+1 vote
in Machine Dynamics by (34.3k points)
If c be the fraction of the reciprocating parts of mass m to be balanced per cyclinder of a steam locomotive with crank radius r, angular speed ω, distance between centre lines of two cylinders a, then the magnitude of the maximum swaying couple is given by

(a) 1 – c / 2 mrω^2a

(b) 1 – c / √2mrω^2a

(c) √2(1 – c)mrω^2a

(d) none of the mentioned

The question was asked in unit test.

My question is from Primary and Secondary Unbalanced Forces of Reciprocating Masses topic in portion Balancing of Reciprocating Masses of Machine Dynamics

1 Answer

0 votes
by (38.6k points)
The correct answer is (b) 1 – c / √2mrω^2a

Explanation: The swaying couple is maximum or minimum when (cosθ+sinθ) is maximum or minimum. For (cosθ+sinθ) to be maximum or minimum

                 ∴ tanθ =1 or θ = 45° or 225°

Maximum value of the swaying couple = 1 – c / √2mrω^2a

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