Concept explainers
Two rods AE and BD pass through holes drilled into a hexagonal block. (The holes are drilled in different planes so that the rods will not touch each other.) Knowing that rod AE has an angular velocity of 20 rad/s clockwise and an angular acceleration of 4 rad/s2 counterclockwise when
Fig. P15.257
(a)
Relative velocity of block with respect to each rod.
Answer to Problem 15.257RP
Relative velocity of block with respect to each rod
Explanation of Solution
Given information:
The angular velocity and angular acceleration of rod AE is
The Coriolis acceleration is a combination of
The Coriolis acceleration id defined as
The velocity is defined as
The normal acceleration is defined as
The tangential acceleration is defined as
Calculation:
When
Apply sine rule,
Therefore,
The angle
Assume, the relative velocity of slider H on rod AH is
The velocity of point
The acceleration of point
The relevant Coriolis acceleration is
The velocity of point H,
The acceleration of point H
Assume, the relative velocity of slider H on rod BD is
The velocity of point
The acceleration of point
The relevant Coriolis acceleration
The velocity of point H,
The acceleration of point H
Equate
Therefore, the relative velocities
Conclusion:
The relative velocities of each rod
(b)
Relative acceleration of block with respect to each rod.
Answer to Problem 15.257RP
Relative acceleration of block with respect to each rod
Explanation of Solution
Given information:
The angular velocity and angular acceleration of rod AE is
The Coriolis acceleration is a combination of
The Coriolis acceleration id defined as
The velocity is defined as
The normal acceleration is defined as
The tangential acceleration is defined as
Calculation:
According to sub part a
Substitute for
Therefore
Therefore
Conclusion:
The relative acceleration of each rod
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Chapter 15 Solutions
Vector Mechanics For Engineers
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