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Four masses attached to a shaft and their respective radii of rotation are given as : m 1 = 180 kg m 2 = 300 kg m 3 = 230 kg m 4 = 260 kg r 1 = 0.2 m r 2 = 0.15 m r 3 = 0.25 m r 4 = 0.3 m The angles between successive masses are 45, 75 and 135. Find th

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Question: 

Four masses attached to a shaft and their respective radii of rotation are given as :
m 1 = 180 kg m 2 = 300 kg m 3 = 230 kg m 4 = 260 kg
r 1 = 0.2 m r 2 = 0.15 m r 3 = 0.25 m r 4 = 0.3 m
The angles between successive masses are 45, 75 and 135. Find the
position and magnitude of the balance mass required, it its radius of rotation is
0.2 m. The masses revolve in same plane.

Answer: 

Given : m1 = 180 kg, m2 = 300 kg, m3 = 230 kg, m4 = 260 kg r1 = 0.2 m, r2 = 0.15 m, r3 = 0.25 m, r4 = 0.3 m ϴ1 = 45, ϴ2 = 75, ϴ = 135 The centrifugal forces are given by - m1r1 = 36, m2r2 = 45, m3r3 = 57.5, m4r4 = 78

 

 

 

From vector diagram the resultant force is at 60 to the mass m1 and is represented by ar ar = 12 kg m Therefore mb * rb = 12 kgm Balancing mass mb = 12/0.2 = 60 kg at an angle of 2400 with the direction of m1 mass