Question

4) four masses A, B, C and D revolve at equal radii and are equally spaced along a shaft. The mass B is 7 kg and the radii of C and D make angles of 90° and 240* respectively with the radius of B. Find the magnitude of the masses A, C and D and the angular position of A so that the system may be completely balanced.​

Answer 1

A= 5 kg ; C = 6 kg ; D = 4.67 kg ;

A = 205° from mass B anticlockwise

Explanation:

                      $In\ equation\ terms,\\ \\B,D\implies 7 = D\ cos(240^o)\\\\C,D \implies C = D\ cos(350^o)\\ \\\implies A = balance\ all\ weights\ above$

Further explanation:

• In rotary or reciprocating machinery, inertia forces associated with moving masses typically cause a force imbalance.
• Balancing is the process of building or altering machinery to reduce or eliminate imbalance to a bearable level, if not entirely eliminated.
• When a mass is attached to a spinning shaft, centrifugal force is generated, bending the shaft and causing vibrations.
• To counteract the impact of centrifugal force, a second mass is attached to the other side of the shaft, balancing the effect of the first mass's centrifugal force.
• This is achieved by ensuring that both masses' centrifugal forces are equal and opposite.
• Balancing spinning masses is the process of adding a second mass to counteract the influence of the first mass's centrifugal force.