Concept explainers
The acceleration of pin P.
Answer to Problem 15.183P
The acceleration of pin P is
Explanation of Solution
Given information:
The constant angular velocity of the bar AD is
The angular velocity of the bar BE is
The angular acceleration of the bar BE is
Calculation:
Calculate the slope of the bar BE
Calculate the position
The position of P with respect to A.
The position of P with respect to B.
Provide the angular velocities of the bar AD
Provide the angular acceleration of the bar BE in vector form as shown below.
Calculate the velocity of a point
Here,
Consider that the point P in the frame AD.
Calculate the velocity component
Substitute
Calculate the velocity component
Here,
Calculate the velocity of a point
Substitute
Consider that the point P in the frame BE.
Calculate the velocity component
Substitute
Calculate the velocity component
Here,
Resolving along x and y direction.
Substitute
Equating Equations (3) and (5) as shown below.
Resolving i and j components as shown below.
For i component.
Substitute
Calculate the velocity component
Substitute
For j component.
Substitute
Calculate the velocity component
Substitute
Calculate the acceleration of a point
Here,
Consider the point P in the frame AD.
Calculate the acceleration component
Here,
Substitute
Calculate the acceleration component
Here,
Substitute
Calculate the Coriolis component of acceleration
Substitute
Substitute
Consider the point P in the frame BE.
Calculate the acceleration component
Substitute
Calculate the acceleration component
Here,
Resolving along x and y direction.
Calculate the Coriolis component of acceleration
Substitute
Calculate the acceleration of a point
Substitute
Equating Equations (7) and (8) as shown below.
Resolving i and j components as shown below.
Substitute
Calculate the acceleration of a point
Substitute
Calculate the magnitude of the acceleration
Therefore, the acceleration of pin P is
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Chapter 15 Solutions
VECTOR MECH...,STAT.+DYNA.(LL)-W/ACCESS
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