Concept explainers
(a)
Find the couple M.
(a)
Answer to Problem 16.136P
The couple M is
Explanation of Solution
Given information:
The mass of the rod BC is
The mass of the disk is
The mass of the rod CD is
The angular velocity is
The angular acceleration is
Calculation:
Consider the acceleration due to gravity as
Calculate the velocity of disk AB
Substitute
Calculate the velocity of rod BC
The velocity of disk AB is equal to the velocity of rod BC.
Substitute
Calculate the angular velocity of rod CD
Substitute
Apply the acceleration analysis as shown below.
Calculate the acceleration for disk AB
Substitute
Calculate the acceleration for rod BC
Substitute
Calculate the acceleration for rod CD
Substitute
Equating the components of Equations (1) and (2) as shown below.
Along x component.
Along y component.
Substitute
Calculate the acceleration of the mass centers as shown below.
Calculate the acceleration of mass center for disk AB
Calculate the acceleration of the mass center at P for rod BC
Substitute
Substitute
Calculate the acceleration of the mass center at Q for rod CD
Substitute
Calculate the inertial terms at mass centers as shown below.
The inertia terms at centers are
For disk AB.
For rod BC.
Substitute
For rod CD.
Substitute
Calculate the mass moment of inertia
For disk AB.
Substitute
For rod BC.
Substitute
For rod CD.
Substitute
Calculate the effective couples at mass centers as shown below.
The inertia terms at centers are
For disk AB.
For rod BC.
Substitute
For rod CD.
Substitute
Sketch the effective force and couples on the system as shown in Figure 1.
Sketch the Free Body Diagram of the rod BC as shown in Figure 2.
Refer to Figure 2.
Apply the Equilibrium of moment about B as shown below.
Substitute
Sketch the Free Body Diagram of the rod CD as shown in Figure 3.
Refer to Figure 3.
Apply the Equilibrium of moment about D as shown below.
Substitute
Sketch the Free Body Diagram of the rod AB and BC as shown in Figure 4.
Refer to Figure 4.
Apply the Equilibrium of moment about A as shown below.
Substitute
Therefore, the couple M is
(b)
The components of force exerted at C on rod BC.
(b)
Answer to Problem 16.136P
The components of force exerted at C on rod BC is
Explanation of Solution
Given information:
The mass of the rod BC is
The mass of the disk is
The mass of the rod CD is
The angular velocity is
The angular acceleration is
Calculation:
Refer to part (a).
The components of force exerted at C on rod BC along x direction is
The components of force exerted at C on rod BC along y direction is
Therefore, the components of force exerted at C on rod BC is
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Chapter 16 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
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