here, the velocity at the point A is
Calculation:
Substitute
Substitute
Conclusion:
The velocity at the point A is
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Chapter 15 Solutions
Package: Vector Mechanics for Engineers: Dynamics with 2 Semester Connect Access Card
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