Reactions at point while the system is rotating, Mechanical Engineering

Reactions at point while the system is rotating:

8 kg ball is mounted on a horizontal bar associated to a vertical shaft. Neglecting the mass of the bar and shaft what are the reactions at B and C while the system is rotating at a constant speed of 90 rpm.

Solution

Free body diagram of the system is illustrated in Figure (b) above. Reactions at B, i.e. Bx and By are marked as shown. Likewise, reaction at C is also marked. As the vertical shaft rotates, the ball shall traverse a horizontal circular path of radius 300 mm, inertia force of mrω2 shall be acting on the ball as illustrated in the diagram.

Now, we write down dynamic equilibrium equations for the same.

∑ Fx  = 0,          ∴ Cx  + Bx  - 8 × 0.3 × ω2 = 0

ω = 2 π n/60 =( 2 π × 90)/60 = 9.42 rad / sec

C x  + Bx  = 8 × 0.3 × (9.42)2

∴ C x  + Bx  = 212.97                                  --------- (1)

∑ Fy  = 0,       By  - 8 × 9.81 = 0                       -------- (2)

∴ By  = 78.48 N

∑ M A  = 0,          ∴ Cx × 0.9 - Bx × 0.3 - By × 0.3 = 0

 or,       0.9 Cx - 0.3 Bx = 23.54

∴ Bx  = 140 N

  C x  = 72.9 N

  By  = 78.48 N

Posted Date: 1/29/2013 6:38:34 AM | Location : United States







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