Concept explainers
A connecting rod is supported by a knife-edge at point A; the period of its small oscillations is observed to be 0.87 s. The rod is then inverted and supported by a knife edge at point B and the period of its small oscillations is observed to be 0.78 s. Knowing that ra + rb = 10 in., determine (a) the location of the mass center G, (b) the centroidal radius of gyration
Fig. P19.47
(a)
The location
Answer to Problem 19.47P
The location
Explanation of Solution
Given information:
The period
The rod is then inverted and supported by a knife-edge at point B and the period
The value of
The acceleration due to gravity (g) is
Calculation:
Show the free body diagram of mass center G as in Figure (1).
The external forces in the system are tension in the force due to the mass of the knife. The effective couple in the system is
Take moment about O in the system for external forces.
Take moment about O in the system for effective forces.
Equate the moment about O in the system for external and effective forces.
For small oscillation
Compare the differential Equation (1) with the general differential equation of motion
Write the expression for period
Substitute
Rewrite the equation (2) for rod suspended at A:
Rewrite the equation (2) for rod suspended at B:
Subtracting equation (4) from equation (3).
Substitute 0.87 s for
Write the relationship
Calculate the value
Substitute
Calculate the value
Substitute
Therefore, the location
(b)
The centroidal radius of gyration
Answer to Problem 19.47P
The centroidal radius of gyration
Explanation of Solution
Given information:
The period
The rod is then inverted and supported by a knife-edge at point B and the period
The value of
The acceleration due to gravity (g) is
Calculation:
Calculate the centroidal radius of gyration
Substitute
Therefore, the centroidal radius of gyration
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Chapter 19 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
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